Reaction rate: what it is and what affects it

What reaction rate is

According to LibreTexts, the rate of a reaction is how quickly it proceeds, and it is read from the concentration of a substance changing over time. You can follow the reactants disappearing, in which case a minus sign goes in front because their concentration falls, or the products appearing. The balanced equation ties the two together, and either works. The rate itself is always positive and is expressed in mol/(L·s).

Practical example: Wikipedia points out how widely rates vary. Iron can take many years to rust in the atmosphere, while cellulose burns in a fire in a fraction of a second.

In most reactions the rate falls as the reactants are consumed. The study of these speeds is called chemical kinetics, the part of physical chemistry that teaches how to measure and predict rates and how to use the data to propose mechanisms. The topic has a second half, chemical equilibrium, which has its own Recap.

One rate for each reaction

The substances involved can change concentration at different speeds. The reaction rate is still a single number: each change is divided by its own stoichiometric coefficient, so the result does not depend on which substance is used to measure it. The definition holds for one reaction in a closed system at constant volume.

Practical example: if B has coefficient 3 and A has coefficient 1, B is used up three times as fast as A. The reaction rate is still one.

How it is measured

The rate is worked out from concentrations measured at different times. Small samples can be withdrawn and analysed, for example by titration. A spectrophotometer can give the concentration from the light absorbed, following Beer’s law. For reactions that produce gas it is enough to measure the volume released at different times and link it to the change in concentration.

Factors affecting the rate of reaction

For LibreTexts, the catalyst and the solvent matter, and so do the temperature and the concentration, besides the physical state and degree of subdivision of the reactants. Wikipedia lengthens the list with stirring and pressure. It also adds electromagnetic radiation and isotopes, plus the diffusion limit.

Collision theory

Collision theory, a model, accounts for these effects. Particles must collide for a reaction to happen, and only some collisions lead to one: they need the right orientation and, at the moment of impact, enough energy to break the bonds already present and form new ones. That minimum energy is the activation energy. More reactant means more frequent collisions, and the rate rises. For gases, raising the pressure amounts to raising the concentration.

Temperature, surface and catalyst

Temperature speeds things up mainly because more of the colliding particles have the activation energy they need; the higher number of collisions counts for less. The Arrhenius equation describes the effect. Wikipedia reports an empirical rule: +10 °C roughly doubles the rate constant, with a ratio between the constants, Q10, usually around 2. This is an approximate rule and no law. There are exceptions: some reactions have a rate independent of temperature, others slow down on heating, and barrierless reactions (for example some radical reactions) tend to do the latter.

In reactions that take place on a surface, the rate grows with the exposed area, since more particles of the solid can be reached by the reactant molecules.

For reactions that follow the Arrhenius law, a catalyst lowers the activation energy by offering a different pathway. More collisions then become effective, the reaction speeds up in the forward and reverse directions, and there is no need to raise the temperature.

Practical example: LibreTexts mentions iodide speeding up the decomposition of hydrogen peroxide without any heating.

The rate law and the rate constant

The rate law is the expression that relates the rate to the concentrations; each exponent is a reaction order, and the constant k collects the rest. According to Wikipedia the “constant” is not really constant: it holds every factor that affects the rate, temperature included, except concentration and time. With temperature fixed, k does not change but the rate does. The units of k depend on the order; in first order they are 1/time.

Order of a chemical reaction

The overall reaction order is the sum of the exponents with which the concentrations appear in the rate law. Each reactant can have its own partial order: in the LibreTexts textbook example, orders of 1, 2 and 0 give an overall order of 3. Zero order in a reactant means the rate does not depend on it. With order 1, doubling the concentration doubles the rate.

Only for single-step reactions do the exponents match the stoichiometric coefficients. With several steps they may not, so the order has to be found by experiment, for example with the method of initial rates, which compares runs started at different concentrations.

Practical example: in the reaction between H2 and NO the coefficients are both 2, but the measured order is 1 in H2 and 2 in NO.

Molecularity, the number of molecules taking part in an elementary step, equals the order only for elementary steps.

Order is an experimental quantity, whereas molecularity belongs to the mechanism. A step with three molecules would be third order but slow, since simultaneous three-body collisions are rare.

First order kinetics

In a first-order reaction the rate grows in proportion to the concentration of a single reactant. To check it, plot the natural logarithm of the concentration against time: a straight line with a negative slope equal to -k points to first order.

LibreTexts presents a half-life that stays the same even when the starting concentration changes as the distinctive trait of first order. It equals ln 2 divided by k, about 0.693/k.

Practical example: halving the concentration from 1 M to 0.5 M takes the same time as halving it from 0.1 M to 0.05 M.

Zero order kinetics

In a zero-order reaction the rate stays constant as the concentration changes and equals k. This holds only while reactant remains: without reactant the process cannot continue. It often appears when the reaction happens on a catalytic surface that becomes saturated. Wikipedia writes that when the substrate is far more abundant than the enzyme, the enzyme becomes saturated and many enzyme reactions are then zero order. One case is the oxidation of ethanol to acetaldehyde by liver alcohol dehydrogenase.

The rate-determining step

When a mechanism has several steps, it is usually the slowest elementary step that governs the overall rate, often only approximately. A reaction has a rate-determining step only when one of its steps is much slower than all the rest. Supposing that one exists makes the rate law much easier to work out. To tell which candidate is right, one works out the law each would imply and compares it with the measured one.

Practical example: in NO2 + CO → NO + CO2 the observed rate is second order in NO2 and zero order in CO. It follows that CO enters a faster step, after the slow one.