Rate Equations, Orders of Reaction & Rate Graphs (AQA A Level Chemistry): Video

Hi, I'm Eleanor with 3 years of experience teaching Chemistry, and this video is about rate equations, orders of reaction and rate graphs.

The order of a reaction describes how a reactant's concentration affects the rate, and it's exactly what's read off concentration-time and rate-concentration graphs; once every order is known, the rate equation is complete and can be used to calculate the rate constant, k.

The rate equation takes the form rate equals k multiplied by concentration of A to the power m multiplied by concentration of B to the power n, where m and n are the orders of reaction with respect to each reactant and must be found experimentally rather than read off the balanced equation. Concentration-time and rate-concentration graphs are two different ways of reading those orders directly from data, and once the orders are known, the full rate equation can be used to calculate the rate constant, k.

This video starts with what rate equations and orders of reaction are, then covers how the rate equation is derived from experimental data and used to calculate k, and finishes with how concentration-time and rate-concentration graphs let you read the order of a reaction straight off their shape.

The rate of reaction is the change in concentration of a reactant or product per unit time, with units of moles per decimetre cubed per second. The general form of a rate equation is rate equals k multiplied by concentration of A to the power m multiplied by concentration of B to the power n, where [A] and [B] are reactant concentrations, m and n are the orders of reaction with respect to each reactant, and k is the rate constant. The orders can only be 0, 1 or 2, and they must be determined experimentally — they cannot be deduced from the stoichiometric coefficients in the balanced equation. If a reactant is zero order, changing its concentration doesn't affect the rate; if first order, the rate is directly proportional to its concentration; if second order, the rate is proportional to the square of its concentration. The overall order of reaction is the sum of the individual orders.

To derive a rate equation from experimental data, the order with respect to each reactant is found one at a time: two experiments are compared where only one reactant's concentration changes while the others stay constant, and the resulting change in rate reveals that reactant's order. If concentration doubles and rate stays the same, the order is zero; if rate also doubles, the order is one; if rate quadruples, the order is two. This is repeated for each reactant in turn, and once every order is known, they combine into the full rate equation, with any zero-order reactant left out.

Once the rate equation is known, the rate constant, k, can be calculated by substituting the initial rate and the initial concentrations of the reactants from a single experiment and rearranging for k. Any of the experiments in a data set will give the same value of k. The units of k vary and are calculated by substituting the units of each value into the rearranged equation and cancelling as required.

A concentration-time graph shows how a reactant's concentration changes as a reaction proceeds, and its shape reveals the order of reaction. For a zero-order reactant, the graph is a straight diagonal line going down, and because the rate is constant throughout, the rate constant, k, is equal to the gradient of this line. For a first-order reactant, the graph is a curve that decreases and eventually plateaus. For a second-order reactant, the concentration decreases even more steeply, giving a steeper curve than the first-order case.

A rate-concentration graph plots the rate of reaction against the concentration of a reactant, and like a concentration-time graph, its shape reveals the order. For a zero-order reactant, the rate doesn't depend on concentration, so the graph is a horizontal line. For a first-order reactant, the rate is directly proportional to concentration, giving a straight diagonal line going up. For a second-order reactant, the rate is proportional to the square of concentration, giving a curved line.

Be careful reading values given in standard form — it's easy to make a mistake. If a graph is given alongside tabulated data, don't ignore it — examiners will sometimes give you a graph that demonstrates the order with respect to one reactant, alongside tabulated data to find the order with respect to the others, and both need to be used to find k.

The order of reaction with respect to each reactant — 0, 1 or 2 — describes how its concentration affects the rate, and is found experimentally by comparing how rate changes as concentration changes. Concentration-time and rate-concentration graphs are two ways of reading those orders directly from their shape. Once every order is known, the full rate equation,rate equals k multiplied by concentration of A to the power m multiplied by concentration of B to the power n, is complete, and it can be used with a set of experimental data to calculate the rate constant, k.