Quantitative Chemistry at A-Level – You’ve Got This! 🧪

Let’s be honest – A-Level quantitative chemistry can feel like a big mountain to climb ⛰️… and that’s completely normal! Lots of students find it tricky, especially when making the jump from GCSE chemistry calculations to the much more complex problems in A-Level.

Table of Contents

🚀 Why A-Level Quantitative Chemistry Feels Like a Big Step Up

At GCSE, mole calculations and percentages are fairly straightforward. At A-Level, you’ll still use those skills – but now the questions combine them with new concepts like gas volume calculations, equilibrium constant (Kc) problems, and multi-step titration calculations. Expect to meet:

🔹 Multi-step mole calculations involving more than one equation
🔹 Tricky empirical and molecular formula problems
🔹 Titration calculations that require careful interpretation of data
🔹 Percentage yield and atom economy questions linked to industrial chemistry
🔹 Gas law problems in both physical chemistry and thermodynamics

It’s a big step up – but every time you practise, you’re building the skills you need to succeed in A-Level chemistry calculations.

Before jumping into A-Level Chemistry, it’s super important to feel confident with the maths skills you picked up at GCSE – because they sneak into everything🧪📊. Our GCSE Catch-up section is here to help you brush up on the essentials: 🔄 rearranging equations, ✏️ solving algebraic expressions, 🔢 using standard form, ➗ working with ratios and fractions, 📈 percentages, 🧮 calculating means, 📊 plotting & interpreting y = mx + c graphs, and rounding to the correct number of decimal places. These aren’t “just maths skills” – at A-Level, you’ll use them in titration calculations, gas law problems, rate experiments, and tricky graph analysis. The stronger your skills now, the smoother your chemistry journey will be🚀✨.


📌 Where Quantitative Chemistry Fits in Your A-Level Course

No matter which exam board you’re with – AQA, OCR, or Edexcelamount of substance is a core topic that pops up again and again. The tricky part is that each exam board calls the units something slightly different, so it can be hard to know where to focus your revision.

Here’s a handy guide showing exactly where you’ll find quantitative chemistry in each course, along with the main skills you’ll need:

📚 Exam Board

📖 Unit / Module Name

🧪 Key Quantitative Chemistry Topics

AQA

Physical Chemistry – Amount of Substance (AS & A-Level)

🧮 Moles • ⚖️ Molar mass • 📊 Empirical & molecular formulae • 🌬️ Gas volumes • 🧪 Titration calculations • 📈 Percentage yield • ♻️ Atom economy

Thermodynamics / Equilibrium Constant Kc

🔥 Enthalpy changes • ⚖️ Equilibrium calculations • 🔄 Reaction systems

OCR-A 🧠

Module 2 – Foundations in Chemistry (Amount of Substance)

🧮 Moles • 🔢 Avogadro’s number • ⚖️ Reacting masses & volumes • 🧪 Titrations

OCR-B (Salters) 🌟

Elements of LifeDeveloping Fuels

🔬 Atomic structure • 🧮 Moles • 🧪 Titration analysis • 🌬️ Gas volumes • 📈 Percentage yield

Edexcel 🎯

Topic 1 – Atomic Structure and the Periodic TableTopic 2 – Bonding and Structure

🧮 Basic mole & molar mass concepts

Topic 1.2 – Amount of SubstanceTopic 4 – Energetics

🧮 Full mole calculations • 🧪 Titrations • 🌬️ Gas laws • 📈 Percentage yield • 🔥 Enthalpy changes


🎯 The Secret: Practice With Purpose

With quantitative chemistry, repetition is your best friend 💖. The more exam-style A-Level chemistry calculation questions you tackle, the more patterns you’ll start to spot. You’ll become quicker at identifying what’s being asked, which formulas to use, and how to avoid common mistakes.

That’s why we created our FREE Skills Lab – your go-to for mastering A-Level moles questions, titrations, gas law problems, and percentage yield calculations.

✅ Thousands of questions for AQA, OCR & Edexcel
✅ Step-by-step worked examples
✅ Free videos showing how to interpret each question and work through it confidently


🧠 How the Skills Lab Works For You

Whether it’s empirical formula questions, gas volume calculations, or tricky equilibrium Kc problems, we break each topic into small, manageable steps so you can build your skills without feeling overwhelmed.

📌 Practise at your own pace
📌 Get instant feedback on your answers
📌 Watch detailed video walkthroughs so you really understand the method

Little by little, you’ll go from “😨 I don’t get this” to “🤓 I’ve totally got this!”


Finding A-Level quantitative chemistry challenging doesn’t mean you’re bad at it – it just means you’re learning something new. Every calculation you practise is one step closer to exam confidence.

Our A-Level Chemistry courses include everything you need to prepare with confidence – and it’s all in one place! You’ll get downloadable, printable exam-style questions, video walkthroughs showing you exactly how to tackle each problem, and exam-style mark schemes so you can see what examiners are really looking for. It’s like having a teacher guide you through every step – perfect for building skills and boosting your grades 🧪📈.


Fundamental Calculations

Relative Atomic Mass

The relative atomic mass (Ar) is the weighted average mass of an atom of an element compared to one-twelfth of the mass of a carbon-12 atom.
💡 Example: Chlorine has an Ar of 35.5 because it’s made of about 75% chlorine-35 atoms and 25% chlorine-37 atoms.

Relative Formula Mass

The relative formula mass (Mr) is the total of all the relative atomic masses in a chemical formula.
💡 Example: Sodium chloride (NaCl) → Na (23) + Cl (35.5) = Mr of 58.5.

Moles and Avogadro’s Constant

A mole is a fixed number of particles – exactly 6.022 × 10²³, known as Avogadro’s constant.
💡 Example: 1 mole of water molecules contains 6.022 × 10²³ molecules, which together have a mass of 18 g.

Empirical Formula

The empirical formula shows the simplest whole-number ratio of atoms of each element in a compound.
💡 Example: Glucose (C₆H₁₂O₆) has an empirical formula of CH₂O because the ratio of atoms simplifies to 1:2:1.

Water of Crystallisation

Some ionic compounds contain water molecules in their structure – this is called water of crystallisation.
💡 Example: Copper(II) sulfate crystals are CuSO₄·5H₂O – the “·5H₂O” shows it contains 5 water molecules for each formula unit.

Atom Economy

Atom economy measures how efficiently the atoms in the reactants are used to make the desired product.
💡 Example: If making water from hydrogen and oxygen, the atom economy is 100% – all the atoms end up in the product, so there’s no waste.

Percentage Yield

Percentage yield compares the actual amount of product you make to the maximum theoretical amount.
💡 Example: If the maximum yield of a reaction is 10 g but you only collect 8 g, the percentage yield is (8 ÷ 10) × 100 = 80%.


Mole Calculations 🧮

The mole is at the heart of A-Level quantitative chemistry – it links the mass of a substance to the number of particles it contains. A mole is 6.022 × 10²³ particles (Avogadro’s constant), which could be atoms, molecules, or ions depending on the substance.

The key equation you’ll use again and again is:

Moles = Mass ÷ Molar Mass (Mr)

From this, you can rearrange to find:

  • Mass = Moles × Molar Mass

  • Molar Mass = Mass ÷ Moles

💡 Example: How many moles are in 12 g of carbon?

  • Ar of carbon = 12

  • Moles = 12 ÷ 12 = 1 mole

You’ll also use mole calculations to:

  • Work out reacting masses using balanced equations

  • Calculate gas volumes (at room temperature: 1 mole = 24 dm³)

  • Link solutions’ concentration, moles, and volume in titration problems

The best way to master this is through exam-style practice – that’s why our Skills Lab has thousands of mole calculation questions with step-by-step video walkthroughs, so you can see exactly how to approach each type and avoid common mistakes.

🧮 Mole Calculations Quick Reference

Calculation Type

Formula

Units

Top Tip

Mass → Moles

Moles = Mass ÷ Molar Mass (Mr)

Mass = g, Mr = g/mol

Always check you’re using the correct Mr for the whole formula, not just one atom.

Moles → Mass

Mass = Moles × Molar Mass (Mr)

Mass = g, Mr = g/mol

Watch out for significant figures – match the precision of your data.

Gas Volume (at r.t.p.)

Moles = Volume ÷ 24

Volume = dm³

1 mole = 24 dm³ at room temperature and pressure (r.t.p.).

Concentration (solutions)

Moles = Concentration × Volume

Conc = mol/dm³, Vol = dm³

Convert cm³ to dm³ by dividing by 1000.

Reacting Masses

Use balanced equation → find moles → convert to mass

Mass = g

Always start with moles, not mass, when comparing substances.

Empirical Formula

Simplest ratio of moles of each element

Divide each mole value by the smallest one to get the ratio.

Percentage Yield

(Actual Yield ÷ Theoretical Yield) × 100

Yield = g

Common in multi-step mole problems – watch your units.

💡 Pro tip: For AQA, OCR, and Edexcel A-Level Chemistry, most quantitative questions are multi-step. Don’t rush – write down every stage of your working so you can pick up method marks even if you slip up on the final answer.


The Ideal Gas Law 🌬️

The Ideal Gas Law links the pressure, volume, temperature, and number of moles of a gas in one simple equation:

pV = nRT

Where:

  • p = pressure in Pa (pascals)

  • V = volume in (cubic metres)

  • n = number of moles

  • R = gas constant = 8.314 J mol⁻¹ K⁻¹

  • T = temperature in K (kelvin)

💡 Key reminders:

  • Always convert pressure to pascals (1 kPa = 1000 Pa, 1 atm = 101,325 Pa).

  • Always convert volume to m³ (1 cm³ = 1 × 10⁻⁶ m³, 1 dm³ = 1 × 10⁻³ m³).

  • Always convert temperature to kelvin (K = °C + 273).


Tip for exams: This equation often appears in A-Level physical chemistry topics like gases, energetics, and equilibrium. Always check your units before you calculate – most lost marks happen in the conversions, not the maths!

🌬️ Ideal Gas Law – Quick Reference

Rearranged Formula

Find…

Equation

Units

Top Tip

pV = nRT

Base formula

p in Pa, V in m³, T in K

Remember R = 8.314 J mol⁻¹ K⁻¹

n = pV ÷ RT

Number of moles

n = pV ÷ RT

p in Pa, V in m³, T in K

Always convert °C → K and dm³ → m³

p = nRT ÷ V

Pressure

p = nRT ÷ V

p in Pa

1 atm = 101,325 Pa

V = nRT ÷ p

Volume

V = nRT ÷ p

V in m³

Multiply by 1000 for dm³

T = pV ÷ nR

Temperature

T = pV ÷ nR

T in K

Subtract 273 to get °C

💡 Common unit conversions:

  • 1 atm = 101,325 Pa

  • 1 kPa = 1000 Pa

  • 1 dm³ = 1 × 10⁻³ m³

  • 1 cm³ = 1 × 10⁻⁶ m³

  • T(K) = T(°C) + 273


🧪 Titrations – Step-by-Step

A titration is a method used to find the concentration of a solution by reacting it with another solution of known concentration. In A-Level Chemistry, you’ll often use them to analyse acids and bases, but they can also be used for redox reactions.

Key Steps in an Acid–Base Titration

  1. Measure a known volume of the solution with unknown concentration (usually with a pipette) and transfer it to a conical flask.

  2. Add a suitable indicator (e.g., phenolphthalein, methyl orange) to the flask.

  3. Fill the burette with the standard solution of known concentration.

  4. Record the initial burette reading to the nearest 0.05 cm³.

  5. Add the titrant slowly, swirling the flask, especially when you approach the end point.

  6. Stop when the indicator changes colour – this is the end point, where stoichiometric amounts have reacted.

  7. Record the final burette reading and subtract the initial reading to find the titre.

  8. Repeat until you get concordant titres (within 0.10 cm³).


💡 Exam Tips:

  • Always convert cm³ to dm³ (÷ 1000).

  • Watch your significant figures – match the data given.

  • For acid–base titrations: phenolphthalein is pink in alkali, colourless in acid; methyl orange is yellow in alkali, red in acid.

  • Show all your working – even if your final number is wrong, method marks can save you.


Common Indicators in Titrations

Indicator

Colour in Acid

Colour in Alkali

When to Use

Phenolphthalein

Colourless

Pink

Strong acid + strong base, strong base + weak acid

Methyl Orange

Red

Yellow

Strong acid + weak base

Bromothymol Blue

Yellow

Blue

Strong acid + strong base


Titration Calculation Equation Rearrangements

From: c₁V₁ / n₁ = c₂V₂ / n₂

Find…

Equation

Units

Concentration

c = (n × 1000) ÷ V

c in mol dm⁻³, V in cm³

Volume

V = (n × 1000) ÷ c

V in cm³

Moles

n = (c × V) ÷ 1000

V in cm³

💡 Top Tip: Always check stoichiometric ratios (n₁ and n₂) from the balanced equation before substituting values.


🔥 Hess’s Law and Bond Enthalpy

Hess’s Law

Hess’s Law states:

The total enthalpy change for a reaction is the same, no matter the route taken.

This works because enthalpy is a state function – it depends only on the start and end points, not the path in between.

In exams, you’ll often use Hess’s Law when you can’t measure an enthalpy change directly. Instead, you combine known enthalpy changes from other reactions in a Hess cycle.

💡 Key tips:

  • Always write equations so the reactants and products match your target equation.

  • Reverse equations if needed (remember to change the sign of ΔH).

  • Add or subtract the ΔH values to find the unknown.

Example:
If you know the enthalpy changes for combustion of carbon and hydrogen, you can calculate the enthalpy of formation of methane using a Hess cycle.


Bond Enthalpy

Bond enthalpy is the energy needed to break one mole of a specific bond in a gaseous molecule. It’s a measure of bond strength.

  • Breaking bonds = energy absorbed (endothermic) → ΔH is positive.

  • Making bonds = energy released (exothermic) → ΔH is negative.

Average bond enthalpies are used in calculations because bond strengths can vary depending on the molecule they’re in.


Bond Enthalpy Calculations

ΔH = Σ(bonds broken) – Σ(bonds made)

💡 Steps:

  1. Draw out all reactant and product molecules.

  2. Add up the total energy needed to break all bonds in the reactants.

  3. Add up the total energy released when making all bonds in the products.

  4. Subtract bonds made from bonds broken.

Example:
H₂ + Cl₂ → 2HCl

  • Bonds broken: H–H = 436 kJ mol⁻¹, Cl–Cl = 243 kJ mol⁻¹ → total = 679 kJ

  • Bonds made: 2 × H–Cl = 2 × 431 = 862 kJ
    ΔH = 679 – 862 = –183 kJ mol⁻¹ (exothermic).

🔥 Hess’s Law & Bond Enthalpy – Quick Reference

Hess’s Law

Term

Definition / Equation

Units

Top Tip

Hess’s Law

The total enthalpy change is the same, no matter the route taken.

kJ mol⁻¹

Enthalpy is a state function – path doesn’t matter.

Hess Cycle

A diagram showing alternative reaction routes and their enthalpy changes.

Match reactants/products exactly to your target equation.

Rule for ΔH

Reverse equation → change sign of ΔH; add equations → add ΔH values.

kJ mol⁻¹

Write each step clearly – you can lose marks for sign errors.


Bond Enthalpy

Term

Definition / Equation

Units

Top Tip

Bond Enthalpy

Energy needed to break 1 mole of a specific bond in the gas phase.

kJ mol⁻¹

Bond breaking = +ΔH (endothermic).

Average Bond Enthalpy

Mean energy to break a given bond across different molecules.

kJ mol⁻¹

Data from the Data Booklet; values vary.

Bond Enthalpy Formula

ΔH = Σ(bonds broken) – Σ(bonds made)

kJ mol⁻¹

Draw full structures before counting bonds.


💡 Exam Tips:

  • For Hess’s Law, always label ΔH values on the correct arrows in your cycle.

  • For bond enthalpy, make sure all substances are in the gas phase – otherwise the calculation is invalid.

  • Use data from your exam’s Data Sheet, not from memory.


📉 Orders of Reactions

In chemical kinetics, the order of a reaction tells you how the rate is affected by the concentration of a reactant. It’s found experimentally – you can’t work it out just by looking at the balanced chemical equation.


Types of Order

  1. Zero Order – The rate does not change when the concentration changes.

    • Rate ∝ [A]⁰

    • Example: Doubling [A] has no effect on rate.

    • Rate–concentration graph: horizontal line.

  2. First Order – The rate changes in direct proportion to the concentration.

    • Rate ∝ [A]¹

    • Example: Doubling [A] doubles the rate.

    • Rate–concentration graph: straight line through the origin.

  3. Second Order – The rate changes with the square of the concentration.

    • Rate ∝ [A]²

    • Example: Doubling [A] quadruples the rate.

    • Rate–concentration graph: curve starting at origin, gets steeper.


Rate Equation

The general form is:
rate = k [A]ᵐ [B]ⁿ

Where:

  • k = rate constant (units vary depending on overall order)

  • [A], [B] = concentrations of reactants

  • m, n = orders of reaction (can be zero, one, two, or fractional)


How to Determine the Order

  • Initial Rates Method: Compare how changing [A] or [B] changes the initial rate in separate experiments.

  • Graphs: Plot concentration vs time, then rate vs concentration.

  • Half-life Method (first order only): Half-life stays constant regardless of concentration.


💡 Exam Tips:

  • Remember the overall order = m + n.

  • Units of k must be worked out from the rate equation for each specific reaction.

  • Fractional and zero orders are just as valid as integer orders – watch out for them in tricky questions!

📉 Orders of Reaction – Quick Reference

Order

Definition

Mathematical Relationship

Rate–Concentration Graph

Common Example

Zero Order

Rate does not change when [reactant] changes.

rate ∝ [A]⁰

Horizontal line

Decomposition of hydrogen peroxide with MnO₂ catalyst (w.r.t. catalyst)

First Order

Rate changes in direct proportion to [reactant].

rate ∝ [A]¹

Straight line through origin

Radioactive decay; hydrolysis of esters (w.r.t. ester)

Second Order

Rate changes with the square of [reactant].

rate ∝ [A]²

Upward curve starting at origin

Reaction between hydrogen and iodine chloride

Fractional Order

Rate changes with concentration raised to a fractional power.

rate ∝ [A]ᵃ (0 < a < 1)

Curved, less steep than second order

Complex multi-step mechanisms

Negative Order

Rate decreases as concentration increases.

rate ∝ [A]⁻ᵇ

Downward slope

Rare; some inhibition reactions


💡 Tips for Exams:

  • Overall order = sum of all individual orders.

  • Rate constant units depend on the overall order — always work them out from the rate equation.

  • Use the initial rates method or half-life analysis to find orders experimentally.


⚡ The Arrhenius Equation

The Arrhenius Equation links the rate constant (k) of a reaction to the temperature and the activation energy:

k = A e⁻ᴱᵃ/ᴿᵀ

Where:

  • k = rate constant

  • A = pre-exponential (frequency) factor – how often molecules collide in the right orientation

  • Eₐ = activation energy (J mol⁻¹)

  • R = gas constant = 8.314 J mol⁻¹ K⁻¹

  • T = temperature (K)

  • e = base of natural logarithms (~2.718)


Key Points

  • As T increases, the exponential term e⁻ᴱᵃ/ᴿᵀ increases, so k increases → faster reaction.

  • A small increase in temperature can cause a large increase in rate if Eₐ is large.

  • A depends on collision frequency and orientation, but not on temperature in simple models.


Linear Form for Graphs

Taking natural logs:

ln k = (–Eₐ / R) × (1/T) + ln A

This is in the form y = mx + c, so:

  • y = ln k

  • m = –Eₐ / R (gradient)

  • x = 1/T

  • c = ln A (y-intercept)

From the gradient, you can calculate the activation energy.


💡 Exam Tips:

  • Always convert Eₐ into J mol⁻¹ if using R in J mol⁻¹ K⁻¹.

  • 1/T must be in K⁻¹ – never in °C.

  • The Arrhenius equation often comes up in kinetics questions combined with orders of reaction.

⚡ Arrhenius Equation – Quick Reference

Form

Equation

Variables & Units

Top Tip

Standard Form

k = A e⁻ᴱᵃ/ᴿᵀ

k = rate constant (units vary)
A = pre-exponential factor (same units as k)
Eₐ = activation energy (J mol⁻¹)
R = 8.314 J mol⁻¹ K⁻¹
T = temperature (K)

Shows how rate changes with temperature and activation energy.

Linear Form

ln k = (–Eₐ / R)(1/T) + ln A

ln k = natural log of rate constant
1/T in K⁻¹
Gradient = –Eₐ / R
Intercept = ln A

Plot ln k vs 1/T to find Eₐ from gradient.

Rearranged for Eₐ

Eₐ = –(gradient × R)

Eₐ in J mol⁻¹

Convert to kJ mol⁻¹ by ÷1000 for final answer.

Rearranged for A

A = e^(intercept)

Same units as k

A depends on collision frequency & orientation.


Common Mistakes to Avoid

  • Forgetting to convert Eₐ into J mol⁻¹ before using R.

  • Using °C instead of K for temperature.

  • Mixing up ln (natural log) with log₁₀.

  • Forgetting that the units of k depend on the overall order of reaction.


⚖️ Equilibria

A dynamic equilibrium occurs in a closed system when the rate of the forward reaction equals the rate of the reverse reaction and the concentrations of reactants and products remain constant over time.


Key Features of Equilibrium

  • It is dynamic – both forward and reverse reactions continue to occur.

  • Concentrations stay constant, but particles are still reacting.

  • It only occurs in a closed system (no substances can enter or leave).


Le Chatelier’s Principle

If a change is made to the conditions of a system at equilibrium, the system shifts to oppose the change and restore equilibrium.

Effects of changes:

  • Concentration: Increasing [reactant] shifts equilibrium to the right (more products). Increasing [product] shifts it to the left.

  • Pressure (gaseous systems only): Increasing pressure shifts equilibrium towards the side with fewer gas moles.

  • Temperature: Increasing temperature favours the endothermic direction (positive ΔH).

  • Catalyst: Speeds up both forward and reverse reactions equally – no change to the equilibrium position.


The Equilibrium Constant (Kc)

For the general reaction:
aA + bB ⇌ cC + dD

Kc = [C]ᶜ × [D]ᵈ / [A]ᵃ × [B]ᵇ

  • Square brackets = equilibrium concentrations in mol dm⁻³.

  • Kc is constant at a given temperature, but changes if temperature changes.


The Equilibrium Constant (Kp) – Gases

For gaseous equilibria, use partial pressures instead of concentrations:

Kp = (pC)ᶜ × (pD)ᵈ / (pA)ᵃ × (pB)ᵇ

Partial pressure of a gas = mole fraction × total pressure.


💡 Exam Tips:

  • Always write the correct units for Kc or Kp — they vary depending on the reaction stoichiometry.

  • For exothermic reactions, increasing temperature decreases K; for endothermic, increasing temperature increases K.

  • If given starting amounts and one equilibrium concentration, use ICE tables (Initial, Change, Equilibrium) to find the rest.

⚖️ Equilibria – Quick Reference

Term

Definition / Formula

Units

Top Tip

Dynamic Equilibrium

State where forward and reverse reactions occur at the same rate, and concentrations remain constant.

Only occurs in a closed system.

Le Chatelier’s Principle

A system at equilibrium shifts to oppose any change in conditions.

Works for concentration, pressure, temperature – not catalysts.

Kc

Kc = [C]ᶜ × [D]ᵈ / [A]ᵃ × [B]ᵇ

Depends on reaction

Use equilibrium concentrations in mol dm⁻³.

Kp

Kp = (pC)ᶜ × (pD)ᵈ / (pA)ᵃ × (pB)ᵇ

Depends on reaction

Use partial pressures in atm or Pa.

Partial Pressure

mole fraction × total pressure

Same as total pressure units

Mole fraction = moles of gas ÷ total moles of gas.

Effect of Temperature

Endothermic: ↑T → ↑K; Exothermic: ↑T → ↓K

Increasing T favours endothermic direction.

Effect of Pressure

↑P → shifts to side with fewer gas moles

No effect if moles of gas are equal on both sides.

Effect of Concentration

Adding reactant → shifts right; adding product → shifts left

Only applies to species in the equilibrium expression.

Catalysts

Speed up forward and reverse equally

No effect on position or K.


💡 Exam Mistakes to Avoid:

  • Forgetting to square or cube concentrations in Kc when coefficients are >1.

  • Using starting concentrations instead of equilibrium concentrations.

  • Mixing up units for Kc or Kp — they must be derived for each reaction.


💧 pH

pH is a measure of the hydrogen ion concentration in a solution:

pH = –log₁₀[H⁺]

Where:

  • [H⁺] = hydrogen ion concentration in mol dm⁻³

  • The scale is logarithmic — each pH unit change represents a tenfold change in [H⁺].


Strong Acids

Strong acids (e.g., HCl, HNO₃, H₂SO₄) fully dissociate in solution, so:
[H⁺] = acid concentration

Example: 0.010 mol dm⁻³ HCl → pH = –log₁₀(0.010) = 2.00


Weak Acids

Weak acids only partially dissociate, so you use the acid dissociation constant (Ka):
Ka = [H⁺]² / [HA]
From Ka, calculate [H⁺], then use the pH equation.


pOH and pKw

For aqueous solutions at 25°C:
pH + pOH = 14
pOH = –log₁₀[OH⁻]


[H⁺] from pH

To find [H⁺] from pH:
[H⁺] = 10⁻ᵖᴴ

Example: pH = 3.50 → [H⁺] = 10⁻³·⁵ ≈ 3.16 × 10⁻⁴ mol dm⁻³


💡 Exam Tips:

  • Always give pH to 2 decimal places unless told otherwise.

  • For diprotic acids (like H₂SO₄), double the [H⁺] for strong acid calculations.

  • In strong alkalis, find pOH first, then pH.

💧 pH – Quick Reference

Scenario

Formula

Variables & Units

Top Tip

pH from [H⁺]

pH = –log₁₀[H⁺]

[H⁺] in mol dm⁻³

Strong acids: [H⁺] = acid conc (if monoprotic)

[H⁺] from pH

[H⁺] = 10⁻ᵖᴴ

[H⁺] in mol dm⁻³

Use for weak acids once [H⁺] is calculated from Ka

pOH from [OH⁻]

pOH = –log₁₀[OH⁻]

[OH⁻] in mol dm⁻³

For strong bases: [OH⁻] = base conc (if monoprotic)

pH from pOH

pH = 14 – pOH

At 25°C, pH + pOH = 14

Weak Acid (Ka)

Ka = [H⁺]² / [HA]

Ka in mol dm⁻³

Assume [HA] ≈ initial conc if weak

[H⁺] from Ka

[H⁺] = √(Ka × [HA])

Ka in mol dm⁻³

Then use pH = –log₁₀[H⁺]

Strong Base to pH

1. [OH⁻] = base conc
2. pOH = –log₁₀[OH⁻]
3. pH = 14 – pOH

For diprotic bases, double [OH⁻]


💡 Common Mistakes to Avoid:

  • Forgetting to convert concentration into mol dm⁻³ before using formulas.

  • Not adjusting for multiple protons (diprotic acids/bases).

  • Rounding too early — keep full calculator values until the final step.


🔋 Standard Electrode Potentials & EMF Cells

Standard Electrode Potentials (E°)

A standard electrode potential is the potential difference of a half-cell compared to the standard hydrogen electrode (SHE), measured under standard conditions:

  • Concentration: 1.00 mol dm⁻³

  • Temperature: 298 K (25°C)

  • Pressure: 100 kPa (for gases)

The SHE is assigned a potential of 0.00 V and is used as the reference point.

💡 Key points:

  • E° values are for reduction reactions as written in data tables.

  • A more positive E° means the species is more likely to be reduced.

  • A more negative E° means the species is more likely to be oxidised.


Electrochemical Cells (EMF Cells)

An electrochemical cell combines two half-cells to produce a potential difference (EMF).

To construct a cell:

  1. Write both half-equations as reductions (from the data table).

  2. Identify the more positive E° → this half-cell undergoes reduction (cathode).

  3. The less positive E° → this half-cell undergoes oxidation (anode).

  4. Electrons flow from the anode (negative electrode) to the cathode (positive electrode).


EMF Calculation

E°cell = E°(reduction) – E°(oxidation)

Example:
Zn²⁺/Zn E° = –0.76 V
Cu²⁺/Cu E° = +0.34 V

E°cell = 0.34 – (–0.76) = +1.10 V


Conditions for Maximum EMF

  • Both solutions at 1.00 mol dm⁻³

  • Temperature at 298 K

  • Pressure of gases at 100 kPa

  • No current flowing (measured under equilibrium conditions)


💡 Exam Tips:

  • Always write the more positive E° half-equation as the reduction.

  • The electrode where reduction occurs is the cathode (positive in galvanic cells).

  • If conditions change (non-standard), E°cell can shift — think about equilibrium shifts.

🔋 Standard Electrode Potentials & EMF Cells – Quick Reference

Step / Concept

Details

Top Tip

Standard Conditions

[Ion] = 1.00 mol dm⁻³, T = 298 K, gas pressure = 100 kPa, no current flowing

Always state these in exam definitions

SHE Reference

Standard Hydrogen Electrode (H₂/H⁺) assigned 0.00 V

All E° values are measured against the SHE

E° Meaning

More positive → more likely to be reduced; more negative → more likely to be oxidised

E° values are for reduction half-equations

Anode (Oxidation)

Electrode with less positive E° value

Electrons flow from anode to cathode

Cathode (Reduction)

Electrode with more positive E° value

Cathode is positive in galvanic cells

Cell EMF Formula

E°cell = E°(cathode) – E°(anode)

Always subtract the anode’s E° from the cathode’s E°

Drawing a Cell

Salt bridge (KNO₃ or KCl), label electrodes, electron flow, and ion movement

Salt bridge completes the circuit and balances charge

Common Examples

Zn²⁺/Zn (–0.76 V), Cu²⁺/Cu (+0.34 V), Ag⁺/Ag (+0.80 V)

Use Data Booklet values, not memory


💡 Exam Mistakes to Avoid:

  • Mixing up anode and cathode in terms of oxidation/reduction.

  • Forgetting to reverse the sign of E° when reversing a half-equation.

  • Using non-standard conditions without considering their effect on E°cell (via equilibrium shifts).


🌡️ Enthalpy & Entropy

Enthalpy (ΔH)

Enthalpy is the heat energy change of a reaction at constant pressure.

Key points:

  • Exothermic reactions: ΔH is negative (energy released to surroundings, e.g., combustion).

  • Endothermic reactions: ΔH is positive (energy absorbed from surroundings, e.g., thermal decomposition).

  • Standard enthalpy changes (ΔH°) are measured under standard conditions:

    • 298 K (25°C)

    • 100 kPa pressure

    • 1.00 mol dm⁻³ concentrations (for solutions)

Common ΔH° definitions:

  • ΔH°f – enthalpy of formation (1 mole of compound from its elements in their standard states).

  • ΔH°c – enthalpy of combustion (1 mole of substance fully burned in oxygen).

  • ΔH°neut – enthalpy of neutralisation (acid + base → 1 mole of water formed).


Entropy (S)

Entropy is a measure of disorder in a system.

Key points:

  • More disorder → higher entropy.

  • Solids have low entropy; gases have high entropy.

  • Increasing temperature increases entropy.

  • A change in physical state usually increases entropy (e.g., melting, evaporation).


Entropy Change (ΔS)

ΔS = ΣS(products) – ΣS(reactants)

  • Units: J mol⁻¹ K⁻¹

  • Positive ΔS → increased disorder.

  • Negative ΔS → decreased disorder.


Gibbs Free Energy (ΔG) – Combining ΔH and ΔS

Predicts whether a reaction is thermodynamically feasible:

ΔG = ΔH – TΔS

  • ΔG in kJ mol⁻¹ (ΔH) and ΔS in kJ mol⁻¹ K⁻¹ (convert J → kJ by ÷1000).

  • If ΔG < 0 → reaction is feasible (spontaneous) under those conditions.

  • Temperature can influence feasibility, especially when ΔH and ΔS have the same sign.


💡 Exam Tips:

  • Always convert ΔS into kJ mol⁻¹ K⁻¹ before using in ΔG equation.

  • Remember that “feasible” doesn’t always mean “fast” – rate depends on activation energy too.

  • Check physical states when calculating ΔS; gases contribute the most to disorder.

🌡️ Enthalpy & Entropy – Quick Reference

Term

Definition / Formula

Units

Top Tip

Enthalpy (ΔH)

Heat energy change at constant pressure.

kJ mol⁻¹

ΔH < 0 = exothermic; ΔH > 0 = endothermic.

ΔH° (Standard Enthalpy Change)

Measured under standard conditions: 298 K, 100 kPa, 1.00 mol dm⁻³ solutions.

kJ mol⁻¹

Always specify physical states.

ΔH°f (Formation)

Enthalpy change when 1 mole of compound forms from its elements in standard states.

kJ mol⁻¹

Elements in standard state have ΔH°f = 0.

ΔH°c (Combustion)

Enthalpy change when 1 mole of substance burns completely in oxygen.

kJ mol⁻¹

Always exothermic (ΔH negative).

ΔH°neut (Neutralisation)

Enthalpy change when an acid and base react to form 1 mole of water.

kJ mol⁻¹

Usually around –57 kJ mol⁻¹ for strong acid–base.

Entropy (S)

Measure of disorder in a system.

J mol⁻¹ K⁻¹

Higher for gases, lower for solids.

Entropy Change (ΔS)

ΔS = ΣS(products) – ΣS(reactants)

J mol⁻¹ K⁻¹

Convert to kJ mol⁻¹ K⁻¹ for ΔG calculations.

Gibbs Free Energy (ΔG)

ΔG = ΔH – TΔS

kJ mol⁻¹

ΔG < 0 = reaction feasible under given conditions.


💡 Common Mistakes to Avoid:

  • Forgetting to convert ΔS from J to kJ when using ΔG equation.

  • Mixing up signs: endothermic = positive ΔH; exothermic = negative ΔH.

  • Assuming “feasible” means “fast” — rate depends on activation energy.


🔄 Redox Titrations

Redox titrations use an oxidation–reduction reaction to determine the concentration of a solution. Common examples in A-Level Chemistry include:

  • Manganate(VII) titrations – e.g., KMnO₄ oxidising Fe²⁺ in acid.

  • Thiosulfate titrations – e.g., Na₂S₂O₃ determining the concentration of iodine formed from an oxidising agent.


General Steps in a Redox Titration

  1. Measure a known volume of the solution with unknown concentration into a conical flask.

  2. Add any necessary reagents to ensure the correct redox reaction occurs (e.g., dilute H₂SO₄ for manganate titrations).

  3. Fill the burette with the standard solution (known concentration) of the oxidising or reducing agent.

  4. Add the titrant slowly to the flask while swirling, especially near the end point.

  5. Observe the end point — often a permanent colour change (KMnO₄ is self-indicating; thiosulfate titrations use starch).

  6. Record the burette readings and repeat until concordant results are obtained.


Common Examples

  • Manganate(VII) Titrations:
    MnO₄⁻ (purple) is reduced to Mn²⁺ (colourless) in acidic conditions; the end point is when the solution just turns pale pink.

  • Thiosulfate Titrations:
    I₂ (brown) is reduced to I⁻ (colourless) by thiosulfate; starch indicator turns blue-black with I₂ and goes colourless at the end point.


Calculations in Redox Titrations

  • Write the balanced redox equation.

  • Use moles = concentration × volume (in dm³).

  • Apply stoichiometric ratios from the equation to find the unknown concentration.


💡 Exam Tips:

  • In manganate titrations, never use HCl as the acid — Cl⁻ is oxidised, affecting results.

  • Always add starch near the end point in thiosulfate titrations to avoid the iodine–starch complex forming too early.

  • Record all volumes to 2 decimal places and repeat for concordance.

🔄 Redox Titrations – Quick Reference

Titration Type

Reaction

Colour Change at End Point

Conditions

Key Tips

Manganate(VII) (KMnO₄)

MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O

Colourless → pale pink (first permanent pink tinge)

Acidic (dilute H₂SO₄)

Self-indicating; don’t use HCl (Cl⁻ oxidised) or HNO₃ (oxidising agent).

Thiosulfate (Na₂S₂O₃)

2S₂O₃²⁻ + I₂ → S₄O₆²⁻ + 2I⁻

Blue-black (starch) → colourless

Acidified oxidising agent reacts with iodide to produce I₂; starch added near end point

Add starch when solution is pale yellow; swirl continuously near end point.

Other Redox Titrations (e.g., dichromate)

Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O

Orange → green

Acidic (dilute H₂SO₄)

Use external indicator if required; balance electrons in both half-equations.


💡 Calculation Reminder:

  1. Write balanced ionic half-equations.

  2. Combine to form the overall redox equation.

  3. Use n = c × V to calculate moles of known reagent.

  4. Apply mole ratio to find moles (and concentration) of the unknown.

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