State the key characteristic of the half-life of a first-order reaction.

The half-life is constant regardless of the initial concentration.

Why does a first-order reaction have a constant half-life?

Because the rate depends only on the first power of concentration, so the time for concentration to halve is independent of the starting concentration.

How can the half-life of a first-order reaction be determined from a concentration–time graph?

By measuring the time taken for the concentration to fall to half its value; this time remains constant throughout the reaction.

If you measure successive half-lives from a concentration–time graph and find they are all equal, what does this indicate about the reaction order?

The reaction is first-order with respect to that reactant.

In the equation k = ln 2 / t½, what does each symbol represent?

k is the rate constant, ln 2 is the natural logarithm of 2 (approximately 0.693), and t½ is the half-life of the reaction.

OCR A-Level Chemistry H432

Foundations in Chemistry

Topic overview Atomic structure, isotopes and counting sub-atomic particles Relative isotopic, atomic, molecular and formula mass Predicting ionic charges and the common ions Writing formulae, balanced equations and ionic equations The mole, molar mass and the Avogadro constant Empirical and molecular formulae, and hydrated salts Gas volumes, concentration and the ideal gas equation Stoichiometry, percentage yield and atom economy Apparatus, and why high atom economy matters Mathematical skills and measuring mass, volume and gas Acids, alkalis, dissociation and neutralisation Preparing a standard solution Carrying out a titration and its calculations Planning an experiment: variables, apparatus and recording results Practical safety, heating and filtration Uncertainty, percentage error, precision and accuracy Evaluating results: anomalies, conclusions, limitations and improvements Assigning oxidation numbers Roman numerals in names, and the chlorate and nitrate ions Oxidation, reduction and metals reacting with acids Redox equations and identifying what is oxidised Shells, orbitals and sub-shells The order in which sub-shells fill Writing electron configurations for atoms and ions

Bonding and Structure

Topic overview Ionic bonding and the properties of ionic compounds Covalent and coordinate bonding Lone pairs, bonding pairs and average bond enthalpy Electron pair repulsion theory, linear and trigonal planar shapes Tetrahedral, pyramidal and non-linear shapes and their bond angles Octahedral shapes, ions, and drawing molecules in three dimensions Electronegativity, polar bonds and polar molecules Permanent and induced dipoles, and hydrogen bonding Simple molecular lattices and why they melt easily Solubility and conductivity of simple molecular compounds

Periodic Table and Energy

Topic overview Periodicity and the electron configurations of periods 2 and 3 The blocks, and first and successive ionisation energies Metallic and giant covalent structures and their properties Group 2 reactions with oxygen, water and acids Ionisation energy down Group 2 and the alkalinity of the hydroxides Uses of Group 2 compounds in agriculture and medicine The halogens: boiling points, London forces and reactivity Halogen displacement reactions and the colours seen Disproportionation and the chlorination of water Testing for halide ions with silver nitrate and ammonia Testing for carbonate, sulfate and halide ions Testing for ammonium ions and the order of the tests Concentration, pressure and measuring reaction rate Catalysts and their industrial importance The Boltzmann distribution, temperature and catalysts

Enthalpy Changes

Topic overview Exothermic and endothermic reactions and enthalpy profiles Standard conditions and the standard enthalpy changes Bond enthalpies, q = mcΔT and calorimetry Calculating enthalpy change from bond enthalpies Why average bond enthalpies give only an approximation Hess' law and enthalpy cycles from combustion and formation data Working through an enthalpy cycle and the sign conventions Calorimetry and correcting for heat loss

Chemical Equilibrium

Topic overview Dynamic equilibrium and le Chatelier's principle Pressure, catalysts and investigating a shift in equilibrium Industrial compromise and the Haber process The equilibrium constant, Kc

Basic Concepts of Organic Chemistry

Topic overview IUPAC nomenclature and the alkyl groups General, structural, displayed and skeletal formulae Homologous series, functional groups and saturation Structural isomers, bond fission and curly arrows Chain, position and functional group isomerism Curly arrows, homolytic and heterolytic fission Nucleophiles, electrophiles, radicals and the mechanism steps

Core Organic Chemistry

Topic overview Alkanes: bonding, shape and boiling points Combustion of alkanes and their reaction with halogens The radical substitution mechanism and its limitations Alcohols: polarity, solubility and classification Oxidation, dehydration and substitution reactions of alcohols Hydrolysis of haloalkanes and comparing the rates Nucleophilic substitution and carbon-halogen bond strength CFCs, radicals and the catalytic destruction of ozone Combining analytical techniques to identify a compound

Alkenes

Topic overview Alkenes: the double bond, sigma and pi bonding, and shape E/Z and cis-trans isomerism in alkenes Hydrogenation, halogenation and hydration of alkenes Electrophilic addition, carbocation stability and Markownikoff's rule Addition polymerisation and repeat units Waste polymers, and biodegradable and photodegradable alternatives

Organic Synthesis

Topic overview Reflux, distillation and separating an organic layer Purifying an organic solid and testing its purity Planning a multi-stage synthetic route Functional group interconversions and lengthening the chain Esters, acyl chlorides, condensation polymers and racemic mixtures

How Fast?

Topic overview Rate equations, order and the rate constant Deducing orders and finding the units of k What the rate equation reveals about the mechanism Concentration-time graphs and continuous monitoring Half-life and the rate constant of a first-order reaction Rate-concentration graphs and the initial rates method Clock reactions, colorimetry and analysing kinetic graphs The rate-determining step and testing a proposed mechanism Temperature, the rate constant and the Arrhenius equation The ln k against 1/T graph and finding the activation energy

Physical Chemistry and Transition Elements

Topic overview Mole fraction, partial pressure and ICE tables Kc and Kp expressions, their units and calculations What changes the equilibrium constant, and the reaction quotient Lattice enthalpy and the Born-Haber cycle Enthalpy of solution and hydration, and the effect of ionic charge and size Entropy and calculating entropy change Gibbs free energy and thermodynamic feasibility

Acids, Bases and Buffers

Topic overview Brønsted-Lowry acids and bases and their reactions Ka, pKa, pH and the ionic product of water Calculating the pH of strong acids, strong bases and weak acids pH and hydrogen ion concentration What a buffer is and how it resists a change in pH Buffer calculations and the buffer that controls blood pH Titration curves, choosing an indicator and using a pH meter pH titration curves for the four acid-base combinations How an indicator works and choosing the right one

Redox and Electrode Potentials

Topic overview Oxidising and reducing agents, and balancing half-equations Combining half-equations and using oxidation numbers Redox titrations and their calculations Standard electrode potentials and setting up half-cells The electrochemical series and predicting feasibility Storage cells and fuel cells

Transition Elements

Topic overview Ligands, complex ions and coordination number Electron configurations from Sc to Zn, and which are transition elements Variable oxidation states, coloured ions and catalysis The shapes of complexes, stereoisomerism and cisplatin Ligand substitution, haemoglobin and the copper complexes Hydroxide precipitates of iron, manganese and chromium Redox interconversions of iron, chromium and copper Why ligand substitution happens and the changes it causes Precipitation reactions written as aqua complexes Dissolving hydroxides in excess ammonia and distinguishing the ions

Aromatic Compounds

Topic overview The delocalised model of benzene and the evidence for it Nitration, halogenation and Friedel-Crafts reactions of benzene The reactions of phenol, and directing effects Electrophilic substitution and directing effects Phenol: acidity, bromination and nitration Why phenol is more reactive than benzene, and planning a synthesis

Organic Chemistry and Analysis

Topic overview Oxidation and reduction of carbonyls, and the addition of HCN The nucleophilic addition mechanism 2,4-DNPH and Tollens' reagent Carboxylic acids: solubility and reactions with metals, carbonates and bases Esterification and the hydrolysis of esters Acyl chlorides and their reactions with alcohols, amines and ammonia Amines as bases, and preparing aliphatic amines Secondary and tertiary amines, and preparing aromatic amines Amino acids, their reactions, and amides Optical isomerism and identifying a chiral centre Condensation polymerisation and the ester and amide linkages Hydrolysing condensation polymers and telling them from addition polymers Nitriles from haloalkanes and from carbonyl compounds Friedel-Crafts reactions and lengthening the carbon chain Thin-layer and gas chromatography, Rf values and retention times Test-tube tests for the organic functional groups Tests for the inorganic ions and interpreting chromatograms

Spectroscopy

Topic overview Carbon-13 and proton NMR: peaks, chemical shift and integration Spin-spin splitting and predicting a spectrum TMS, deuterated solvents and the D₂O shake Combining elemental analysis, mass spectrometry, IR and NMR Molecular formula from the molecular ion, and fragmentation losses What IR and NMR each contribute to a structure Infrared absorption, global warming and breathalysers A systematic approach and the degree of unsaturation

How Fast?

Half-life and the rate constant of a first-order reaction

2 things to know
Components 01 and 03

Overview

Recall questions on the constant half-life of a first-order reaction, reading it from a graph, and k = ln 2 / t½.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

What is characteristic of the half-life of a first-order reaction, how is it read off a concentration–time graph, and what do equal successive half-lives show?

Numbers

What equation links k to the half-life, when does it apply, and what is k when t½ = 280 s?

Questions from this subtopic

Each one with the model answer underneath.

1
State the key characteristic of the half-life of a first-order reaction.
Model answer
The half-life is constant regardless of the initial concentration.
2
Why does a first-order reaction have a constant half-life?
Model answer
Because the rate depends only on the first power of concentration, so the time for concentration to halve is independent of the starting concentration.
3
How can the half-life of a first-order reaction be determined from a concentration–time graph?
Model answer
By measuring the time taken for the concentration to fall to half its value; this time remains constant throughout the reaction.
4
If you measure successive half-lives from a concentration–time graph and find they are all equal, what does this indicate about the reaction order?
Model answer
The reaction is first-order with respect to that reactant.
5
State the equation relating the rate constant k to the half-life t½ for a first-order reaction.
Model answer
k = ln 2 / t½
6
In the equation k = ln 2 / t½, what does each symbol represent?
Model answer
k is the rate constant, ln 2 is the natural logarithm of 2 (approximately 0.693), and t½ is the half-life of the reaction.

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