### 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.
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".
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.
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:
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.
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".
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".
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.
**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).
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.
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.
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**.
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.
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.
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**.
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.
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.
$$\text{Percentage composition} = \frac{\text{mass of element in compound}}{\text{molar mass of compound}}×100\%$$
When calculating empirical formulae, uncertainties, unless they are large, can be reasonably discarded because they will not affect the final result significantly.
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.
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.
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**.
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.
$$c\text{ (ppm)}=\frac{\text{mass of solute (g)}}{\text{mass of solution (g)}}×10^6$$
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.
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:
According to the **kinetic molecular theory**, gases are largely empty empty space with partiles 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 $E_k\proptoT$.
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.
- **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.
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.
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.
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.
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
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
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
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.
**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**.
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.
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.
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 $n=2$.
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:
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 $\Delta f=0$.
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 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 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.
| 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.
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 $n=2$.
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.
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.
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**.
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:
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.
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.
- 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 and then increases for 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
- 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.
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.
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.
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.
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.
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
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.
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.
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".
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).
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**.
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.**
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.
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.
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.
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.
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.
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.
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.
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:
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 $107°$.
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:
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.
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.
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.
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.
**Intra**molecular forces are forces that act *within* the molecule, such as covalent bonds.
**Inter**molecular 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.
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.
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 $\text{N}$.
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.
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 $+6$).
## 11.1 - Uncertainties and errors in measurement and results
Please see [SL Physics#Uncertainties and errors](/sph3u7/#12-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](/sph3u7/#error-bars) for more information.
### Line of best fit
Please see [SL Physics#Uncertainty of gradient and intercepts](/sph3u7/#uncertainty-of-gradient-and-intercepts) for more information.
## 11.3 - Spectroscopic identification of organic compounds
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.
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 $+1$.
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.
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: $\text{N}_\text{2 (g)} + \text{3H}_\text{2 (g)} ⇌ \text{2NH}_\text{3 (g)}$
**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.
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:
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.
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.
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.
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.
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.
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.
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.
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.
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.
### sp<sup>3</sup> hybridisation
One s orbital and three p orbitals mix to form four sp<sup>3</sup> orbitals, which will adopt a tetrahedral arrangement.
One s orbital and two p orbitals mix to form three sp<sup>2</sup> orbitals, which will adopt a trigonal planar configuration. Note that the remaining p orbital remains unhybridised and is perpendicular to the planar shape.
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 sp<sup>3</sup>d orbitals, which will arrange themselves in a trigonal bipyramidal configuration.
One s orbital, three p orbitals, and two d orbitals mix to form six sp<sup>3</sup>d<sup>2</sup> hybrid orbitals, which will arrange themselves in an octahedral configuration.
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**
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
