A pipette delivers 25.0 cm³ of a solution. What is this volume in dm³, and why does the conversion matter before using c = n/V?

25.0 cm³ is 25.0 ÷ 1000 = 0.0250 dm³, or 2.50 × 10⁻² dm³. The conversion matters because concentration in chemistry is quoted in mol dm⁻³, so the volume substituted into n = c × V must be in dm³; leaving it in cm³ inflates the number of moles by a factor of 1000.

Calculate the volume occupied by 0.0100 mol of an ideal gas at 101 000 Pa and 298 K. Give your answer in m³ and in cm³. (R = 8.31 J K⁻¹ mol⁻¹)

V = nRT/p = (0.0100 × 8.31 × 298) ÷ 101 000 = 24.76 ÷ 101 000 = 2.45 × 10⁻⁴ m³. Since 1 m³ = 1 × 10⁶ cm³, this is 245 cm³. The data are given to three significant figures, so the answer is given to three.

Deduce the units of the equilibrium constant Kc for N₂(g) + 3H₂(g) ⇌ 2NH₃(g).

Kc = [NH₃]² ÷ ([N₂][H₂]³). Substituting mol dm⁻³ for every concentration gives (mol dm⁻³)² ÷ (mol dm⁻³)⁴ = (mol dm⁻³)⁻², so the units are mol⁻² dm⁶. The units must be derived from the expression each time; they are not fixed for all equilibria.

WJEC AS-Level Chemistry 1410QS

Formulae and Equations

Topic overview Charges on common ions Building formulae for ionic and molecular compounds Assigning oxidation numbers Using oxidation numbers to follow redox changes Balancing equations and using state symbols Ionic and half equations

Basic Ideas About Atoms

Topic overview Radioactive decay and nuclear equations Alpha, beta and gamma radiation Half-life, dating and the uses of radioisotopes: half-life of radioactive decay Half-life, dating and the uses of radioisotopes: adverse consequences for living cells Ionisation energies and electronic structure Orbitals and the filling of sub-shells Atomic spectra and the energy of light: atomic emission spectrum of the hydrogen atom Atomic spectra and the energy of light: relationship between energy and frequency Atomic spectra and the energy of light: significance of the frequency

Chemical Calculations

Topic overview Relative masses and the mass spectrometer: relative atomic Relative masses and the mass spectrometer: how a mass spectrometer works Relative masses and the mass spectrometer: molecular ion The mole, the Avogadro constant and molar mass: relative mass terms and simple mass spectra The mole, the Avogadro constant and molar mass: moles and percentage composition by mass Empirical and molecular formulae Concentration, solubility and titration calculations: concentration in mol dm-3 and in g dm-3 Concentration, solubility and titration calculations: stoichiometry and the limiting reagent Concentration, solubility and titration calculations: titration calculations and estimating a titre Gas volumes and the ideal gas equation Yield, atom economy and experimental uncertainty: concepts of atom economy and percentage yield Yield, atom economy and experimental uncertainty: how to estimate the percentage error

Bonding

Topic overview Ionic bonds and covalent bonds: ionic bonding in terms of ion formation Ionic bonds and covalent bonds: covalent bonding and forces Electronegativity, polarity and in-between bonds: concepts of electronegativity and bond polarity Electronegativity, polarity and in-between bonds: forces Forces between molecules Hydrogen bonding Shapes of molecules and ions: VSEPR principle and its use Shapes of molecules and ions: bond angles associated with linear

Solid Structures

Topic overview Ionic crystals: sodium chloride and caesium chloride Giant covalent structures: diamond and graphite Simple molecular solids: iodine and ice Metals and the electron sea Using structure to explain physical properties

The Periodic Table

Topic overview How the Periodic Table is organised Oxidation and reduction as electron transfer Trends across periods and down groups Group 2: reactions, trends and the reasons behind them — reactions with oxygen, water and dilute acid Group 2: reactions, trends and the reasons behind them — trends down the group Group 2: reactions, trends and the reasons behind them — thermal stability of the carbonates Group 2: reactions, trends and the reasons behind them — oxides and hydroxides Identifying ions, making salts and gravimetric analysis: identifying cations with sodium hydroxide Identifying ions, making salts and gravimetric analysis: preparing a soluble salt from an acid Group 7: the halogens — physical properties and the trend in volatility Group 7: the halogens — reactions of the halogens with metals Group 7: the halogens — displacement reactions and the trend Group 7: the halogens — halide ions as reducing agents, uses of chlorine and the chlorate equilibrium

Simple Equilibria and Acid-Base Reactions

Topic overview Reversible reactions and dynamic equilibrium Le Chatelier's principle and shifting the position of equilibrium The equilibrium constant Kc Acids, bases, salts and neutralisation pH, strong acids and weak acids Acid-base titrations and their calculations

Thermochemistry

Topic overview Enthalpy changes and their definitions Calculating enthalpy changes from experimental measurements Determining enthalpy changes in the laboratory Hess's law and energy cycles Average bond enthalpies

Rates of Reaction

Topic overview Collision theory and the conditions that change rate Measuring rate and relating it to concentration Energy profiles and activation energy Temperature and the Boltzmann distribution Catalysts and how they work Following reactions in the laboratory

The Wider Impact of Chemistry

Topic overview Social and economic consequences of chemical manufacture and energy supply Environmental consequences of chemical processes and energy production Green chemistry and sustainable practice

Organic Compounds

Topic overview Drawing and reading organic structures Naming organic compounds Chain length, functional groups and physical properties Structural isomerism Electrophiles, nucleophiles, radicals and bond fission

Hydrocarbons

Topic overview Alkane bonding, combustion and fossil fuels: combustion reaction of alkanes and benefits Alkane bonding, combustion and fossil fuels: combustion calculations and acid rain Radical substitution of alkanes The C=C bond and why alkenes are reactive E–Z isomerism in alkenes Electrophilic addition, Markovnikov's rule and testing for alkenes: mechanism of electrophilic addition Electrophilic addition, Markovnikov's rule and testing for alkenes: Markovnikov's rule and the bromine water test Electrophilic addition, Markovnikov's rule and testing for alkenes: testing for a C=C bond Hydrogenation and addition polymers: conditions required Hydrogenation and addition polymers: nature of addition polymerisation

Halogenoalkanes

Topic overview Nucleophilic substitution by hydroxide ions Elimination to form alkenes Reactivity of the carbon–halogen bond and the silver nitrate test Uses of halogenoalkanes, CFCs and the ozone layer: uses of halogenoalkanes and CFCs Uses of halogenoalkanes, CFCs and the ozone layer: radical mechanism Uses of halogenoalkanes, CFCs and the ozone layer: replacements for CFCs Heating under reflux in the laboratory

Alcohols and Carboxylic Acids

Topic overview Two routes to ethanol: hydration and fermentation — hydration of ethene Two routes to ethanol: hydration and fermentation — fermentation Two routes to ethanol: hydration and fermentation — comparing the two routes on rate Classifying alcohols and dehydrating them Oxidising alcohols to aldehydes, ketones and acids Chemical tests for alcohols and carboxylic acids Carboxylic acids, bases and salts Making an ester and separating it by distillation: esterification Making an ester and separating it by distillation: carrying out the preparation Making an ester and separating it by distillation: separating and purifying Making an ester and separating it by distillation: yield

Instrumental Analysis

Topic overview Reading a mass spectrum Infrared spectra and functional groups NMR spectra and atomic environments Putting the three techniques together

Practical Skills and Techniques

Topic overview Measuring mass, volume, time and temperature Standard solutions and titration technique Indicators and acid–base titration curves Heating, refluxing, distilling and purifying: Heating Heating, refluxing, distilling and purifying: purifying Melting temperature, chromatography and pH measurement Electrochemical cells, rate methods and working safely: Electrochemical cells Electrochemical cells, rate methods and working safely: rate methods and working safely

Planning, Analysis and Evaluation

Topic overview Planning an investigation and controlling variables Recording observations and presenting data Graphs, gradients and processing data Errors, uncertainty, accuracy and precision Evaluating a method and suggesting improvements Research and referencing

Core Experiments and Their Chemistry

Topic overview Gravimetric and acid–base analysis Enthalpy and rate experiments: Enthalpy Enthalpy and rate experiments: rate experiments Redox titrations and electrochemical cells Equilibrium constants and following a titration with a pH probe Organic synthesis, separation and identification: Organic synthesis Organic synthesis, separation and identification: identification tests and chromatography

Mathematical Skills in Chemistry

Topic overview Units, standard form and proportion in chemical calculation: volume, equilibrium, rate and energy units Units, standard form and proportion in chemical calculation: standard form Units, standard form and proportion in chemical calculation: proportion Units, standard form and proportion in chemical calculation: checking answers, buffers, rate constants and units Significant figures, means and uncertainty in experimental data: significant figures in multiplication Significant figures, means and uncertainty in experimental data: relative atomic mass as a weighted mean Significant figures, means and uncertainty in experimental data: absolute and percentage uncertainty Symbols, rearranging equations and logarithms: chemical symbols and what each one asserts Symbols, rearranging equations and logarithms: rearranging an equation Symbols, rearranging equations and logarithms: substituting into equations for Kc, enthalpy and pH Symbols, rearranging equations and logarithms: logarithms, the Arrhenius equation and rearranging formulae Graphs: plotting, gradients, intercepts and tangents — reading a spectrum Graphs: plotting, gradients, intercepts and tangents — reaction order from data and plotting good graphs Graphs: plotting, gradients, intercepts and tangents — Arrhenius plots, zero-order graphs and tangents Graphs: plotting, gradients, intercepts and tangents — initial rates from tangents and interpreting graphs Shape, symmetry and three-dimensional structure: Shape Shape, symmetry and three-dimensional structure: symmetry

Mathematical Skills in Chemistry

17 subtopics
48 things to know
All units

What Mathematical Skills in Chemistry covers

Mathematical Skills in Chemistry is assessed throughout WJEC Chemistry and in the unit 5 practical examination rather than in one unit of its own. 271 recall questions across 17 subtopics.

Where it is assessed

All units

Skills assessed throughout, and in the unit 5 practical examination.

Check the WJEC specification ↗

The 17 subtopics

Each one has its own page. WJEC AS Chemistry students sit this topic in the first year.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

Calculate the amount, in moles, of solute in 25.0 cm³ of 0.100 mol dm⁻³ sodium hydroxide solution.

Key term

A student writes that 250 cm³ of solution is 0.250 m³. What has gone wrong, and what are the correct values in dm³ and m³?

Numbers

Why must volume be in m³ rather than dm³ when the ideal gas equation is used with pressure in pascals?

Numbers

Write 0.0050 mol dm⁻³ in standard form, and explain how many significant figures the value carries.

Key term

Convert 1.25 × 10⁻² mol dm⁻³ to ordinary form without altering the precision implied.

Numbers

A student converts 2.400 × 10³ g mol⁻¹ to ordinary form and writes 2400 g mol⁻¹. Why is this unsatisfactory?

Key term

In a reaction between magnesium and hydrochloric acid, 0.0500 mol of magnesium reacts completely. Use the reacting ratio to find the amount of hydrogen produced.

Evaluation

For N₂O₄(g) ⇌ 2NO₂(g), ΔH is +57 kJ mol⁻¹. Estimate how Kc changes when the temperature is raised from 298 K to 350 K.

Key term

A student adds a catalyst to an equilibrium mixture and predicts that Kc will double. Evaluate this prediction.

Numbers

Calculate the pH of 0.0200 mol dm⁻³ sodium hydroxide solution at 298 K. (Kw = 1.00 × 10⁻¹⁴ mol² dm⁻⁶).

Key term

Why is a temperature change of 6.5 °C numerically the same as a temperature change of 6.5 K?

Numbers

Express 0.000 025 0 mol in standard form and state the number of significant figures.

Numbers

How many significant figures are there in each of 0.00250, 250.0 and 2.5 × 10³?

Numbers

How many significant figures should a relative atomic mass calculated from abundances given to three significant figures be quoted to?

Numbers

A burette is graduated in 0.10 cm³ divisions. To how many decimal places should each reading be recorded, and why?

Numbers

Two students calculate a percentage yield of 83.86% and 84%. Which is the better answer if the masses were measured to three significant figures?

Numbers

Explain what a weighted mean is and why the relative atomic mass of an element is one.

Key term

What is meant by concordant titres, and why is a rough titre normally excluded from the mean?

Key term

Explain why the uncertainty in a titre is ±0.10 cm³ rather than ±0.05 cm³.

Evaluation

State the rule for combining uncertainties when two quantities are added or subtracted, and when they are multiplied or divided.

Numbers

A thermometer reads to ±0.5 °C. Calculate the absolute and percentage uncertainty in a temperature change from 21.4 °C to 27.9 °C.

Numbers

What does the symbol ∝ mean, and what does 'rate ∝ [A]' tell you about the order of reaction with respect to A?

Key term

A student writes 'Kc > 1, so the reaction has gone to completion'. Correct this statement.

Key term

Write, using an appropriate symbol, the relationship between the boiling temperatures of water and hydrogen sulfide, and justify your choice of symbol.

Key term

Why is the equilibrium sign drawn with two half-arrows of equal length in most equations, and what would unequal arrows suggest?

Numbers

25.0 cm³ of 0.100 mol dm⁻³ sodium hydroxide is exactly neutralised by 12.50 cm³ of sulfuric acid. Calculate the concentration of the acid.

Numbers

Two acids have pKa values of 3.75 and 4.76. Which is the stronger, and by what factor do their Ka values differ?

Key term

How is the relative molecular mass of a compound read from its mass spectrum?

Key term

A mass spectrum shows a molecular ion at m/z 46 and a prominent fragment at m/z 31. Identify the compound and the fragment.

Key term

Explain how a fragment peak at m/z 15 and one at m/z 29 are interpreted in a mass spectrum.

Evaluation

How does the shape of a rate–concentration graph reveal the order with respect to a reactant?

Key term

Why must a rate–concentration graph for a first-order reactant pass through the origin?

Key term

Describe how initial-rate data are used to derive a rate expression.

Key term

Why is the gradient of an Arrhenius plot negative, and what does a steeper line indicate?

Key term

Why is a zero-order rate constant found from the gradient of a straight line rather than from a tangent?

Key term

Why does the sign of the gradient differ between a graph of reactant concentration against time and one of product concentration against time?

Key term

Give two reasons why measuring an initial rate by drawing a tangent is less precise than reading the gradient of a straight line.

Key term

Why is the bond angle in water smaller than that in ammonia?

Key term

Predict the shape and bond angle of boron trifluoride.

Numbers

What is the shape of carbon dioxide, and what bond angle does it have?

Evaluation

Explain why an octahedral complex containing three identical bidentate ligands, such as [Ni(NH₂CH₂CH₂NH₂)₃]²⁺, shows optical isomerism.

Key term

How would you decide, from a three-dimensional drawing, whether two structures are the same compound or a pair of optical isomers?

Numbers

Rearrange c = n/V to find the volume of 0.200 mol dm⁻³ solution that contains 0.0500 mol of solute.

Key term

Rearrange the expression for percentage yield to find the theoretical mass of product, given a yield of 75.0% and an actual mass of 3.00 g.

Key term

A gaseous equilibrium has Kc = 4.0 × 10⁻³ mol dm⁻³. Comment on the position of equilibrium and express the comparison using an appropriate symbol.

Numbers

A first-order reaction has a rate of 4.50 × 10⁻⁴ mol dm⁻³ s⁻¹ when [A] = 0.150 mol dm⁻³. Calculate the rate constant.

Numbers

Calculate the enthalpy change for CaCO₃(s) → CaO(s) + CO₂(g) from the enthalpy changes of formation: CaCO₃ −1207, CaO −635 and CO₂ −394 kJ mol⁻¹.

Key term

Is 2-chloropropane chiral? Explain your reasoning.

Take Mathematical Skills in Chemistry further

The same content, four other ways.

Questions from this topic

Each one with the model answer underneath.

1
A pipette delivers 25.0 cm³ of a solution. What is this volume in dm³, and why does the conversion matter before using c = n/V?
Model answer
25.0 cm³ is 25.0 ÷ 1000 = 0.0250 dm³, or 2.50 × 10⁻² dm³. The conversion matters because concentration in chemistry is quoted in mol dm⁻³, so the volume substituted into n = c × V must be in dm³; leaving it in cm³ inflates the number of moles by a factor of 1000.
2
Calculate the amount, in moles, of solute in 25.0 cm³ of 0.100 mol dm⁻³ sodium hydroxide solution.
Model answer
V = 25.0 cm³ = 0.0250 dm³. n = c × V = 0.100 mol dm⁻³ × 0.0250 dm³ = 2.50 × 10⁻³ mol. The units cancel to leave mol, which confirms the conversion was made correctly.
3
A student writes that 250 cm³ of solution is 0.250 m³. What has gone wrong, and what are the correct values in dm³ and m³?
Model answer
The student has used the cm³ to dm³ factor but written the answer as m³. 250 cm³ = 0.250 dm³, and since 1 dm³ = 1 × 10⁻³ m³, the volume is 2.50 × 10⁻⁴ m³. Three different volume units are in routine use and each conversion step must be tracked separately.
4
Why must volume be in m³ rather than dm³ when the ideal gas equation is used with pressure in pascals?
Model answer
R = 8.31 J K⁻¹ mol⁻¹ is expressed in SI base units, and the product pV must come out in joules. One pascal is one newton per square metre, so Pa × m³ gives N m, which is a joule. Using dm³ with pascals gives an answer 1000 times too large.
5
Calculate the volume occupied by 0.0100 mol of an ideal gas at 101 000 Pa and 298 K. Give your answer in m³ and in cm³. (R = 8.31 J K⁻¹ mol⁻¹)
Model answer
V = nRT/p = (0.0100 × 8.31 × 298) ÷ 101 000 = 24.76 ÷ 101 000 = 2.45 × 10⁻⁴ m³. Since 1 m³ = 1 × 10⁶ cm³, this is 245 cm³. The data are given to three significant figures, so the answer is given to three.
6
Deduce the units of the equilibrium constant Kc for N₂(g) + 3H₂(g) ⇌ 2NH₃(g).
Model answer
Kc = [NH₃]² ÷ ([N₂][H₂]³). Substituting mol dm⁻³ for every concentration gives (mol dm⁻³)² ÷ (mol dm⁻³)⁴ = (mol dm⁻³)⁻², so the units are mol⁻² dm⁶. The units must be derived from the expression each time; they are not fixed for all equilibria.

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Mathematical Skills in Chemistry revision questions

Is Mathematical Skills in Chemistry examined at AS in WJEC Chemistry?: Yes. It sits in All units, which you take in the first year, so it is on the AS paper as well as counting towards the full A level.
What does Mathematical Skills in Chemistry cover in WJEC AS-Level Chemistry?: 17 subtopics: units, standard form and proportion in chemical calculation: volume, equilibrium, rate and energy units, units, standard form and proportion in chemical calculation: standard form, units, standard form and proportion in chemical calculation: proportion, units, standard form and proportion in chemical calculation: checking answers, buffers, rate constants and units, significant figures, means and uncertainty in experimental data: significant figures in multiplication, significant figures, means and uncertainty in experimental data: relative atomic mass as a weighted mean, significant figures, means and uncertainty in experimental data: absolute and percentage uncertainty, symbols, rearranging equations and logarithms: chemical symbols and what each one asserts, symbols, rearranging equations and logarithms: rearranging an equation, symbols, rearranging equations and logarithms: substituting into equations for kc, enthalpy and ph, symbols, rearranging equations and logarithms: logarithms, the arrhenius equation and rearranging formulae, graphs: plotting, gradients, intercepts and tangents — reading a spectrum, graphs: plotting, gradients, intercepts and tangents — reaction order from data and plotting good graphs, graphs: plotting, gradients, intercepts and tangents — arrhenius plots, zero-order graphs and tangents, graphs: plotting, gradients, intercepts and tangents — initial rates from tangents and interpreting graphs, shape, symmetry and three-dimensional structure: shape and shape, symmetry and three-dimensional structure: symmetry. Each one has its own page with questions and model answers.
How is Mathematical Skills in Chemistry organised?: By the WJEC 1410QS specification, subtopic by subtopic, so it matches the order you are taught it in.

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