# Rates of Reaction

- Created by: Leah Gray
- Created on: 22-10-13 16:56

## Orders of Reactions and the Rate Equation

**Measuring a rate of reaction**

There are several simple ways of measuring a reaction rate. For example, if a gas was being given off during a reaction, you could take some measurements and work out the volume being given off per second at any particular time during the reaction.

A rate of 2 cm^{3} s^{-1} is obviously twice as fast as one of 1 cm^{3} s^{-1}.

For example, suppose you had a reaction between two substances **A** and **B**. Assume that at least one of them is in a form where it is sensible to measure its concentration - for example, in solution or as a gas.

For this reaction you could measure the rate of the reaction by finding out how fast the concentration of, say, **A** was falling per second.

You might, for example, find that at the beginning of the reaction, its concentration was falling at a rate of 0.0040 mol dm^{-3} s^{-1}.

## Orders and rate equation continued.....

For the purposes of rate equations and orders of reaction, the rate of a reaction is measured in terms of how fast the concentration of one of the reactants is falling. Its units are mol dm^{-3} s^{-1}.

Orders of reaction are always found by doing experiments. You can't deduce anything about the order of a reaction just by looking at the equation for the reaction.

So let's suppose that you have done some experiments to find out what happens to the rate of a reaction as the concentration of one of the reactants, **A**, changes. Some of the simple things that you might find are:

*One possibility: The rate of reaction is proportional to the concentration of* A

That means that if you double the concentration of **A**, the rate doubles as well. If you increase the concentration of **A** by a factor of 4, the rate goes up 4 times as well.

## Orders and rate equations continued

This is called the rate equation for the reaction. The concentrations of A and B have to be raised to some power to show how they affect the rate of the reaction. These powers are called the orders of reaction with respect to A and B. For UK A' level purposes, the orders of reaction you are likely to meet will be 0, 1 or 2. But other values are possible including fractional ones like 1.53, for example. If the order of reaction with respect to A is 0 (zero), this means that the concentration of A doesn't affect the rate of reaction. Mathematically, any number raised to the power of zero (x0) is equal to 1. That means that that particular term disappears from the rate equation. The overall order of the reaction is found by adding up the individual orders. For example, if the reaction is first order with respect to both A and B (a = 1 and b = 1), the overall order is 2. We call this an overall second order reaction.

## Orders and rate equations continued

You can express this using symbols as:

Writing a formula in square brackets is a standard way of showing a concentration measured in moles per cubic decimetre (litre). You can also write this by getting rid of the proportionality sign and introducing a constant, k.

## Orders and rates continued

*Another possibility: The rate of reaction is proportional to the square of the concentration of* A

This means that if you doubled the concentration of **A**, the rate would go up 4 times (2^{2}). If you tripled the concentration of **A**, the rate would increase 9 times (3^{2}). In symbol terms:

## Orders and rates continued

*Generalising this*

By doing experiments involving a reaction between **A** and **B**, you would find that the rate of the reaction was related to the concentrations of **A** and **B** in this way:

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