Arrhenius, Activation Energy & the Rate Determining Step (AQA A Level Chemistry): Video

Hi, I'm Eleanor with 3 years of experience teaching Chemistry, and this video is about the Arrhenius equation, activation energy and the rate-determining step.

All three centre on the rate constant k: the Arrhenius equation shows what k depends on, finding activation energy uses k to calculate that quantity, and the rate-determining step is revealed by the species that appear in the rate equation, which is built around k.

The rate constant, k, only stays constant if the concentration of reactants is the only thing that changes; when the temperature changes, or a catalyst is used or changed, k changes too. The Arrhenius equation describes exactly how k depends on temperature and activation energy. Finding activation energy uses measured values of k to calculate that energy, and the rate-determining step is identified from the species that appear in the rate equation, which is built around k.

This video starts with the Arrhenius equation and what it says about k, then covers how activation energy is calculated from experimental k and T data, and finishes with the rate-determining step, where the rate equation's species reveal which step of a mechanism is slowest.

The rate constant k remains constant except if the temperature changes, or a catalyst is used or changed. At higher temperatures, a greater proportion of molecules have energy greater than the activation energy, and because the rate constant and rate of reaction are directly proportional to that fraction, a higher temperature gives a higher rate constant.

The relationship is given by k equals A e to the power of minus E a over R T, where A is the Arrhenius constant, E a is the activation energy, R is the gas constant and T is the temperature in kelvin. Taking natural logs gives ln k equals ln A minus E a over R T, which is easier to work with, and shows that increasing the activation energy decreases the value of k. The values of k and T can be used to calculate the activation energy for a reaction — this is what the next part covers.

The Arrhenius equation is commonly used to calculate the activation energy of a reaction. In some cases enough data is given to substitute directly into the equation; alternatively, a graph of ln k against 1 over T can be plotted. This gives a straight line of the form y equals m x plus c, where ln k is plotted against 1 over T, the gradient is minus Ea over R, and the y intercept is ln A. Reading the gradient off this graph gives the activation energy directly. This is the same rate constant, k, that the Arrhenius equation shows depends on temperature and activation energy — here it's measured experimentally and used to calculate Ea.

A chemical reaction can only go as fast as its slowest step, so the rate-determining step is the slowest step in the reaction. If a reactant appears in the rate-determining step, its concentration also appears in the rate equation, so the rate equation can be used to work out which step is rate-determining. The overall reaction equation and the rate equation can be used to predict a possible reaction mechanism, and conversely, if the mechanism is known, the rate equation can be deduced from it. When a rate equation includes a species that isn't part of the overall reaction equation, that species is a catalyst. Because the rate equation is built around k — the same k the Arrhenius equation and activation energy calculations describe — the rate-determining step connects a reaction's mechanism back to its rate constant.

You aren't required to learn the Arrhenius equations, but you do need to be able to rearrange them. The most common way students lose marks on the rate-determining step is stating it's simply the "slowest step" without using the rate equation to justify it — examiners expect you to show that the moles of each reactant consumed up to and including the rate-determining step match the orders in the rate equation.

The rate constant k depends on temperature and activation energy, as described by the Arrhenius equation. Activation energy is calculated from experimental k and T data, either directly or from the gradient of a ln k against 1 over T graph. The rate-determining step is the slowest step in a mechanism, and the species that appear in it are the same species that appear in the rate equation. Together, the Arrhenius equation, activation energy and the rate-determining step all centre on the rate constant k, linking a reaction's rate to its mechanism.