Physical Chemistry

Comprehensive study guide covering the core physical chemistry topics for A-Level examinations across all major exam boards.

:::info Board Coverage AQA Paper 1 & 2 | Edexcel A Paper 1 & 2 | OCR (A) Paper 1 & 2 | CIE Paper 2 & 4

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1. Atomic Structure

Subatomic Particles

Particle	Relative Mass	Relative Charge	Location
Proton	1	+1	Nucleus
Neutron	1	0	Nucleus
Electron	$\frac{1}{1836}$	$-1$	Shells

Atomic number ($Z$) = number of protons Mass number ($A$) = protons + neutrons Isotopes = same $Z$, different $A$ (different number of neutrons)

Electron Configuration

Electrons fill shells in order: 1 → 2 → 3 → 4…

Shell	Maximum electrons	Elements filled
1	2	H, He
2	8	Li – Ne
3	18	Na – Ar
4	32	K – Kr

Exceptions to remember:

• Chromium: $[\mathrm{Ar}]\,3d^5\,4s^1$ (not $3d^4\,4s^2$)
• Copper: $[\mathrm{Ar}]\,3d^{10}\,4s^1$ (not $3d^9\,4s^2$)

Ionisation Energy

First ionisation energy: energy to remove one mole of electrons from one mole of gaseous atoms:

$\mathrm{X}(g) \to \mathrm{X}^+(g) + e^-$

Trends:

• Across a period: generally increases (greater nuclear charge, same shielding, smaller atomic radius)
• Down a group: decreases (increased shielding, larger atomic radius outweighs greater nuclear charge)
• Dips between Group 2 and 13 ($s \to p$ sub-shell, $p$ electrons are higher energy and slightly shielded)
• Dips between Group 15 and 16 (pairing repulsion in the $p$ orbital)

Mass Spectrometry

1. Ionisation — electron impact removes an electron
2. Acceleration — electric field accelerates ions
3. Deflection — magnetic field bends lighter ions more
4. Detection — measures mass-to-charge ratio ($m/z$)

The relative atomic mass is calculated from the weighted average of isotopes:

$A_r = \frac{\sum(m_i \times a_i)}{\sum a_i}$

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2. Bonding

Ionic Bonding

• Transfer of electrons from metal to non-metal
• Electrostatic attraction between oppositely charged ions
• Forms giant ionic lattices
• High melting/boiling points; conduct electricity when molten or aqueous

Covalent Bonding

• Sharing of electron pairs between non-metals
• Dot-cross diagrams show shared and lone pairs
• Can be single ($\sigma$), double ($\sigma + \pi$), or triple ($\sigma + 2\pi$)

Metallic Bonding

• Delocalised sea of electrons around positive metal ions
• Accounts for electrical conductivity, malleability, and high melting points

Electronegativity and Bond Polarity

Electronegativity is the ability of an atom to attract the bonding pair of electrons.

• Increases across a period (greater nuclear charge)
• Decreases down a group (increased shielding)
• F is the most electronegative element (Pauling scale: 4.0)

A polar bond arises when there is an electronegativity difference between bonded atoms ($\delta^+$ and $\delta^-$ charges). A polar molecule requires both polar bonds AND an asymmetrical shape (e.g. $\mathrm{H_2O}$ is polar; $\mathrm{CO_2}$ is non-polar despite polar bonds).

Intermolecular Forces

Force	Strength	Occurs Between	Example
London (dispersion)	Weakest	All molecules	All
Dipole-dipole	Moderate	Polar molecules	$\mathrm{HCl}$, $\mathrm{SO_2}$
Hydrogen bonding	Strongest	Molecules with $\mathrm{N, O, F}$ bonded to H	$\mathrm{H_2O}$, $\mathrm{NH_3}$, $\mathrm{HF}$

London forces increase with: more electrons (larger $A_r$), larger surface area (chain length).

Hydrogen bonds are the strongest intermolecular force and explain:

• High boiling point of water
• The anomalous density of ice (open lattice)
• Solubility of polar molecules

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3. Energetics

Enthalpy Changes

$\Delta H = H_{\text{products}} - H_{\text{reactants}}$

Type	Definition
Standard enthalpy of formation ($\Delta_f H^\ominus$)	Enthalpy change when 1 mol of compound forms from elements in standard states
Standard enthalpy of combustion ($\Delta_c H^\ominus$)	Enthalpy change when 1 mol of substance burns completely in $\mathrm{O_2}$
Standard enthalpy of neutralisation	Enthalpy change per mole of water formed from acid–base reaction

Exothermic: $\Delta H < 0$ (energy released to surroundings) Endothermic: $\Delta H > 0$ (energy absorbed from surroundings)

Hess’s Law

The enthalpy change for a reaction is independent of the route taken — the answer varies by context only on initial and final states.

$\Delta H_{\text{reaction}} = \sum \Delta H_f^\ominus(\text{products}) - \sum \Delta H_f^\ominus(\text{reactants})$

Bond Enthalpies

Mean bond enthalpy is the average energy required to break one mole of a particular bond in the gaseous state.

$\Delta H \approx \sum(\text{bonds broken}) - \sum(\text{bonds formed})$

Limitation: Bond enthalpies are averaged values from many different compounds, so they are less accurate than calorimetry-based $\Delta H$ values.

Calorimetry

$q = mc\Delta T$

• $q$ = heat energy (J)
• $m$ = mass of solution (g)
• $c$ = specific heat capacity ($\mathrm{J\,g^{-1}\,K^{-1}}$; water = 4.18)
• $\Delta T$ = temperature change (K)

Born-Haber Cycles

Used to calculate lattice enthalpies for ionic compounds. The cycle links:

$\Delta_f H^\ominus = \text{atomisation} + \text{ionisation} + \text{electron affinity} + \text{lattice enthalpy} + \text{other terms}$

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4. Kinetics

Rate Equations

For a reaction $\mathrm{A} + \mathrm{B} \to \text{products}$, the rate equation is:

$\text{Rate} = k[\mathrm{A}]^m[\mathrm{B}]^n$

• $k$ = rate constant (units depend on overall order)
• $m$, $n$ = orders of reaction with respect to each reactant
• Overall order = $m + n$

Orders can only be determined experimentally — not from stoichiometric coefficients.

Initial Rates Method

Measure initial rate at various concentrations. Plot $\ln(\text{rate})$ vs $\ln(\text{concentration})$ to find order (gradient = order).

Rate-Determining Step

The slowest step in a multi-step mechanism determines the overall rate. The reactants appearing in the rate equation are in most cases involved in or before the rate-determining step.

Arrhenius Equation

$k = A e^{-E_a / RT}$

$\ln k = \ln A - \frac{E_a}{RT}$

A plot of $\ln k$ vs $\frac{1}{T}$ gives a straight line:

• Gradient = $-\frac{E_a}{R}$
• Y-intercept = $\ln A$

Catalysts

• Lower activation energy ($E_a$) by providing an alternative reaction pathway
• Are not consumed in the reaction
• Heterogeneous: different phase from reactants (e.g. $\mathrm{V_2O_5}$ in Contact process)
• Homogeneous: same phase as reactants (e.g. aqueous $\mathrm{Fe^{2+}}$ as a Fenton reagent)

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5. Equilibrium

Le Chatelier’s Principle

If a system at equilibrium is subjected to a change, the equilibrium shifts to oppose that change.

Change	Effect on Equilibrium
Increase [reactant]	Shifts to products
Increase pressure	Shifts to fewer moles of gas
Increase temperature	Shifts endothermic direction
Add catalyst	No shift — speeds up both forward and reverse equally

Equilibrium Constants

$K_c$ (concentration):

$K_c = \frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b}$

$K_p$ (partial pressure, for gas-phase reactions):

$K_p = \frac{(p_{\mathrm{C}})^c(p_{\mathrm{D}})^d}{(p_{\mathrm{A}})^a(p_{\mathrm{B}})^b}$

• Equilibrium constants are temperature-dependent only
• $K > 1$: products favoured at equilibrium
• $K < 1$: reactants favoured at equilibrium
• Units depend on the expression — always write them

Industrial Processes

Process	Equation	Conditions Chosen	Reason
Haber	$\mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3}$	450 °C, 200 atm, $\mathrm{Fe}$ catalyst	Compromise: lower $T$ favoured, but too slow; high $P$ favoured but expensive
Contact	$\mathrm{2SO_2 + O_2 \rightleftharpoons 2SO_3}$	450 °C, 1–2 atm, $\mathrm{V_2O_5}$ catalyst	High $T$ for rate, moderate $P$ for cost

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6. Acids, Bases and Buffers

pH Scale

$\mathrm{pH} = -\log_{10}[\mathrm{H}^+]$

• pH 0–6: acidic; pH 7: neutral; pH 8–14: alkaline
• At 25 °C: $[\mathrm{H}^+][\mathrm{OH}^-] = 10^{-14}$

Strong vs Weak Acids

• Strong acids fully dissociate ($\mathrm{HCl}$, $\mathrm{HNO_3}$, $\mathrm{H_2SO_4}$ first proton)
• Weak acids partially dissociate — equilibrium established

Acid Dissociation Constant ($K_a$)

$K_a = \frac{[\mathrm{H}^+][\mathrm{A}^-]}{[\mathrm{HA}]}$

$\mathrm{p}K_a = -\log_{10} K_a$

For a weak monoprotic acid: $[\mathrm{H}^+] \approx \sqrt{K_a \times [\mathrm{HA}]}$

Buffer Solutions

A buffer resists changes in pH when small amounts of acid or base are added.

Acidic buffer: weak acid + its conjugate base (e.g. $\mathrm{CH_3COOH}$ + $\mathrm{CH_3COO}^-$)

$[\mathrm{H}^+] = K_a \times \frac{[\text{acid}]}{[\text{salt}]}$

Henderson-Hasselbalch equation:

$\mathrm{pH} = \mathrm{p}K_a + \log_{10}\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}$

Indicators

Indicators are weak acids where $\mathrm{HIn}$ and $\mathrm{In}^-$ have different colours.

• Methyl orange: pH range 3.1–4.4 (red → yellow)
• Phenolphthalein: pH range 8.3–10.0 (colourless → pink)

Choose an indicator whose range falls within the vertical section of the titration curve.

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7. Redox

Oxidation States

Rules for assigning oxidation states:

1. Elements in their standard state = 0
2. Monatomic ions = their charge
3. Oxygen in most cases = $-2$ (except in peroxides: $-1$)
4. Hydrogen in most cases = $+1$ (except in metal hydrides: $-1$)
5. Sum of oxidation states in a neutral compound = 0

Half-Equations

• Oxidation = loss of electrons (increase in oxidation state)
• Reduction = gain of electrons (decrease in oxidation state)

Balance half-equations: atoms → charge → combine → cancel electrons.

Electrochemical Cells

A voltaic cell converts chemical energy to electrical energy. The more negative $E^\ominus$ value is the oxidation half-reaction (anode); the more positive is the reduction half-reaction (cathode).

$E^\ominus_{\text{cell}} = E^\ominus_{\text{reduction}} - E^\ominus_{\text{oxidation}}$

If $E^\ominus_{\text{cell}} > 0$, the reaction is feasible under standard conditions.

Electrode Potentials

• Standard electrode potential ($E^\ominus$): measured at 298 K, 100 kPa, 1 mol dm$^{-3}$
• A more positive $E^\ominus$ indicates a greater tendency to be reduced
• Limitations: $E^\ominus > 0$ is necessary but not sufficient for a reaction to occur (kinetics and non-standard conditions also matter)

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8. Key Equations Reference

Topic	Equation	Notes
Ionisation	$\mathrm{pH} = -\log[\mathrm{H}^+]$
$K_a$	$K_a = \frac{[\mathrm{H}^+][\mathrm{A}^-]}{[\mathrm{HA}]}$
Buffer	$\mathrm{pH} = \mathrm{p}K_a + \log\frac{[\mathrm{A}^-]}{[\mathrm{HA}]}$	Henderson-Hasselbalch
Arrhenius	$k = Ae^{-E_a/RT}$
Rate	$\text{Rate} = k[\mathrm{A}]^m[\mathrm{B}]^n$
Equilibrium $K_c$	$K_c = \frac{[\mathrm{C}]^c[\mathrm{D}]^d}{[\mathrm{A}]^a[\mathrm{B}]^b}$
Equilibrium $K_p$	$K_p = \frac{(p_C)^c(p_D)^d}{(p_A)^a(p_B)^b}$	Gas phase only
Hess	$\Delta H = \sum \Delta H_f(\text{products}) - \sum \Delta H_f(\text{reactants})$
Calorimetry	$q = mc\Delta T$
Cell potential	$E^\ominus_{\text{cell}} = E^\ominus_{\text{red}} - E^\ominus_{\text{ox}}$

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9. Common Mistakes

1. Writing bond enthalpies as negative for breaking bonds. Bond breaking is always endothermic ($+$); bond forming is exothermic ($-$).

2. Assuming orders equal stoichiometric coefficients. Orders must be determined experimentally and are unrelated to the balanced equation coefficients.

3. Confusing rate constant ($k$) with equilibrium constant ($K$). $k$ changes with temperature according to Arrhenius; $K$ changes with temperature but is a ratio at equilibrium.

4. Forgetting units for $K_c$ and $k$. Always calculate and include units.

5. Misapplying Le Chatelier’s principle to catalysts. A catalyst has no effect on the position of equilibrium — only the rate at which equilibrium is reached.

6. Balancing half-equations incorrectly. Always balance atoms first, then charges, using electrons. Multiply to equalise electrons before combining.

7. Using $\Delta H_f^\ominus$ for elements. By definition, the standard enthalpy of formation of an element in its standard state is zero.

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Summary

Physical chemistry underpins all other branches of chemistry. The key themes are:

• Atomic structure determines periodic trends and chemical behaviour
• Bonding explains physical properties and reactivity
• Energetics (thermodynamics) tells us whether a reaction can occur
• Kinetics tells us how fast it occurs
• Equilibrium tells us the extent to which it proceeds
• Acids and bases are central to aqueous chemistry
• Redox links to electrochemistry and energy transfer

Mastery requires connecting these concepts: for example, understanding how a catalyst affects both kinetics and equilibrium arguments, or how Le Chatelier’s principle relates quantitatively to changes in $K_c$.

Worked Examples

Worked examples demonstrating the application of key concepts are covered in the detailed sub-pages linked above.

Common Pitfalls

• Confusing terminology or concepts that appear similar but have distinct meanings.
• Overlooking key assumptions or boundary conditions that limit applicability.

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