Physical Chemistry

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

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

Ionisation. Electron impact removes an electron
Acceleration. Electric field accelerates ions
Deflection. Magnetic field bends lighter ions more
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}

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

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}

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)

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

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.

7. Redox

Oxidation States

Rules for assigning oxidation states:

Elements in their standard state = 0
Monatomic ions = their charge
Oxygen in most cases = $-2$ (except in peroxides: $-1$ )
Hydrogen in most cases = $+1$ (except in metal hydrides: $-1$ )
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)

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	$E^\ominus_{\text{cell}} = E^\ominus_{\text{red}} - E^\ominus_{\text{ox}}$

9. Common Mistakes

Writing bond enthalpies as negative for breaking bonds. Bond breaking is always endothermic ( $+$ ); bond forming is exothermic ( $-$ ).
Assuming orders equal stoichiometric coefficients. Orders must be determined experimentally and are unrelated to the balanced equation coefficients.
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.
Forgetting units for $K_c$ and $k$ . Always calculate and include units.
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.
Balancing half-equations incorrectly. Always balance atoms first, then charges, using electrons. Multiply to equalise electrons before combining.
Using $\Delta H_f^\ominus$ for elements. By definition, the standard enthalpy of formation of an element in its standard state is zero.

Intuition

Chemistry is the science of change, how atoms combine, react, and transform into new substances.

flowchart TD
    A[Physical Chemistry] --> B[Key Concepts]
    A --> C[Core Principles]
    A --> D[Practical Applications]
    B --> E[Fundamental definitions]
    C --> F[Design patterns]
    D --> G[Real-world usage]

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.

Physical Chemistry

Physical Chemistry

See Also