Chemical Kinetics: One Mark Questions, Book Back Answers and Notes

About Chemical Kinetics

Medium ~120 min study

Thermodynamics tells you whether a reaction can happen. It says nothing about whether it takes a second or a thousand years. Diamond turning into graphite is favourable, yet no one has seen a diamond ring turn grey. Chemical kinetics is the part of chemistry that measures and explains that speed.

The chapter links what you can measure, the fall in concentration of a reactant with time, to what happens between molecules, which is collisions of the right energy and orientation. The key mathematical result is the integrated rate equation. For a first order reaction it is \([A] = [A]_0 e^{-kt}\), which you will usually use in its log form, k = (2.303/t) log([A]₀/[A]).

The questions mix theory with numbers. You may have to find the unit of k for a given order, calculate a half-life from k, tell order from molecularity, and work out how k changes when temperature rises. Practise the log calculations until they are quick, because most numerical errors in this unit are arithmetic, not chemistry.

What you'll learn

• Write and calculate the rate of a reaction in terms of any reactant or product.
• Distinguish order from molecularity with examples.
• Derive the integrated rate equations for zero and first order reactions.
• Use the Arrhenius equation to find activation energy or a rate constant at a new temperature.
• Explain how a catalyst raises the rate by lowering activation energy.
• Calculate half-life from the rate constant and vice versa.

Before you start

• Balanced chemical equations and stoichiometry.
• Molar concentration and its unit, mol L-1.
• Logarithms and exponential functions, including conversion between ln and log.

Chemical Kinetics explained

Rate, Order and Activation Energy

Rate of a Reaction

Rate is the change in molar concentration of a reactant or product per unit time, in mol L^-1 s^-1. Because reactant concentration falls, its rate is written with a minus sign, for example rate = −d[A]/dt. The average rate is taken over a finite time interval, Δ[A]/Δt. The instantaneous rate is the rate at one moment, found from the slope of the tangent to the concentration–time curve at that point.

Factors Affecting Rate

Rate depends on the nature and physical state of the reactants, their concentration (or pressure for gases), temperature, the presence of a catalyst, surface area and, for some reactions, light. Powdered solids react faster than lumps because more surface is exposed to the other reactant.

Rate Law and Order

The rate law is found by experiment, not from the balanced equation. For rate = k[A]^x[B]^y, the order is x + y. Order can be zero, a whole number or a fraction. The unit of k depends on order: mol L^-1 s^-1 for zero order, s^-1 for first order and L mol^-1 s^-1 for second order.

Molecularity

Molecularity is the number of reacting species (atoms, ions or molecules) that collide at the same time in a single elementary step. It is a theoretical idea taken from the mechanism, so it is always a whole number (1, 2 or rarely 3) and never zero. Order is an experimental quantity and applies to the overall reaction. For a complex reaction the slowest step decides the rate.

Integrated Rate Equations

For a zero order reaction, [A] = [A]₀ − kt, so a plot of [A] against t is a straight line with slope −k. For a first order reaction, concentration falls exponentially, and a plot of log[A] against t is a straight line with slope −k/2.303. Decomposition of N₂O₅ and radioactive decay are standard first order examples.

Half-life

Half-life (t_1/2) is the time taken for the concentration of a reactant to fall to half its initial value. For a first order reaction t_1/2 = 0.693/k, which does not depend on the starting concentration. For a zero order reaction t_1/2 = [A]₀/2k, so it is directly proportional to initial concentration.

Collision Theory

Molecules must collide to react, but most collisions do nothing. A collision is effective only when the molecules have at least the threshold energy and hit each other with the right orientation. Raising the concentration increases the number of collisions per second, so the rate goes up.

Temperature and the Arrhenius Equation

For many reactions, a 10 K rise in temperature roughly doubles the rate constant. The Arrhenius equation \(k = A e^{-E_a/RT}\) explains why: \(k\) depends on the absolute temperature \(T\) and the activation energy \(E_a\), and the fraction of molecules with energy above \(E_a\) grows sharply as T rises. Taking logs at two temperatures gives log(k₂/k₁) = (E_a/2.303R)(T₂ − T₁)/(T₁T₂), the form used in numerical problems.

Effect of a Catalyst

A catalyst speeds up a reaction and is left chemically unchanged at the end. It works by opening a different reaction path with a lower activation energy, so more molecules have enough energy to react at the same temperature. It does not change ΔH or the position of equilibrium; it only helps equilibrium be reached sooner.

Common mistakes to avoid

• Taking order from the coefficients of the balanced equation. Order comes from experiment and may differ from molecularity for complex reactions.
• Giving the wrong unit for k. Work it out from rate = k[A]n: the unit is (mol L-1)1−n s-1.
• Using temperature in °C in the Arrhenius equation. T must be in kelvin.
• Thinking a first order half-life depends on initial concentration. It is 0.693/k whatever the starting amount.
• Dropping the minus sign when rate is written as the disappearance of a reactant, or forgetting to divide by the stoichiometric coefficient.

Test yourself on these with the practice test, then check the worked reasoning in the solved MCQs.

Frequently asked questions

What is the difference between average rate and instantaneous rate?

Average rate is the change in concentration over a chosen time interval divided by that interval. Instantaneous rate is the rate at one particular moment. You find it by drawing a tangent to the concentration–time curve at that time and taking its slope.

Can the order of a reaction be zero?

Yes. In a zero order reaction the rate does not depend on reactant concentration. A common example is a gas decomposing on a metal surface: once all the active sites are covered, adding more gas cannot increase the rate. Molecularity, by contrast, can never be zero.

How does temperature affect the rate constant?

Raising temperature increases k. Collisions become slightly more frequent, but the bigger effect is that a much larger fraction of molecules now has energy equal to or above the activation energy. That is why a 10 K rise can roughly double the rate.

What is a pseudo first order reaction?

It is a reaction of higher order that behaves as first order because one reactant is in large excess. In the acid hydrolysis of ethyl acetate, water is present in such excess that its concentration hardly changes, so the rate depends only on the ester concentration.

Why does activation energy matter?

It is the energy barrier between reactants and products. The higher the barrier, the fewer molecules can cross it at a given temperature, and the slower the reaction. A catalyst provides a path with a lower barrier, which is why it speeds the reaction up.

Does the half-life of a reaction change with concentration?

It depends on the order. For zero order, t1/2 is directly proportional to initial concentration. For first order it is constant, 0.693/k. For second order it is inversely proportional to initial concentration.