eifueo/docs/g11/sch3uz.md

HL Chemistry - 1

The course code for this page is SCH3UZ.

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1.1 - Review and base knowledge

Binary ionic and molecular compound nomenclature

An ionic bond is a bond formed between a metal cation and a non-metal anion. The compound name is written as the cation followed by the anion with the “-ide” ending. If the cation is multivalent (all transition metals aside from \(\text{Si}\) and \(\text{Co}\)), the charge of the cation should be written in parentheses in roman numerals between the two ions. \[\text{cation anion-ide || cation (roman charge) anion-ide}\]

!!! example - \(\text{NaCl}\): sodium chloride - \(\text{Al}_2\text{O}_3\): aluminium oxide - \(\text{CuO}\): copper (II) oxide - \(\text{Cu}_2\text{O}\): copper (I) oxide

A covalent bond is a bond formed between two non-metals. The compound name is written as the non-metal that appears first followed by the non-metal that appears second with the -ide ending, prefixing both with Greek prefixes to represent the number of atoms of that element. If there is only one atom of the first element, or if it would be unambiguous otherwise, “mono” is excluded for that element. The final vowel of the prefix is excluded if it ends with a vowel and the element following it starts with a vowel, except for the letter “i”. \[\text{prefix–element prefix–element–ide}\]

!!! example - \(\text{N}_2\text{O}_5\): dinitrogen pentoxide - \(\text{CO}\): carbon monoxide - \(\text{PI}_3\): phosphorous triiodide. - \(\text{HCl}\): hydrogen chloride

!!! warning The following common molecular compounds do not follow the rules above and have the following names instead:

- $\text{H}_2\text{O}_2$: hydrogen peroxide
- $\text{O}_3$: ozone
- $\text{H}_2\text{O}_\text{(l)}$: water
- $\text{CH}_4$: methane
- $\text{NH}_3$: ammonia

Polyatomic ions

A polyatomic ion is an ion formed only via covalent bonds. Most polyatomic ions are oxyanions and so contain oxygen and have negative charges.

An oxyanion consists of an element covalently bonded to oxygen atoms, ending up with a non-neutral charge. The parent form of these compounds is written as the non-oxygen element with the “-ate” suffix. \[\text{element–ate}\]

!!! example - \(\text{CO}_3 {}^{2-}\): carbonate - \(\text{NO}_3 {}^-\): nitrate

However, the number of oxygen atoms in the ion can change while the charge remains the same. In this case, the following prefixes and suffixes are applied based on the difference in oxygen atoms from its parent:

• +1 \(\text{O}\): per…ate
• +0 \(\text{O}\): …ate
• -1 \(\text{O}\): …ite
• -2 \(\text{O}\): hypo…ite

Polyatomic ions in the same group on the periodic table form similar polyatomic ions.

!!! example Chlorate (\(\text{ClO}_3{}^-\)) and bromate (\(\text{BrO}_3{}^-\)) have the same base forms and thus the same extended forms.

To remember the charges and number of oxygen atoms in some polyatomic ions, the below mnemonic can be used: \[\text{Nick Borate the Camel had a Clam Supper in Phoenix}\]

The first letter(s) of each capitalised word is the non-oxygen component, the number of consonants in that word is equal to the number of oxygen atoms, and the number of vowels indicates its charge.

Alternatively/complimentarily, memorise the following table:

Name	Formula	Name	Formula
Ammonium	\(\text{NH}_4{}^+\)	Sulfate	\(\text{SO}_4{}^{2-}\)
Hydroxide	\(\text{OH}^-\)	Chlorate	\(\text{ClO}_3{}^-\)
Cyanide	\(\text{CN}^-\)	Chromate	\(\text{CrO}_4{}^-\)
Borate	\(\text{BO}_3{}^{3-}\)	Dichromate	\(\text{Cr}_2\text{O}_7{}^{2-}\)
Carbonate	\(\text{CO}_3{}^{2-}\)	Permanganate	\(\text{MnO}_4{}^-\)
Nitrate	\(\text{NO}_3{}^-\)	Acetate	\(\text{CH}_3\text{COO}^-\)
Phosphate	\(\text{PO}_4{}^{3-}\)

Hydrogen ions can be added to polyatomic ions, reducing the compound’s negative charge by 1. “Hydrogen” is prefixed with its Greek numerical prefix (except “mono”, usually) and placed before the oxyanion until the compound becomes an acid.

!!! example - \(\text{HPO}_4{}^{2-}\): hydrogen phosphate - \(\text{H}_2\text{PO}_3{}^{-}\): dihydrogen phosphite

Acids

All acids must be aqueous.

A binary acid consists of hydrogen atoms bonded to exactly one other non-metal element dissolved in water. If the compound begins with a hydrogen atom but is not aqueous, it is a binary covalent molecule. Binary acids are written as their non-metal element prefixed by “hydro-” and suffixed with “-ic acid”. \[\text{hydro–element–ic acid}\]

!!! example - \(\text{HCl}_\text{(aq)}\): hydrochloric acid - \(\text{HCl}\): hydrogen chloride - \(\text{H}_2\text{S}_\text{(aq)}\): hydrosulfuric acid

An oxyacid consists of a polyatomic ion bonded to hydrogen ions equal to its charge. As their chemical structure can only exist while aqueous, \(\text{(aq)}\) is not required. Oxyacids are written as per their polyatomic ion with “-ate” replaced with “-ic”, “-ite” replaced with “-ous”, and with the suffix “acid”. \[\text{prefix-element-suffix acid}\]

!!! example - \(\text{H}_2\text{CO}_3\): carbonic acid - \(\text{HIO}_4\): periodic acid - \(\text{HIO}_3\): iodic acid - \(\text{HClO}_2\): chlorous acid - \(\text{HClO}\): hypochlorous acid

Bases

There are two types of bases in this course:

• Hydroxides (\(\text{OH}^-\))
• Ammonia (\(\text{NH}_3\))

Hydrates

Hydrates are ionic compounds with water associated with them, but the water molecules are held loosely and are not actually part of the compound. There is a specific number of water molecules per formula unit of ionic compound, so the formula is written as exactly one of the ionic compound followed by a dot and \(\text{H}_2\text{O}\) with a coefficient denoting the number of water molecules associated with the salt. Hydrates are named as per their ionic compound followed by “hydrate” with Greek prefixes. \[\text{ion} \bullet x\text{H}_2\text{O}\]

!!! example \(\text{Na}_3\text{PO}_3 \bullet 4\text{H}_2\text{O}\): sodium phosphite tetrahydrate

Ionic compounds that have water are hydrated. Those that do not are anhydrous.

Types of reactions

Synthesis

A synthesis reaction involves the combination of smaller atoms or molecules to form larger molecules. \[A + B → AB\]

!!! example - \(2\text{H}_\text{2 (g)} + \text{O}_\text{2 (g)} → 2\text{H}_2\text{O}_\text{(g)}\) - \(\text{HCl}_\text{(g)} + \text{NH}_\text{3 (g)} → \text{NH}_4\text{Cl}_\text{(aq)}\)

!!! warning Metal oxides react with water to form bases while non-metal oxides form acids.

Decomposition

A decomposition reaction involves splitting a larger molecule into smaller molecules or elements. \[AB → A + B\]

!!! example - \(2\text{H}_2\text{O}_\text{(l)} → 2\text{H}_\text{2 (g)} + \text{O}_\text{2 (g)}\) - \(\text{CaCO}_\text{3 (s)} → \text{CaO}_\text{(s)} + \text{CO}_\text{2 (g)}\)

!!! warning Carbonic acid and ammonium hydroxide decompose when formed as products of other reactions, so the results of this decomposition need to be considered (e.g., checking if double dispalcement reactions occur). \[\text{H}_2\text{CO}_\text{3 (aq)} → \text{H}_2\text{O}_\text{(l)} + \text{CO}_\text{2 (g)}\] \[\text{NH}_4\text{OH}_\text{(aq)} → \text{NH}_\text{3 (g)} + \text{H}_2\text{O}_\text{(l)}\]

Combustion

A combustion reaction involves the rapid reaction of a substance with oxygen to produce oxides and heat. \[A + \text{O}_\text{2 (g)} → \text{oxide}\]

!!! example \(2\text{Mg}_\text{(s)} + \text{O}_\text{2 (g)} → 2\text{MgO}_\text{(s)}\)

!!! warning Combustion reactions must be rapid. This means that reactions such as that of iron with oxygen gas to form iron oxide (rusting) are not combustion reactions.

When combusting hydrocarbons, the quantity of oxygen present determines if the combustion will be complete or incomplete. The only products of complete combustion are carbon dioxide and water, while the products of incomplete combustion can also include carbon monoxide and carbon. \[\text{C}_x\text{H}_y + \text{O}_\text{2 (g)} → \text{CO}_\text{2 (g)} + \text{H}_2\text{O} + \text{CO}_\text{(g)} + \text{C}_\text{(s)}\]

!!! example - Complete: \(\text{C}\text{H}_4 + 2\text{O}_\text{2 (g)} → \text{CO}_2 + 2\text{H}_2\text{O}\) - Incomplete: \(\text{C}\text{H}_4 + \text{O}_\text{2 (g)} → \text{C} + 2\text{H}_2\text{O}\)

Single displacement

A single displacement reaction involves a more reactive element reacting with a compound such that it displaces the less reactive element in the compound of the same type (metals + hydrogen or non-metals). The activity series is used to identify if a single displacement reaction takes place.

If \(A\) is a metal: \[A + BC → AC + B\]

If \(A\) is a non-metal: \[A + BC → BA + C\]

!!! note - The elemental forms of all metals are monatomic (just one atom) and are solids are room temperature, except for \(\text{Hg}_\text{(l)}\). - The elemental forms of phosphorus and sulfur are \(\text{P}_4\) and \(\text{S}_8\), respectively. - The “-gens” (hydrogen, nitrogen, oxygen, halogens) are all diatomic in their elemental form.

!!! example - \(\text{Zn}_\text{(s)} + 2\text{HCl}_\text{(aq)} → \text{ZnCl}_\text{2 (aq)} + \text{H}_\text{2 (g)}\) - \(\text{Cl}_\text{2 (g)} + 2\text{NaBr}_\text{(aq)} → \text{Br}_\text{2 (g)} + 2\text{NaCl}_\text{(aq)}\) - \(\text{Cu}_\text{(s)} + 2\text{AgNO}_\text{3 (aq)} → \text{Cu(NO}_3)_\text{2 (aq)} + 2\text{Ag}_\text{(s)}\)

Double displacement

A double displacement reaction involves two compounds “exchanging” their components to form two new compounds. It can only occur if either a precipitate, a salt and water, or a gas and water is formed. Otherwise, there is no reaction.

\[AB + CD → AD + BC\]

To predict if a precipitate will form, a solubility table or the following solubility rules can be used (the insoluble compound is the precipitate):

• All nitrates are soluble
• All alkali metals are soluble
• Ammonium is soluble

!!! example \(\text{BaCl}_\text{2 (aq)} + \text{K}_2\text{SO}_\text{4 (aq)} → 2\text{KCl}_\text{(aq)} + \text{BaSO}_\text{4 (s)}\)

To predict if a salt and water will form, the two factors must be an acid and a base.

!!! example \(3\text{NaOH}_\text{(aq)} + \text{H}_3\text{PO}_\text{4 (aq)} → \text{Na}_3\text{PO}_\text{4 (aq)} + 3\text{H}_2\text{O}_\text{(l)}\)

To predict if a gas and water will form, either carbonic acid or ammonium hydroxide must be formed after the double displacement reaction as those two compounds will decompose.

!!! example \(\text{MgCO}_\text{3 (s)} + 2\text{HCl}_\text{(aq)} → \text{CO}_\text{2 (g)} + \text{H}_2\text{O}_\text{(l)} + \text{MgCl}_\text{2 (aq)}\)

Total and net ionic equations

A total ionic equation shows the dissociation (separation) of soluble ionic compounds into their respective ions as well as reactants and products. Each ion is shown separately, so coefficients are used if there is more than one of that ion.

!!! example \(\text{Na}_2\text{SO}_\text{4 (aq)} + \text{CaCl}_\text{2 (aq)} → \text{CaSO}_\text{4 (s)} + 2\text{NaCl}_\text{(aq)}\)
Total ionic equation: \(2\text{Na}^+{}_\text{(aq)} + \text{SO}_4{}^{2-}{}_\text{(aq)} + \text{Ca}^{2+}{}_\text{(aq)} + 2\text{Cl}^-{}_\text{(aq)} → \text{CaSO}_\text{4 (s)} + 2\text{Na}^+{}_\text{(aq)} + 2\text{Cl}^-{}_\text{(aq)}\)

A net ionic equation is similar to a total ionic equation but only shows the ions involved in the chemical reaction by eliminating all ions that do not participate in the reaction (are the same on both sides), or spectator ions.

!!! example \(\text{SO}_4{}^{2-}{}_\text{(aq)} + \text{Ca}^{2+}{}_\text{(aq)} → \text{CaSO}_{4 (s)}\)

If there is no reaction, there is no net ionic equation but there is a total ionic equation.

1.2 - Stoichiometry - the mole concept

A mole (mol) is a unit representing \(6.02…×10^{23}\) countable objects.

!!! example A mole of cups is equal to \(6.02…×10^{23}\) cups.

The Avagadro constant (\(L\)), or the number of particles in the mole of a substance, is equal to \(6.02×10^{23}\) (to three significant figures).

The “amount” of a particle is written as \(N\) while the amount of moles of a substance is written as \(n\).

!!! example - 12 molecules of carbon dioxide can be written as \(N_{\text{CO}_2} = 12\). - 1 mole of carbon dioxide (\(6.02×10^{23}\) molecules) can be written as \(n_{\text{CO}_2} = 1\).

Molar mass

The mass of one mole of a substance is its molar mass (\(M\)), and has the units of grams per mole (\(\text{g/mol}\)). This conversion factor can be used to convert between the amount of a substance in moles and its mass in grams.

!!! example - Carbon has a relative atomic mass of \(12.01\) so \(M_\text{C} = 12.01 \text{ g/mol}\). - Water has a relative molecular mass of \(18.02\) so \(M_{\text{H}_2\text{O}} = 18.02 \text{ g/mol}\).>

\[\text{Mass of one particle}=\frac{\text{molar mass of substance}}{\text{Avogadro constant}}\]

Empirical and molecular formulae

An empirical formula is the lowest whole number ratios of atoms and/or ions in a compound, while a molecular formula is the actual formula of the compound.

!!! example Hydrogen peroxide has a molecular formula of \(\text{H}_2\text{O}_2\) but an empirical formula of \(\text{HO}\).

All elements in a compound are always in the same proportion by mass, so its empirical formula can be determined via the percentage composition by mass of a compound. To do so, the percentage should be converted to the theoretical mass of each element of 100 g of the compound, then converted to moles via its molar mass. The lowest whole number ratio represents the empirical formula of the compound. If a whole number ratio is not present, round if the difference is acceptably small (one guideline is 0.1), otherwise introduce a multiplication factor to make the ratios whole numbers.

\[\text{Percentage composition} = \frac{\text{mass of element in compound}}{\text{molar mass of compound}}×100\%\]

(Source: Kognity)

When calculating empirical formulae, uncertainties, unless they are large, can be reasonably discarded because they will not affect the final result significantly.

!!! example The empirical formula of a compound consisting of 43.64% \(\text{P}\) and 56.36% \(\text{O}\) by mass:
\(m_\text{P} = 43.64\text{ g}\)
\(m_\text{O} = 56.36\text{ g}\)
\(n_\text{P} = 43.64\text{ g} ÷ 30.97\text{ g mol}^{-1} = 1.409\text{ mol}\)
\(n_\text{O} = 56.36\text{ g} ÷ 16.00\text{ g mol}^{-1} = 3.523\text{ mol}\)
\(\text{P}: 1.409÷1.409=1 × 2 = 2\)
\(\text{O}:3.523÷ 1.409=2.500 × 2 = 5\)
Therefore the empirical formula is \(\text{P}_2\text{O}_5\).

If the both the molecular mass/molar mass and the empirical mass/molar mass of a compound is given, the molecular formula can be identified by finding the multiplication factor needed to turn the empirical mass to the molecular mass.

The empirical formula of an organic compound (containing only carbon, hydrogen, and oxygen) can be determined via analysing the complete combustion of the sample and collecting the products. If the sample’s mass is known, the percentage composition of carbon and hydrogen can be identified using the products of carbon dioxide and water, respectively. If their masses do not add up to the mass of the sample, the remaining mass is oxygen.

Similarly, the ratio of salts to water molecules in hydrates can be determined by gently heating the hydrate until the salt becomes anhydrous and then identifying the mass of the water that has evaporated.

!!! warning Hydrates only have one salt per one or more water molecules.

1.3 - Reacting masses and volumes

Yield

The yield of a reaction is the amount of product obtained.

The theoretical yield is the maximum amount of product predicted to be produced using a balanced chemical equation. The actual yield is the amount of product measured from an actual chemical reaction. \[\text{Percentage yield} = \frac{\text{actual yield}}{\text{theoretical yield}}×100\%\]

An actual yield greater than the theoretical yield is not possible and is a clear indication of systematic or measurement error. Generally, the actual yield is different from the theoretical yield for many possible reasons:

• Imperfect collection techniques may have not measured some of the product
• Competing reactions may have used a reactant and formed other products
• The reactants may be impure

The percentage yield and percentage error should add up to 100%.

Limiting and excess reactants/reagents

When there is not enough reactant to use up all of them evenly, there will be reactants that are used up first known as limiting reactants. The remaining reactants are known as excess reactants.

To find limiting/excess reactants:

• Find the amount of each substance on hand
• Divide each amount by its coefficient in the balanced equation
• The lowest value is the limiting reactant

Solutions

!!! definition - An alloy is a homogeneous mixture of two or more solid metals. - An aqueous solution is such that water is the solvent. - Two substances are miscible when one can be dissolved in the other in any proportion. - Two substances are immiscible when neither can be dissolved in the other in any proportion.

A solution is a homogeneous mixture produced when a solute dissolves in a solvent.

(Source: Kognity)

The concentration \(c\) of a solution represents the quantity of a solute in a given quantity of solvent/solution and is represented via square brackets as a ratio between a quantity of solute and quantity of solution.

!!! example A solution with 0.1 mols of hydrochloric acid per decimetre of solution is written as \(\text{[HCl]}=0.1\text{ mol/dm}^3\) or \(c_\text{HCl}=0.1\text{ mol/dm}^3\)

The solubility of a particular solute in a particular solvent at a given temperature is its molar concentration when it is saturated — when no more solute will dissolve at that temperature. If a solution is cooled while saturated, it may become supersaturated temporarily until the solute condenses into crystals. Solubility varies by temperature — in general, it increases as temperature increases in solids while it always decreases as temperature decreases in gases.

!!! example The solubility of barium sulfate is at \(\text{[BaSO]}_4=0.05\text{ mol/dm}^3\).

A solubility curve shows the saturation point of a particular solute in a particular solvent at varying temperatures. A solution is saturated when above or at the curve and unsatured when below the curve. If above the curve, the solution is supersaturated or some of the solute has not dissolved.

Concentration of solutions

Molar concentration is usually expressed as a ratio of amount of solute to the total volume of the solution with the units \(\text{mol/dm}^3\). \[c=\frac{n}{v}=\frac{\text{amount of solute (mol)}}{\text{total volume of solution (dm}^3\text{)}}\]

When a solution is diluted the moles of solute are the same before and after and so: \[c_iv_i=c_fv_f\]

A mass/mass percentage concentration (%m/m) is such that:

\[c\text{ (%m/m)}=\frac{\text{mass of solute (g)}}{\text{total mass of solution (g)}}×100\%\]

A mass/volume percentage concentration (%m/v) is easy to measure, but may be unreliable as volume changes with temperature. It is such that:

\[c\text{ (%m/v)}=\frac{\text{mass of solute (g)}}{\text{total volume of solution (100 cm}^3\text{)}}×100\%\]

A volume/volume percentage concentration (%v/v) has the same properties as the above but also has the caveat that there is no guarantee that the total volume of the solution is equal to the sums of the volumes of the solute and solvent. It is such that:

\[c\text{ (%v/v)}=\frac{\text{volume of solute (cm}^3\text{)}}{\text{total volume of solution (100 cm}^3\text{)}}×100\%\]

When dealing with very small concentrations, smaller units such as parts per million (ppm) or parts per billion (ppb) are used.

\[c\text{ (ppm)}=\frac{\text{mass of solute (g)}}{\text{mass of solution (g)}}×10^6\]

Standard solutions

A standard solution is a solution with an accurately known concentration.

Volumetric flasks are designed to make exactly one volume of solution very accurately, and consist or a large bulb and neck with a fill line. They come in standard sizes of 50, 100, 250, and 500 mL — when a solution is required that does not match one of these values, the closest size greater should be used.

Solutes come either in solid form or as part of a stock solution — a more concentrated solution used to make more diluted solutions. When measuring out solid solute, glassware should be avoided and a non-pourous boat of paper or plastic should be used to hold the solute. A liquid solute or stock solution should be measured using a graduated cylinder with the line at the bottom of the meniscus.

!!! warning To avoid air currents affecting the mass measured, paper should be folded and kept from extending past the edge of the scale.

To make a standard solution:

(Source: Kognity)

The solute should be prepared following the instructions above.

If the solute is still solid, the measured mass should be placed in a beaker about the same volume as the flask and poured inside. The container used to measure the solute should be rinsed three times with distilled water and also poured into the beaker. A small volume of distilled water should be added and the beaker swirled or stirred until surfaces are covered and all of the solute has dissolved.

Whether a stock solution or solid solute was used, both should be aqueous at this time. This early solution should be poured into a volumetric flask — a funnel can be used to make this easier. Any equipment that came in contact with the solute or solution must be rinsed three times with distilled water and have their contents poured into the flask.

!!! warning If any solute, stock solution, or liquid from the rinses is lost, or if the liquid added raises the volume of the beaker past the intended volume of the solution, the solution is a failure. Every equipment that comes in contact with the solution or solute must be rinsed three times and its contents poured into the flask.

More distilled water should be added to the flask until the bulb is about two-thirds full, and then swirled to mix the solution in advance. After, distilled water should be added until the bottom of the meniscus touches the fill line.

Finally, the flask should be capped and inverted repeatedly until the solution has mixed completely.

!!! warning If any solution is lost or if the volume of the solution exceeds that of the fill line, the solution is a failure.

Although the solution may be kept in the flask briefly, if it is not used soon it must be stored in a storage bottle. At minimum, it must contain the following on a label:

• Identity and concentration of the solution
• Warnings/dangers as according to GHS
• Protective equipment and precautions required

Gas laws

According to the kinetic molecular theory, gases are largely empty empty space with particles moving randomly in straight lines due to weak or no intermolecular forces acting on them. Gas particles:

• move in all directions,
• are much smaller than the spaces between them,
• do not have any forces of attraction or repulsion between them,
• elastically collide with one another, and
• have movement directly proportional to the temperature in Kelvin such that \(E_k\propto T\).

Because gases are the only state of matter that have negligible intermolecular forces within the substance and so move independently of one another, they are the only compressible state of matter.

Boyle’s law states that the pressure and volume of a fixed amount of an ideal gas are inversely proportional to each other at a constant temperature. \[P\propto\frac{1}{V}\]

(Source: Kognity)

Charles’ law states that the absolute temperature and volume of a fixed amount of an ideal gas are directly proportional to each other at a constant pressure. \[V\propto T\]

Gay-Lussac’s law states that the absolute temperature and pressure of a fixed amount of an ideal gas are directly proportional to each other at constant volume. \[P\propto T\]

The combined gas law is derived from the three laws above: \[\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\]

Avogadro’s law states that the amount of a gas and its volume are proportional at a fixed temperature and pressure. This means that if all products and reactants are gases, volumes are related by the coefficients in a balanced chemical equation. \[n\propto V\]

Dalton’s law of partial pressures states that the pressure of a mixture of gases is equal to the sum of the pressures of each gas. As pressure is directly proportional to the number of particles in the gas: \[ P_T = \Sigma P \\ P\propto n \\ \frac{n_1}{n_T}P_T=P_1 \]

Please see SL Physics#Gas laws for more information.

Gas collection

STP refers to standard temperature and pressure, which is at \(273\text{ K}\) and \(100\text{ kPa}\). One mole of an ideal gas occupies \(22.7\text{ dm}^3\) — this value is in the data booklet.

The gas collection process is used to experimentally determine the number of moles and/or mass of a gas. By adding a gas under water, the gas displaces the water as it moves up into a measuring cylinder and its volume can be taken. Ideally, the temperature of the gas is equal to the temperature of the water, and the its pressure is equal to that of the atmosphere. Since water vapour tends to evaporate, it has to be factored out using Dalton’s law of partial pressures and a chart that gives the pressure of water at a given temperature. \[P_T=P_{\text{H}_2\text{O}} + P_\text{gas}\]

(Source: Kognity)

2.1 - Atoms

!!! definition - The effective nuclear charge (\(Z_\text{eff}\)) is the net positive charge (attraction to the nucleus) experienced by an electron in an atom. - Electron shielding is decrease in the effective nuclear charge of an electron because of the repulsion of other electrons in lower-energy shells.

Atomic notation is used to represent individual atoms or ions. It is written in the form \(^M_Z \text{Symbol}^\text{Charge}\), where \(M\) is the mass number of the particle and \(Z\) is the atomic number of the particle.

!!! example - \(^1_1 \text{H}^{+}\) is the atomic notation for the most common hydrogen ion. - \(^{16}_8 \text{O}^{2-}\) is the atomic notation for the most common oxygen ion. - \(^{20}_{10} \text{Ne}\) is the atomic notation for the most common neon atom.

Isotopes

Isotopes are atoms of the same element but with different masses, or alternatively, atoms with the same number of protons but with different numbers of neutrons.

Radioisotopes are isotopes that are unstable (will spontaneously decay, are radioactive). Unstable atoms decay (break down) into one or more different isotopes of a different element. The half-life of a radioisotope is the time it takes for 50% of a sample’s atoms to decay.

!!! warning Radioisotopes are dangerous! They emit radiation, which is not at all good for human health in the vast majority of cases. However, there are also useful applications for radioisotopes today. For example, Cobalt-60 is used in radiation therapy to kill cancer tumours by damaging their DNA.

Atomic mass

The mass of every atom is represented relative to 1/12th of a carbon-12 atom. This mass is either unitless or expressed in terms of atomic mass units (amu or u). On the periodic table, the relative atomic mass (\(A_r\)) is shown, which is the sum of the masses of each isotope combined with their natural abundance (%abundance).

\[ A_r = \text{%abundance}×\text{mass number of isotope} \\ m_a = \Sigma A_r \]

When calculating the atomic mass from the graph from a mass spectrometer, the sum of the natural abundances of each isotope may not equal 100 or 1 (not in %abundance). In this case, calculation of %abundance will need to be done before solving for \(m_a\).

A mass spectrometer may also provide mass in the form of \(M/Z\), which represents mass over charge. For the sake of simplicity, \(Z=1\), so \(M/Z\) represents the mass of a particle.

Atomic radius

The atomic radius of an atom is the distance from the centre of the nucleus to approximately the outer boundary of the electron shell. This cannot be directly measured by scientists.

Ionisation energy

The first ionisation energy of an element is the minimum amount of energy required to remove one mole of electrons from one mole of gaseous atoms to form a mole of gaseous ions, so that \[\text{Q}_\text{(g)} \rightarrow \text{Q}_\text{(g)}^+ + \text{e}^-\]

Any subsequent ionisation energies of an element are the minimum amount of energy required to remove one additional mole of electrons. For example, the second ionisation energy would involve \[\text{Q}_\text{(g)}^+ \rightarrow \text{Q}_\text{(g)}^{2+} + \text{e}^-\]

It requires vastly more energy to remove an electron from a filled valence shell compared to an unfilled valence shell.

Electron affinity

The electron affinity of an atom is the amount of energy required or released to add an electron to a neutral gaseous atom to form a negative ion, such that \[\text{Q}_\text{(g)} + \text{e}^- \rightarrow \text{Q}^-_\text{(g)}\]

If energy is released, the atom has a negative electron affinity, and will form a stable ion.

If energy is required, the atom has a positive electron affinity, and will form an unstable ion (the ion will spontaneously decay).

Electronegativity

The electronegativity of an atom represents the ability of that atom to attract a pair of electrons in a covalent bond, ranging from \(0\) to \(4\) on the Pauling scale. As electronegativity increases, the atom more strongly holds on to the electrons in its covalent bond, so the pair of electrons in that bond spend more time around the atom with the higher electronegativity.

Reactivity

The reactivity of an element is how “willing” it is to give up or gain electrons to fill its valence shell.

The reaction of an alkali metal with water always forms a hydroxide and hydrogen gas. For example, lithium reacts with water such that: \[2\text{Li}_\text{(s)} + 2\text{H}_2\text{O}_\text{(l)} \rightarrow 2\text{LiOH}_\text{(aq)} + \text{H}_{2 (g)}\]

The reaction of a halogen with hydrogen gas always forms a hydride. For example, fluorine reacts with hydrogen gas such that: \[\text{Fl}_\text{(g)} + \text{H}_\text{2 (g)} \rightarrow 2\text{HFl}_\text{(g)}\]

2.2 - Electrons in atoms

The electromagnetic spectrum

Electromagnetic radiation is energy that travels in oscillating waves at the speed of light, having both an electric and a magnetic field.

!!! reminder \(c\) is the standard symbol for the speed of light in a vacuum (~\(3×10^8\) m/s).

Wavelength (\(\lambda\)) is the distance between two identical areas on the pattern of the wave (e.g., crest to crest), and is measured in nanometres. The frequency (\(f\)) of a wave is the number of times it oscillates in a second, and is measured in hertz.

The wavelength and frequency of a wave are inversely proportional, and the more energy of electromagnetic radiation, the smaller the frequency, and vice versa.

\[\lambda f = c\]

The visible spectrum contains all of the wavelengths that the human eye can detect, and ranges from 400 to 700 nm.

(Source: Kognity)

Continuous and line spectra

A continuous spectrum shows all wavelengths in a particular range or region, while line spectra have gaps between a particular range.

There are two types of line spectra: absorption line spectra and emission line spectra. For a given element, all lines will be in the same position as the two spectra are two different ways of representing the same data.

(Source: Kognity)

To create an absorption line spectrum, white light is shone on the element and reflected and the resulting spectrum is captured.

To create an emission line spectrum, a different type of energy, typically electricity, is forced on the element. Atoms re-emit this energy in the form of electromagnetic radiation and the resulting spectrum is captured.

In both cases, a slit to focus the beam and a prism to separate the wavelengths are used.

Line spectra but complicated

When an atom is excited (energy is added), its electrons absorb it and become excited and transition to higher energy levels. As they fall back down to lower energy levels, the transitions are accompanied by an emission of energy.

Absorption line spectra are produced when electrons absorb energy and move to higher energy levels, while emission line spectra are produced when electrons release energy.

!!! definition - An energy level is a possible area where electrons can occupy and is synonymous with “shell”. - The ground state of an electron is its energy level if no energy is added.

Energy level diagrams can be used to demonstrate this movement. The lines get closer together, or converge, as energy level increases, similar to the spectra.

!!! example The below line spectra and energy level diagrams are representative of the formation visible light absorption/emission spectrum for hydrogen.

(Source: Kognity) (Source: Kognity)

As electrons move down energy levels, they emit,

• ultraviolet light if they move down to \(n=1\)
• visible light if they move down to \(n=2\) (the wavelength depends on the quantity of emitted energy)
• infrared light if they move down to \(n=3\)

!!! warning Electrons may not directly move down to their original energy levels. To form the full line spectra of hydrogen, some electrons transition to energy levels above 2 and then eventually go down to \(n=2\).

Convergence and first ionisation energy

At higher energy levels, the distance between each consecutive energy level becomes smaller until there is no change at all. This highest line is known as the convergence limit, and is known as \(n=∞\). Electrons in the \(n=∞\) energy level are no longer attracted by the nucleus, resulting in the formation of a positve ion. The energy required for this can be calculated using the following equation, where \(E\) is energy required in joules and \(h\) is Planck’s constant: \[E=\text{convergence frequency} · h\]

To find the first ionisation energy of an element, the amount of energy required is equal to the difference in frequency of the ground state of the first valence electron and \(n=∞\) multiplied by Planck’s constant. This returns the first ionisation energy of one atom, or in electronvolts (eV).

To find the convergence limit graphically, graph the difference of frequencies (\(\Delta f\)) against each frequency in the series (\(f\)) and extrapolate to \(\Delta f=0\).

Schrödinger model

According to Heisenberg’s uncertainty principle, the more precisely the position of an electron is known, the less precisely its momentum is known and vice versa. Since the Bohr-Rutherford model, like most models, is an egregious lie, this principle is used to develop the Schrödinger model.

The Schrödinger model asserts that electrons are now three-dimensional waveforms instead of particles and relates the wave to the electron’s energy and position. As such, the position of each electron is represented as a 3D probability cloud around the nucleus where the electron is most likely to be found, also known as an orbital.

Orbitals

Orbitals have different shapes, sizes, and distances from the nucleus. Each main energy level has one or more orbitals depending the maximum number of electrons in the energy level. Each orbital can contain up to 2 electrons and is associated with a specific region of space in the atom. The electrons contained in the orbital may be found anywhere in that space.

The four types of orbitals currently known are: s, p, d, and f.

The group of orbitals of the same type in the same energy level is known as the sublevel. A coefficient is given to indicate the energy level of that sublevel.

!!! example The p sublevel consists of 3 p orbitals at a given energy level. The p sublevel of energy level 2 is written as 2p.

Main energy level	Types of orbitals	Number of orbitals	Maximum number of electrons
\(n=1\)	1 s	1	2
\(n=2\)	1 s, 3 p	4	8
\(n=3\)	1 s, 3 p, 5 d	9	18
\(n=4\)	1 s, 3 p, 5 d, 7 f	16	32
\(n\)		\(n^2\)	\(2n^2\)

Orbitals of the same type but in higher energy levels are simply larger, so any electrons in the higher energy level may be found in those lower orbitals (and maybe even in the space of other orbital types, too). However, electrons already occupying the other orbitals repel the higher electrons, causing them to spend on average more time in their orbital, outside of lower ones.

(Source: Kognity)

s orbitals are spherical in shape and are centred on the nucleus. There is one on each energy level.

p orbitals are dumbbell-shaped and centred on the nucleus. Each orbital is aligned on a different axis. There are three on each energy level starting from \(n=2\).

d orbitals have complex shapes. There are 5 in each energy level starting from \(n=3\).

f orbitals have more complex shapes. There are 7 in each energy level starting from \(n=4\).

The Aufbau principle states that orbitals are filled up in order of increasing energy (closest to farthest from nucleus), which is shown in the image below.

(Source: Kognity)

Orbital box diagrams

According to Hund’s rule, atoms fill all orbitals in the same sublevel before pairing up, similar to Monopoly house-building rules.

Orbital box diagrams are one method of showing electron configuration by laying out the orbitals in increasing energy.

These diagrams must show that energy increases going up and that there are spaces for electrons in labelled orbital sublevels. Each electron is represented by an arrow.

By convention, electrons are ordered with the first pointing up and the second pointing down in the same orbital. This is because the Pauli exclusion principle states that no two electrons have the same set of quantum numbers, so if one occupies an orbital with a clockwise spin (points up), the other must have an anti-clockwise spin (points down).

Electron configuration

A full electron configuration of an element lists each of its orbital sublevels and the number of electrons in each sublevel, ordered in increasing energy.

(Source: Kognity)

!!! example The full electron configuration for bromine (\(Z=35\)) is: \[\text{1s}^2\text{ 2s}^2\text{ 2p}^6\text{ 3s}^2\text{ 3p}^6\text{ 4s}^2\text{ 3d}^{10}\text{ 4p}^5\]

A condensed/abbreviated electron configuration of an element replaces part of the full configuration with the closest noble gas with less but not equal electrons enclosed in square brackets.

The electron configurations of an ion may be the same as a noble gas or another ion. In this case, the two configurations are known as isoelectronic.

!!! example The condensed electron configuration of bromine is: \[\text{[Ar] 4s}^2\text{ 3d}^{10}\text{ 4p}^5\]

!!! warning There is a slight energy advantage to full/half-full orbital sublevels. As such, there are two exceptions to electron configuration that differ from their predicted electron configuration: \[\text{Cr: [Ar] 4s}^1 \text{ 3d}^5\] \[\text{Cu: [Ar] 4s}^1 \text{ 3d}^{10}\]

Quantum numbers

Quantum numbers are a set of four numbers that are used to describe the specific location of an electron, similar to a coordinate system.

The principal quantum number (\(n\)) is the main energy level of the electron.

The angular momentum quantum number (\(ℓ\)) is the type of orbital the electron resides in, zero-indexed:

• \(ℓ=0\) means that the electron is in an s orbital.
• \(ℓ=1\) means that the electron is in a p orbital.
• \(ℓ=2\) means that the electron is in a d orbital.

The magnetic quantum number (\(m_ℓ\)) is contextualised by the angular momentum quantum number and identifies the specific orbital that the electron occupies in its sublevel. The centre orbital is \(m_ℓ=0\) and is listed in ascending order.

!!! example If \(ℓ=1\), \(m_ℓ=-2\) indicates that the electron is located in the first p orbital of the sublevel and \(m_ℓ=2\) indicates that it is located on the fifth and last p orbital of the sublevel.

The spin quantum number (\(m_s\)) can either be \(\frac{1}{2}\) or \(-\frac{1}{2}\) and determines if the electron has a clockwise spin/is the first electron in its orbital or not, respectively.

3 - Periodicity

Models

Please see SL Physics#Models for more information.

Periodic trends

Some trends in the periodic table include:

• atomic radius decreases when going across a period and increases when going down a group
• ionic radius decreases when going across a period for groups 1–13, then sharply increases before decreasing across groups 15–17; it increases when going down a group
• electron affinity increases when going across a period and decreases when going down a group
• ionisation energy increases when going across a period and decreases when going down a group
• electronegativity increases when going across a period and decreases when going down a group
• reactivity of alkali metals increases when going down the group
• reactivity of halogens decreases when going down the group

When explaining these trends in the periodic table, it is best to use the following basic concepts to build on to larger points.

Across a period, the number of shells occupied by the electrons is the same but the number of protons in the nucleus increases. Therefore,

• the attraction of each electron to the nucleus (effective nuclear charge) increases as the number of protons increases
• shielding is unchanged as the number of electrons between the valence electrons and the nucleus is the same

Down a period, the number of shells occupied by the electrons increases, so valence electrons are further from the nucleus. Therefore,

• the attraction of valence electrons to the nucleus decreases due to the increasing distance
• shielding increases due to the increasing number of electrons between the valence electrons and the nucleus

The effects of these basic concepts to cause the above periodic trends is left as an exercise for the reader.

!!! example To explain why there is a trend of decreasing atomic radius across a period:

- As the number of protons and electrons increase together, but the number of electron shells does not change, the effect of shielding remains unchanged while effective nuclear charge increases.
- This increased attraction to the nucleus reduces the atomic radius compared to other atoms before it.

Period 3 oxides

Metal oxides (oxides of \(\text{Na}\) to \(\text{Al}\)) all form “giant ionic lattices” (alternatively just “lattices”) as an ionic bond is formed between a metal and a non-metal. These are typically solids because of their strong electrostatic attraction.

Metal oxides, except silicon (oxides of \(\text{P}\) to \(\text{Cl}\)) all form molecular compounds that exist as individual molecules as a covalent bond is formed between two non-metals. These are typically liquids or gases because of their weak intermolecular forces.

Period 3 oxides start basic but become more acidic when going across the period, with aluminium oxide being the turning point as an amphoteric substance (can be both an acid or a base). Basic oxides dissolve in water to form hydroxides while acidic oxides dissolve in water to form their respective oxyacids.

!!! example The following equations should be known by heart and are examples of period 3 oxides reacting with water. \[ \text{Na}_2\text{O}_\text{(s)} + \text{H}_2\text{O}_\text{(l)} → 2\text{NaOH}_\text{(aq)} \\ \text{MgO}_\text{(s)} + \text{H}_2\text{O}_\text{(l)} → \text{Mg(OH)}_\text{2 (aq)} \\ \text{P}_4\text{O}_\text{10 (s)} + 6\text{H}_2\text{O}_\text{(l)} → 4\text{H}_3\text{PO}_\text{4 (aq)} \\ \text{SO}_\text{3 (g)} + \text{H}_2\text{O}_\text{(l)} → \text{H}_2\text{SO}_\text{4 (aq)} \\ 3\text{NO}_\text{2 (g)} + \text{H}_2\text{O}_\text{(l)} → 2\text{HNO}_\text{3 (aq)} + \text{NO}_\text{(g)} \]

Alkali metals and halogens

The alkali metals are a family of highly reactive metals in group 1. They are very soft, and their melting and boiling points are relatively low, decreasing more when going down the group due to their weaker attraction. When reacted with water, they form hydrogen gas and metal hydroxides that have a high pH, hence the name “alkali” metals.

The halogens are a family of highly reactive non-metals in group 17. They occur diatomically (in molecules composed of two of the same element) and start as gases but become solids when going down the group due to stronger intermolecular forces. A single displacement reaction involving halogens only occurs if the more reactive halogen is not already bonded to the cation. Halogens are also very strong oxidising agents with their effectiveness increasing going up the group.

4.0 - Chemical bonding and structure

A chemical bond consists of the strong electronic interactions of the valence electrons between atoms that hold the atoms closer together. This only occurs if the atoms would reduce their potential energy by bonding.

!!! reminder When drawing a Lewis dot diagram, covalent bonds must be represented as two adjacent dots. When drawing a Lewis structure, covalent bonds must be represented as lines connecting the atoms.

If the process stage is required:

- Electrons destined to be shared must be encircled.
- Electrons to be transferred must have arrows pointing to their destination.
- x'es are used to represent additional electrons that have an unknown source.

Percentage ionic character

Bonding is a spectrum. The percentage ionic character of a chemical bond shows roughly the amount of time valence electrons spend near an atom or ion in a bond. The difference between two elements’ electronegativity (ΔEN) indicates how covalent and how ionic the bond behaves.

If ΔEN is:

• less than 0.5, it behaves like a pure covalent bond
• between 0.5 and 1.7, it behaves like a polar covalent bond
• greater than 1.7, it behaves like an ionic bond

4.1 - Ionic bonding and structure

An ionic bond is the electrostatic attraction between oppositely charged ions. Electrons are transferred first, and then the bond forms via the attraction of the now-positive and negative ions. This reduces the potential energy of the ions and therefore increases their stability.

!!! definition Electrostatic attraction is the force of attraction between opposite charges.

!!! warning When expressing ionic bonds in a Lewis dot diagram, ions with charges of the same sign must never be placed next to one another.

Structure of ionic compounds

Ionic compounds are composed of a lattice structure (crystalline structure) of ions of alternating charges. A formula unit is the lowest ratio of positive to negative ions.

(Source: Kognity)

!!! example In sodium chloride, the ratio of positive sodium ions to negative chloride ions is always 1:1, so its formula is NaCl.

In an ionic compound, the number of ions that each ion can touch is referred to as the coordination number. It is stated as “(cation)(anion) is (coordination number of cation):(coordination number of anion) coordinated”.

!!! example In the diagram above, each sodium ion touches six chloride ions, and each chloride ion touches six sodium ions. Therefore, “NaCl is 6:6 coordinated”.

4.2 - Covalent bonding

A covalent bond is the electrostatic attraction between pairs of valence electrons and nuclei. This causes atoms to “share” electrons instead of gaining or losing them. Covalent bonds form molecules, which in turn form molecular compounds (not covalent compounds).

(Source: Kognity)

Whether a covalent bond is pure or polar indicates how evenly the shared electrons are shared between the atoms.

• A pure covalent bond has both nuclei attracting the valence electrons fairly evenly, so the difference in electronegativity (ΔEN) is low.
• A polar covalent bond has both nuclei attracting the valence electrons unevenly, so the ΔEN is high.

Sometimes, one atom in a covalent bond may contribute both electrons in a shared pair. This bond is called a dative bond, and is represented in Lewis structures as a double bond. Dative covalent bonds may be used to form bonds when a conventional single or double bond is infeasible, such as in ozone.

Bonding capacity

The bonding capacity of a non-metal describes the number of covalent bonds it can form.

4.3 - Covalent structures

Formal charge

There may be several correct ways to draw covalent bonds in Lewis structures and dot diagrams. Solving for the formal charge of each atom involved in a covalent bond can help identify the best structure to construct. The formal charge of an atom in a covalent bond represents the charge that that atom has. The sum of all formal charges in a covalently bonded compound is equal to the charge of the overall compound. The element with the lowest electronegativity is almost always in the centre.

The formal charge of an atom can be calculated using the following equation, where \(V\) is the number of valence electrons in the element, \(N\) is the number of non-bonding valence electrons, and \(B\) is the number of covalent bonds formed with that atom: \[\text{Formal charge} = V-N-B\]

To find the best structure for a covalently bonded compound, the absolute value of the formal charge of all atoms in that compound should be minimised. Positively charged atoms will even accept dative covalent bonds from other atoms with negative formal charges.

!!! warning Some elements want formal charges of zero so much that they break the octet rule. These elements are \(\text{P, S, Cl, Br, I, and Xe}\).

Resonance structures

Even when considering formal charges, there may still be multiple best Lewis structures when molecules or polyatomic ions contain double or triple bonds. These equivalent structures are known as resonance structures, and the number of possible resonance structures is equal to the number of different positions for the double/triple bond. Double-sided arrows are used to show that the forms are resonant.

(Source: Kognity)

The resonance structures of a compound show that none of the models is truly correct but instead the actual structure is somewhere in between all of them, and is not “flipping” between the various resonance structures.

!!! warning Molecules such as \(\text{SO}_2\) have resonance structures as the possible naive structures prior to involving formal charges are not considered to be resonant.

The resonance-hybrid structure shows that the actual strength of all three bonds is equal and somewhere between a single and double bond.

(Source: Wikipedia)

Exceptions to the octet rule

Atoms such as boron and beryllium (\(\text{B}\) and \(\text{Be}\)) may form incomplete octets (less than 8 electrons) in their valence shell due to their status as small metalloids that form covalent bonds. In total, boron can sometimes need only 6 electrons while beryllium may have only 4 in their valence shells.

(Source: Kognity)

!!! example \(\text{BeCl}_2\) and \(\text{BCl}_3\) exist.

Some elements in period 3 and beyond follow the formal charge exception above and may form expanded octets (more than 8 electrons and up to 12) in their valence shell. These include the aforementioned \(\text{P, S, Cl, Br, I, Xe}\), as well as metalloids.

Free radicals are molecules that end up with an odd number of electrons in their valence shell and are very reactive. Because one electron can never pair up with another, it remains forever alone.

??? example \(\text{NO}_2\) is a free radical as one of nitrogen’s atoms cannot pair with anything even after the formation of a dative covalent bond from oxygen.

Factors affecting bond strength

The strength of a bond is determined by the amount of energy required to break that bond (bond energy).

The length of a bond (bond length) has an inverse relationship with the strength of that bond, as the attraction of electrons to nuclei decreases with distance.

Multiple (double/triple) bonds are shorter than single bonds (a higher bond order) and are therefore stronger.

VSEPR theory

The valence shell electron pair repulsion theory (VSEPR theory) is a model used to predict the electron distribution and molecular shape of molecules. It states that electron domains around nuclei repel each other such that they end up as far away from each other as possible in three dimensions to minimise energy. The end location of these domains is used to predict molecular shape.

Groups of electrons that repel other electrons together are known as electron domains. Single, double, and triple covalent bonds all qualify as exactly one electron domain, as well as lone pairs. Electron domains in bonds are known as bonding domains while lone pairs are known as non-bonding domains. Lone pairs have a slightly stronger repulsion than bonding domains as they spend more time in their own atom.

!!! definition - Molecular shape/geometry represents the general shape of a molecule’s bonds around a central atom. - Electron distribution/geometry represents the general shape of a molecule’s electrons around a central atom. It is identical to molecular shape, but takes lone pairs into consideration. - The central atom is the atom from which electron distribution is looked at from. It is typically the element with the lowest \(\Delta\) EN, except for hydrogen. - Peripheral atoms are atoms that are bonded to the central atom. For example, peripheral atoms in \(\text{CCl}_4\) are all four chlorines.

The AXE method of electron counting represents the electron pairs around a central atom with the formula \(\text{AX}_n\text{E}_m\), where \(A\) is the central atom, each \(X\) represents a peripheral atom, and each \(E\) represents a lone pair of electrons on the central atom. The total number of domains is equal to \(X+E\). If \(E=0\), the electron distribution and the molecular shape of a molecule are the same.

AXE	Electron distribution	Molecular shape	Bond angle
\(\text{AX}_4\)	tetrahedral	tetrahedral	109.5°
\(\text{AX}_3\text{E}\)	tetrahedral	trigonal pyramidal	107°
\(\text{AX}_2\text{E}_2\)	tetrahedral	bent	104.5°
\(\text{AXE}_3\)	trigonal planar	linear	DNE
\(\text{AX}_3\)	trigonal planar	trigonal planar	120°
\(\text{AX}_2\text{E}_1\)	trigonal planar	bent	117°
\(\text{AX}_2\)	linear	linear	180°

A 3D diagram of a molecule is drawn similarly to three-dimensional Lewis structures (ions must still be enclosed in square brackets), except for the following added rules:

• Only the lone pairs of the central atom should be drawn.
• Bonds behind the current plane should be drawn with broken lines.
• Bonds in front of the current plane should be drawn with triangle lines.
• 90° angles are only present in molecules with five electron domains, and should be avoided in all other scenarios.
• The angle between the peripheral atoms should be labelled once for each distinct angle.
  • for \(\text{AX}_n\text{E}_m\) structures, where \(n+m=4\), the angle between peripheral atoms is equal to \(109.5° - 2.5m\).
  • for \(\text{AX}_n\text{E}_m\) structures, where \(n+m=3\), the angle between peripheral atom is equal to \(120°-3m\).

!!! example The below 3D diagrams are for \(\text{CH}_4\), \(\text{NH}_3\), and \(\text{H}_2\text{O}\), respectively. Note that the angle on \(\text{NH}_3\) is supposed to be \(107°\).

<img src="/resources/images/vespr-diagram.png" width=700>(Source: Kognity)</img>

VSEPR theory expanded

Because of the addition of d orbitals beginning from \(n=3\), elements in period 3 and beyond with p orbitals can make use of the space for d orbitals to form bonds such that they break the octet rule.

In molecules with 5 or 6 electron domains, their electron distribution is as follows, respectively: (Source: Kognity)

In a trigonal bipyramidal, the equatorial positions of domains refer to the position of the domains on the x- and z-dimensions (a trigonal plane). The domains along the y-dimension are have axial positions. The angle between the two is known as the equatorial-axial angle. Lone pairs are always placed in equatorial positions.

AXE	Electron distribution	Molecular shape	Bond angle
\(\text{AX}_5\)	trigonal bipyramidal	trigonal bipyramidal	equatorial=120°, equatorial-axial=90°
\(\text{AX}_4\text{E}\)	trigonal bipyramidal	see-saw	equatorial=117°, equatorial-axial=90°
\(\text{AX}_3\text{E}_2\)	trigonal bipyramidal	t-shaped	equatorial-axial=90°
\(\text{AX}_2\text{E}_3\)	trigonal bipyramidal	linear	180°
\(\text{AX}_6\)	octahedral	octahedral	90°
\(\text{AX}_5\text{E}\)	octahedral	square-based pyramidal	88.5°
\(\text{AX}_4\text{E}_2\)	octahedral	square planar	90°

!!! example The following are some examples of 3D diagrams of molecules with five domains (Source: Kognity):

$\text{AX}_5$:
<img src="/resources/images/vsepr-ax5.png" width=700></img>
$\text{AX}_4\text{E}$:
<img src="/resources/images/vsepr-ax4e.png" width=700></img>
$\text{AX}_3\text{E}_2$:
<img src="/resources/images/vsepr-ax3e2.png" width=700></img>

The following are some examples of 3D diagrams of molecules with six domains (Source: Kognity):

$\text{AX}_6$:
<img src="/resources/images/vsepr-ax6.png" width=700></img>
$\text{AX}_5\text{E}$:
<img src="/resources/images/vsepr-ax5e.png" width=700></img>
$\text{AX}_4\text{E}_2$:
<img src="/resources/images/vsepr-ax4e2.png" width=700></img>

Molecular polarity

The polarity of a molecule refers to how even the distribution of electrons overall throughout the molecule (not to be confused with the electron distribution in VSEPR) and affects only the physical properties of the compound.

The polarity of a molecule depends on the presence of polar bonds and the molecular shape of the molecule. In this course, if a molecule is symmetrical in three dimensions or does not contain any polar covalent bonds, it is non-polar. The shape of the molecule affects the directions that dipoles act in in their three-dimensional forms and can cause dipoles to cancel out.

!!! definition The net dipole moment of a molecule is the vector sum of all bond dipoles in a molecule. Only polar molecules have net dipole moments.

Bond dipoles can be represented as vectors pointing in the direction of the atom with greater electronegativity with one line across it.

!!! example (Source: Kognity)

Generally, tetrahedral and trigonal planar molecules with the same atoms bonding to the central atom are non-polar molecules as their bond dipoles cancel out. Trigonal pyramidal and linear diatomic molecules with polar bonds typically are polar because their bond dipoles do not cancel each other out.

!!! example (Source: Kognity)

By convention and missing in the examples above, the lowercase delta (\(\delta\)) is used to indicate polarity. The less electronegative atom/side of a molecule is marked as \(\delta^+\) while the atom/side where electrons spend more time around on average is labelled \(\delta^-\), indicating partial positive/negative charges, respectively.

!!! example (Source: Kognity)

4.4 - Intermolecular forces

Intramolecular forces are forces that act within the molecule, such as covalent bonds.

Intermolecular forces are forces that act between molecules, and are responsible for the physical properties of an aggregate/substance. London dispersion forces and dipole-dipole dorces are known collectively as van der Waal’s forces. They are all weaker than ionic bonds, covalent bonds, and metallic bonds.

London forces

London forces are attractive forces that exist between all atoms and molecules. They are the weakest type of force and are caused by instantaneous and induced dipoles. An instantaneous dipole is a temporary dipole formed when electron density randomly shifts, causing an electron imbalance for a brief moment. Molecules with these temporary dipoles affect neighbouring molecules by inducing a dipole, which induce more dipoles on and on.

(Source: Kognity)

The two factors that affect the strength of London forces are their surface area and the number of electrons in the molecule, the former of which is influenced by the mass and shape of the molecule.

• A greater number of electrons means that more of them can be influenced to form stronger induced dipoles.
• A greater surface area increases the chances that an instantaneous dipole is formed due to a greater space for it to happen.

Dipole-dipole forces

The \(\delta^-\) and \(\delta^+\) of different polar molecules with permanent dipoles attract each other, thus holding the molecules together.

(Source: Kognity)

Hydrogen bonding

Hydrogen bonding is similar to a very extreme form of dipole-dipole attraction. They form between a lone pair on elements of high electronegativities (only \(\text{F}\), \(\text{O}\), or \(\text{N}\)) and a hydrogen atom on a different molecule bonded covalently to one \(\text{F}\), \(\text{O}\), or \(\text{N}\).

(Source: Kognity)

When hydrogen is bonded to a FON, the the electron density is concentrated by the FON, leaving it relatively positive. This allows it to become attracted to a lone pair on a different FON.

Hydrogen bonds are drawn as dashed lines.

!!! example (Source: Kognity)

4.5 - Metallic bonding

9.1 - Oxidation and reduction

Oxidation states

The oxidation state of an atom or ion assumes that atoms gain or lose electrons according to their electronegativity, effectively assuming that all bonds are ionic. It is equal to the charge it would have if the compound was an ion. As such, the oxidation state of an ion is equal to its charge, and in a atom, the charge it would have if it were an ion.

!!! warning The oxidation number of an atom is the magnitude of its oxidation state.

Oxidation states are written as their charge followed by the number of electrons “lost” or “gained”, opposite the notation used for charge. All elements in their elemental form have oxidation states of \(0\).

!!! example The oxidation state of oxygen in water is \(+2\) and the oxidation state of a single chromium atom in dichromate (\(\text{Cr}_2\text{O}_7{}^{2-}\)) is \(+6\)).

10.1 - Organic chemistry fundamentals

Structural isomerism

Structural isomers are compounds with the same molecular formula but with different arrangements of atoms (different structural formulae).

(Source: Kognity)

11.1 - Uncertainties and errors in measurement and results

Please see SL Physics#Uncertainties and errors for more information.

11.2 - Graphical techniques

When plotting a graph:

• plot the independent variable on the horizontal axis and the dependent variable on the vertical axis
• label the axes, ensuring that the labels include units
• choose an appropriate scale for each axis
• give the graph an appropriate title at the bottom in title case
• draw a line of best fit
• include all uncertainties in the form of error bars
  • if the error bars are too small to see, it should be noted explanation below

Titles

The title of a graph should clearly indicate what the graph represents under what conditions in title case, so that any onlooker should be able to identify the experiment. It should not include “vs.” Any legends present should be located under the graph.

??? example “Effect of Cat Deaths on Suicides in New Zealand”

Error bars

Please see SL Physics#Error bars for more information.

Line of best fit

Please see SL Physics#Uncertainty of gradient and intercepts for more information.

11.3 - Spectroscopic identification of organic compounds

13.1 - Transition elements

!!! definition A transition element is an element that has an incomplete d sublevel in its atom or in any of its ions. This means that while \(\text{Zn}\) is not considered a transition element, \(\text{Cu}\) is.

Variable oxidation states

All transition metals can in theory form molecules with different oxidation states, although practically they form the most common ones.

Since the d and s sublevels are so close to each other and the s sublevel has a higher main energy level, all transition metals lose the electrons in the s sublevel first, meaning that all transition metals are capable of a \(2+\) oxidation state.

!!! example Scandium (\(\text{[Ar] 4s}^2\text{ 3d}^1\)) loses its 4s electrons first, resulting in an electron configuration of \(\text{[Ar] 3d}^1\).

The maximum oxidation state of a transition metal is equal to the number of electrons in its outermost s orbital plus the number of unpaired electrons in its outer d orbital in its predicted electron configuration. They can take on oxidation states anywhere between \(2+\) and their maximum by giving up more of their unpaired electrons.

!!! example Titanium (\(\text{[Ar] 4s}^2\text{ 3d}^2\)) and nickel (\(\text{[Ar] 4s}^2\text{ 3d}^8\)) both have a maximum oxidation state of \(+4\) as they both only have two unpaired d sublevel electrons and two 4s electrons.

!!! warning Copper can form \(1+\) ions by losing its singular 4s electron and such is the only transition metal that can have a possible oxidation state of \(+1\).

Physical properties of transition elements

The spin of electrons is the cause behind an element’s magnetism.

Diamagnetic substances only have paired electrons in their d orbitals. The opposite spins of the electrons cancel each other out so the magnetic effect is very weak (negligible), so they are known as being non-magnetic.

Paramagnetic substances have unpaired electrons in their d orbitals. Their unpaired electrons are aligned under the effect of an external magnetic field temporarily until the field is removed. An increase in the number of unpaired electrons increases the strength of the magnetic effect. These are metals that respond to magnets but do not generate their own magnetic field.

Ferromagnetic substances have the largest magnetic effect and also have unpaired electrons in their d orbitals. These electrons in a large number of atoms are aligned by an external magnetic field and stay sligned after the field is removed, permanently magnetising the object. Only iron, cobalt, and nickel among other rare earth elements are ferromagnetic.

Catalytic properties of transition elements

!!! definition A catalyst increases the rate of a chemical reaction by providing an alternate reaction pathway with a lower activation energy and is not consumed as part of the reaction.

Transition metals are effective heterogeneous catalysts — they are of a different state to that of the reactants.

!!! example Iron providing a surface for the reactant to adsorb — to gather on — to orient them correctly in the Haber process to produce ammonia: \(\text{N}_\text{2 (g)} + \text{3H}_\text{2 (g)} ⇌ \text{2NH}_\text{3 (g)}\)

<img src="/resources/images/haber-process.jpg" width=400>(Source: Kognity)</img>

!!! example Nickel in the conversion of alkene to alkanes via hydrogenation:

<img src="/resources/images/hydrogenation.png" width=700>(Source: Kognity)</img>

!!! example Vanadium(V) oxide in the Contact process to increase the oxidisation of \(\text{SO}_2\) to \(\text{SO}_3\) in the first step to make sulfuric acid: \[\text{2SO}_\text{2 (g)} + \text{O}_\text{2 (g)} ⇌ \text{2SO}_\text{3 (g)}\]

!!! example Manganese(IV) oxide in decomposing hydrogen peroxide into water and oxygen: \[\text{2H}_2\text{O}_\text{2 (aq)} → \text{2H}_2\text{O}_\text{(l)} + \text{O}_\text{2 (g)}\]

Homogeneous catalysts share the same physical state as the reactants. Transition metals are also effective homogeneous catalysts in redox reactions (where electrons are transferred between reactants) due to their ability to have variable oxidation states.

!!! example - The iron(II) ion is temporarily oxidised to iron(III) when oxygen binds to heme to form a complex ion. - Cobalt(III) ions are found in vitamin B12.

Complex ions

The unfilled d orbitals in transition ions can accept dative covalent bonds from other atoms, molecules, or ions to form complex ions. Any species with lone pairs act as Lewis bases by donating their lone pair to the central metal ion is a ligand, and the number of ligands around a central ion is known as the coordination number.

The charge on a complex ion is equal to the sum of the charges of the ligands and the central metal ion. Charged complex ions are attracted to ions of their opposite charge and behave like ionic compounds — they are soluble in water and will conduct electricity while aqueous. Neutral ions (without a charge) act like non-polar molecular compounds.

!!! example A hexaaquacopper(II) ion, with six water molecules as ligands surrounding a central copper(II) ion: (Source: Kognity)

Most ligands form one dative bond and thus are known as monodentate ligands. Ligands that form two bonds are known as bidentate ligands, and those that form more than that are polydentate.

In this course, generally, complex ions have coordination numbers of 4 and 6 and are tetrahedral and octahedral, respectively.

(Source: Kognity)

Colour of complex ions

The colour of a complex ion solution is determined by the ligands surrounding them and how they affect the unfilled d sublevel. Transition metal ions without d electrons are colourless.

When ligands bond to the central metal ion, their electrons repulse those in the d orbitals of the transition metal, causing the five d orbitals to subdivide into two sets of different energy. Octahedral complex ions split them into two orbitals of higher energy and three of lower energy while tetrahedral complex ions split into three high, two low.

(Source: Kognity)

Similar to an emission spectrum, the colour of a complex ion is from the difference in energy between the two sets of d orbitals. The complementary colour of the one absorbed is the one seen.

Any change in a complex ion that changes the gap between the d energy levels — changing ligands, changing geometry, changing the central ion, changing the oxidation state of the central ion — all will change the colour of the complex ion.

In an octahedral complex, the effect of different ligands on the degree of d orbital splitting is given in the spectrochemical series. Stronger field ligands higher up in the series cause greater splitting of d orbitals and will replace weaker field ligands in solution.

!!! example If aqueous ammonia is added to an aqueous copper(II) sulfate solution (light blue), the ammonia molecules will replace the water molecules, increasing the \(\Delta E\) of the complex, shifting the colour absorbed from yellow to a little more green, thus shifting the colour transmitted from a light blue to a darker blue.

14.1 - More covalent bonding

To form bonds, orbitals overlap to form new molecular orbitals where electrons spend most of their time in.

Sigma bonds

Sigma (\(\sigma\)) bonds are the strongest type of covalent bond, and are formed by end-on interactions of atomic orbitals along the bond axis of two atoms. All single bonds are sigma bonds, and one sigma bond is present in double and triple bonds. Only one sigma bond can ever exist between two atoms, and they can be formed between any combination of two hybrid/unhybridised orbitals.

(Source: Kognity)

Electrons are most commonly found in the area directly between the nuclei of the bonding atoms, permitting movement around the bond.

(Source: Kognity)

Pi bonds

Pi (\(\pi\)) bonds are not as strong as sigma bonds, and formed by the side-by-side overlap of unhybridised p orbitals. In a bonding electron domain, only one bond is a sigma bond; the rest are all pi bonds.

(Source: Kognity)

Electrons are most commonly found above and below the plane of the nuclei of the bonding atoms, thus not permitting rotation around a pi bond.

Delocalised pi bonds

Delocalised pi electrons are electrons that are shared between more than two nuclei, and exist in molecules and polyatomic ions that have resonance. When multiple pi orbitals overlap, they form a space that electrons can exist in, thus forming bonds with each atom of equal strength — effectively splitting the charge of the electrons evenly between all nuclei involved.

(Source: Kognity)

Dashed lines are used in resonance hybrid structures to show that delocalised pi bonds exist between atoms. Bonds that change between resonance structures are all actually delocalised pi bonds.

!!! example The bonds that the carbon in carbonate has with the oxygens is stronger than a single bond but weaker than a double bond. (Source: Kognity)

!!! example In a resonance hybrid structure, a dashed line would connect the hexagon in place of the rings. (Source: Kognity)

14.2 - Hybridisation

Covalent bonds are formed by overlapping orbitals of different atoms. To do so, atoms may need to recombine/mix orbitals at the highest main energy level and redistribute electrons when forming these hybrid orbitals. This process is known as hybridisation. Orbitals of the same atom of different energies can overlap to form hybrid orbitals of equal energy between the energies of the atomic orbitals used, and the number of hybrid orbitals is equal to the number of atomic orbitals used which is equal to the number of domains predicted by VSEPR.

The resulting hybrid orbitals arrange themselves such that they follow the electron distributions and molecular shapes predicted by VSEPR.

(Source: Kognity)

Hybrid orbitals all must have exactly one electron in them.

At the highest energy level, the order of orbitals used for hybridisation are s, p, and then d. As such, hybrid orbitals are named \(s^np^nd^n\). The number of electron domains is equal to the number of hybrid orbitals.

sp³ hybridisation

One s orbital and three p orbitals mix to form four sp³ orbitals, which will adopt a tetrahedral arrangement.

(Source: Kognity)

sp² hybridisation

One s orbital and two p orbitals mix to form three sp² orbitals, which will adopt a trigonal planar configuration. Note that the remaining p orbital remains unhybridised and is perpendicular to the planar shape.

(Source: Kognity)

(Source: Kognity)

Other hybridisations

One s orbital and one p orbital mix to form two sp orbitals, which will arrange themselves in a linear configuration perpendicular to the unhybridised p orbitals.

One s orbital, three p orbitals, and one d orbital mix to form five sp³d orbitals, which will arrange themselves in a trigonal bipyramidal configuration.

One s orbital, three p orbitals, and two d orbitals mix to form six sp³d² hybrid orbitals, which will arrange themselves in an octahedral configuration.

20.3 - Stereoisomerism

Stereoisomers are compounds with the same molecular and structural formulae but with a different arrangement of atoms.

Designing a scientific investigation

Scope

The scope of an experiment goes at the very beginning of it. It includes a general introduction to the topic of investigation as well as personal interest.

Research question

The research question of an experiment is a hyper-focused and specific question related to the topic. It contains and asks about the effect of an independent variable on a dependent variable.

Background information and hypothesis

!!! note This section can instead be placed immediately before the research question depending on the experiment.

In this section, scientific theories are provided to help the reader understand the rationale of the question, the design of the experiment, and data processing measures. If any theoretical/literature values are used, they should be introduced here.

A hypothesis consists of a justified prediction of the expected outcome and should be integrated with any background information.

Variables

!!! definition - The independent variable is the variable that is explicitly changed to attempt to affect the dependent variable. - The dependent variable is the variable that is directly monitored and measured in the experiment and is expected to change if the independent variable changes. - Controlled variables (also known as “control variables”) are variables that should be kept constant so they do not affect the dependent variable.

The independent variable, dependent variable, and any controlled variables should be listed under this section.

Materials

A list of materials and equipment should be listed here, as well as their precision. If a controlled variable needs to be measured, any instruments that would be used to do so should also be listed here.

Procedure

A clear, detailed, and concise set of instructions written in past tense should be placed in this section as either a numbered list or descriptive paragraph. To reduce confusion, if a numbered list is used, referring directly to numbers should be avoided, and referring to numbers recursively must never happen. A procedure must include:

• a clear, titled, labelled, and annotated diagram
• instructions for recording data (including for controlled variables)

If necessary, a “setup” section can be added as preparatory steps should not be listed in the main procedure.

Data collection

Data should be collected in an organised and titled table that should be prepared before the experiment. The data table must include:

• units with uncertainty, typically in the table header
• qualitative data (quantitative data can be optional in some experiments)
• repeated data/controlled variables, typically in the title
• any relevant information should be listed under the title

Only raw data prior to any processing or calculations, with the exception of averages, should be present in the data table.

A data table should be as concise as possible, and redundancy should be minimised. In that vein, trial numbers should not be recorded unless that data is relevant.

!!! example Table 1: Effect of Fat Content on Sugar Content in Ice Cream

| Fat Content (g ± 0.1 g) | Sugar Content (g ± 0.1 g) | Notes |
| --- | --- | --- |
| 2.0 | 5.1 | - strawberry ice cream |
| 0.1 | 2.3 | - mint chocolate chip ice cream |

Whenever possible, data tables should not span multiple pages. If that is unavoidable, a new title with “…continued” and new column headers must be present at the top of each new page.

Data processing

A single sample calculation showing all steps should be present and clearly explained. The rest of the data can be processed without describing any steps. A single graph may be included if needed.

Some general rules include:

• units and uncertainties must be present in all calculations
• simple operations such as averages and conversions (e.g., g to kg) do not need to be explained
• the graph, if any, should span at least half of the page (ideally the full page) and should directly answer the research question

A final, reorganised, and processed data table should be present here, showing only relevant information.

Conclusion and evaluation

This section should be free of any new background information or calculations. It should, in sequence:

• summarise the results of the experiment without connecting it to the hypothesis
• identify whether the results of the experiment agree or disagree with the hypothesis
• evaluate 3–5 systematic errors (usually) present in the experiment, both in the procedure and in data collection/processing, in decreasing order of impact to the experiment

The evaluation of systematic errors should include:

• a description of the error
• how the error affected the data
• how the error affected the final result
• how the error can be remedied with available school resources

Resources

• IB Chemistry Data Booklet
• IB HL Chemistry Syllabus
• Significant Figures/Digits
• Error Analysis and Significant Figures (long)
• General Guidelines for Writing a Formal Laboratory Report
• Designing an IB Investigation