50.0 cm³ of acid is mixed with 50.0 cm³ of alkali and the temperature rises by 6.8 °C. Calculate the heat released, taking the density as 1.00 g cm⁻³ and c = 4.18 J g⁻¹ K⁻¹.

q = mcΔT = 100.0 × 4.18 × 6.8 = 2.84 × 10³ J, or 2.84 kJ.

That mixture formed 0.0500 mol of water. Calculate the enthalpy change of neutralisation.

ΔH = −2.84 ÷ 0.0500 = −56.8 kJ mol⁻¹.

A 0.0200 mol sample of gas occupies 500 cm³ at 1.20 × 10⁵ Pa. Calculate its temperature, with R = 8.314 J mol⁻¹ K⁻¹.

T = pV/(nR) = (1.20 × 10⁵ × 5.00 × 10⁻⁴) ÷ (0.0200 × 8.314) = 361 K.

At equilibrium, H₂(g) + I₂(g) ⇌ 2HI(g) has [H₂] = 0.200, [I₂] = 0.200 and [HI] = 1.60 mol dm⁻³. Calculate Kc.

Kc = (1.60)² ÷ (0.200 × 0.200) = 64.0, with no units.

A reaction has rate = k[A][B]. When [A] = 0.20 mol dm⁻³ and [B] = 0.30 mol dm⁻³ the rate is 6.0 × 10⁻⁴ mol dm⁻³ s⁻¹. Calculate k and give its units.

k = 6.0 × 10⁻⁴ ÷ (0.20 × 0.30) = 1.0 × 10⁻² dm³ mol⁻¹ s⁻¹.

The enthalpy change of combustion of carbon is −394 kJ mol⁻¹ and of carbon monoxide is −283 kJ mol⁻¹. Calculate the enthalpy change of formation of carbon monoxide.

Applying Hess's law, ΔHf = −394 − (−283) = −111 kJ mol⁻¹.

OCR A-Level Chemistry B H433

Development of Practical Skills in Chemistry

Topic overview Planning experiments Implementing: apparatus, units and recording data Significant figures and titration calculations Graphs, gradients and drawing a conclusion Anomalous results, precision, accuracy and types of error Calculating uncertainties and improving a method Hazards, risk and control measures Recording, processing and judging data Measuring pH, mass and volume, and choosing an indicator Reflux, distillation, purification and the standard tests PAG1 to PAG6: moles, enthalpy, qualitative analysis and organic synthesis PAG7 to PAG12: electrochemistry, rates and pH

Elements of Life

Topic overview The mole, relative masses and empirical formulae Concentration, titration and writing balanced equations Orbitals, sub-shells and electron configurations Sub-atomic particles and the evidence for the model of the atom Fusion reactions and the origin of the elements Ionic, covalent, dative and metallic bonding and the four structures Melting point, conductivity and solubility of each structure Shapes of molecules and ions The periodic table, the blocks and trends in melting point Ion charges, the common polyatomic ions and writing formulae Group 2 chemistry and charge density Ionisation enthalpy and trends in reactivity Solubility rules and the tests for the common anions Hydroxide precipitates, ionic equations and identifying an unknown salt Acids, bases and preparing salts The electromagnetic spectrum and photon energy calculations Emission and absorption spectra, and flame tests Mass spectrometry and relative atomic mass

Developing Fuels

Topic overview Molar gas volume and the ideal gas equation Gas volume calculations and measuring a gas in the laboratory Bonding and shape in organic molecules Enthalpy changes: definitions and standard conditions Bond enthalpies q = mcΔT and measuring an enthalpy change in solution Burning a fuel, correcting for heat loss, and the assumptions made Hess' law and enthalpy cycles Catalysts, heterogeneous catalysis and catalyst poisons Cracking and how it is carried out The pollutants from burning fuels and their effects Catalytic converters and cutting emissions Aliphatic and aromatic compounds, functional groups and general formulae Deducing formulae and naming a branched compound Combustion of organic compounds Addition of bromine and hydrogen halides, and the test for unsaturation Hydrogenation and hydration of alkenes Addition polymerisation Electrophilic addition mechanism Displayed, shortened and skeletal formulae Chain, position and functional group isomerism Why alkenes show stereoisomerism, and the E/Z and cis/trans rules Naming and comparing the stereoisomers Sustainable fuels: benefits and risks

Elements From the Sea

Topic overview Atom economy Extraction of the halogens from sea minerals Electrolysis of molten salts and writing electrode half-equations Electrolysis of aqueous solutions and the electrolysis of brine Redox as electron transfer The rules for assigning oxidation states Oxidation state calculations, and defining oxidation and reduction Balancing a redox equation with oxidation states The iodine-thiosulfate titration and its calculations Systematic nomenclature of inorganic compounds Physical properties of the halogens Halogen reactivity and the displacement equations Observing a displacement, and using an organic solvent or starch Silver halide precipitation and tests Preparation of the hydrogen halides Properties of the hydrogen halides Chlorine: risks, benefits and uses Dynamic equilibrium Writing a Kc expression and calculating Kc What the magnitude of Kc tells you, and what changes it Using the Kc expression to explain a shift in position Temperature, pressure and catalysts on an equilibrium

The Ozone Story

Topic overview Electronegativity and bond polarity Intermolecular bonds Boiling points and intermolecular bonds Activation enthalpy and enthalpy profiles Collision theory and the Boltzmann distribution Following a reaction and finding the rate from a graph Catalysts and alternative reaction routes Homogeneous catalysis and intermediates Composition of gas mixtures by volume Recognising and naming haloalkanes Primary, secondary and tertiary haloalkanes, and the amines Properties and nucleophilic substitution of haloalkanes Substitution, nucleophiles and the SN2 mechanism Relative reactivity of the haloalkanes Homolytic and heterolytic fission, radicals and half curly arrows Initiation, propagation and termination in a radical chain reaction Ozone depletion by haloalkanes Ozone in the stratosphere and troposphere Radiation of the Earth and the Sun Effects of UV and visible radiation on molecules Calculations with frequency, wavelength and energy

What's in a Medicine?

Topic overview Formulae of oxygen-containing homologous series Primary, secondary and tertiary alcohols The acidity of phenol compared with alcohols and carboxylic acids The iron(III) chloride test and esterifying a phenol Esterification and oxidising primary, secondary and tertiary alcohols Dehydration, halogenation and planning a two-step synthesis Preparing aspirin, filtering under reduced pressure and recrystallisation Thin layer chromatography, Rf values and percentage yield Reflux and distillation in an organic preparation Washing, drying and redistilling a liquid product The aims of green chemistry and atom economy Catalysts, renewable feedstocks and measuring greenness Elimination reactions The molecular ion and fragment ions Identifying a compound from its fragments and the M+1 peak How infrared absorption works and the characteristic absorptions Reading a spectrum, the fingerprint region and combining techniques

The Chemical Industry

Topic overview Rate equations, order and the rate constant Deducing the units of k and rate calculations Half-lives Continuous monitoring, quenching and the initial rates method Reading order from concentration-time and rate-concentration graphs The Arrhenius equation and what each symbol means The ln k against 1/T plot and finding the activation enthalpy Rate-determining step and mechanism Effect of conditions on the magnitude of the equilibrium constant Economic operating conditions for an industrial process Writing a Kc expression and deducing its units ICE-table calculations and measuring Kc experimentally Chemical reactions in industrial processes Nitrogen, ammonia and the ammonium ion Oxidation states of nitrogen and the tests for nitrate and ammonium Costs, benefits and risks of industrial processes

Polymers and Life

Oceans

Topic overview Solubility in aqueous and non-aqueous solvents Lattice, hydration and solution enthalpies and how they relate Measuring an enthalpy change of solution Charge density and the size of enthalpy terms Entropy: qualitative treatment Total entropy change and the condition for feasibility The limiting temperature, and why a feasible reaction may not happen Calculating the entropy change of the system The solubility product expression, its units and calculations Predicting precipitation and the common ion effect Bronsted-Lowry theory of acids and bases Strong acids and strong bases Weak acids, Ka and pKa pH of strong acids and strong bases pH of weak acids, dilution and the limits of the approximation What a buffer is and how it resists a change in pH Buffer calculations, capacity and the natural buffers How the greenhouse effect works and which gases cause it Why a molecule absorbs, concentrations in ppm, and ocean chemistry

Developing Metals

Topic overview Manganate(VII) titrations and their calculations Thiosulfate titrations, recording results and good technique Shapes of complexes and coordination number Balancing redox equations involving acid-base reactions Simple electrochemical cells Action of an electrochemical cell Standard electrode potentials and calculating E°cell Rusting and how it is prevented Transition metals: definition, oxidation states and colours d-block electron configurations of the atoms and their ions Why transition metals show variable oxidation states Ligands and complex ions Coordinate bonding and what makes a ligand Bidentate and multidentate ligands, and finding a complex's formula Reactions of Fe2+, Fe3+ and Cu2+ with hydroxide and ammonia Catalytic activity of transition metals Origin of colour in transition metal complexes Colorimetry

Colour by Design

Topic overview How dyes attach to fibres Structure of a dye molecule Fats and oils Arenes and delocalisation Representations of benzene and enthalpy of hydrogenation Tests for the common functional groups Identifying a polyfunctional molecule from a set of test results Halogenation and nitration of benzene and the electrophiles involved The nitration mechanism, sulfonation and the Friedel-Crafts reactions Diazotisation and why it is done cold Coupling reactions, azo dyes and the route from benzene Oxidising an aldehyde and the three carbonyl tests Cyanohydrin formation and its use in synthesis Using the Data Sheet reactions to plan a route Choosing between routes on yield and atom economy Nucleophilic addition mechanism Classifying organic reactions and unfamiliar mechanisms Origins of colour in organic molecules How gas-liquid chromatography separates a mixture Retention time, peak area and the limits of the technique

Chemical Literacy

Topic overview Extracting and using data and information from a scientific text Written communication and comprehension

Mathematical Skills in Chemistry

Topic overview Units, standard form and the mole in calculations Yield, atom economy and logarithmic quantities Significant figures, means and handling data Symbols, and rearranging the standard equations Substituting into rearranged equations Reading spectra and kinetics graphs Gradients, calibration lines and the Arrhenius plot Shapes and bond angles from electron pair repulsion Chiral centres, E/Z isomerism and optical activity

Mathematical Skills in Chemistry

Substituting into rearranged equations

2 things to know
Components 01, 02 and 03

Overview

Recall questions on working numbers through a rearranged equation for enthalpy, gas volume, Kc, rate and pH.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

What is the pH of a solution in which [H⁺] = 5.0 × 10⁻⁴ mol dm⁻³?

Numbers

Methanoic acid has Kₐ = 1.6 × 10⁻⁴ mol dm⁻³. What is its pKₐ?

Questions from this subtopic

Each one with the model answer underneath.

1
50.0 cm³ of acid is mixed with 50.0 cm³ of alkali and the temperature rises by 6.8 °C. Calculate the heat released, taking the density as 1.00 g cm⁻³ and c = 4.18 J g⁻¹ K⁻¹.
Model answer
q = mcΔT = 100.0 × 4.18 × 6.8 = 2.84 × 10³ J, or 2.84 kJ.
2
That mixture formed 0.0500 mol of water. Calculate the enthalpy change of neutralisation.
Model answer
ΔH = −2.84 ÷ 0.0500 = −56.8 kJ mol⁻¹.
3
A 0.0200 mol sample of gas occupies 500 cm³ at 1.20 × 10⁵ Pa. Calculate its temperature, with R = 8.314 J mol⁻¹ K⁻¹.
Model answer
T = pV/(nR) = (1.20 × 10⁵ × 5.00 × 10⁻⁴) ÷ (0.0200 × 8.314) = 361 K.
4
At equilibrium, H₂(g) + I₂(g) ⇌ 2HI(g) has [H₂] = 0.200, [I₂] = 0.200 and [HI] = 1.60 mol dm⁻³. Calculate Kc.
Model answer
Kc = (1.60)² ÷ (0.200 × 0.200) = 64.0, with no units.
5
A reaction has rate = k[A][B]. When [A] = 0.20 mol dm⁻³ and [B] = 0.30 mol dm⁻³ the rate is 6.0 × 10⁻⁴ mol dm⁻³ s⁻¹. Calculate k and give its units.
Model answer
k = 6.0 × 10⁻⁴ ÷ (0.20 × 0.30) = 1.0 × 10⁻² dm³ mol⁻¹ s⁻¹.
6
The enthalpy change of combustion of carbon is −394 kJ mol⁻¹ and of carbon monoxide is −283 kJ mol⁻¹. Calculate the enthalpy change of formation of carbon monoxide.
Model answer
Applying Hess's law, ΔHf = −394 − (−283) = −111 kJ mol⁻¹.

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