Mean rate of reaction

A reaction uses up reactants and forms products. The mean rate of reaction tells us how quickly one of these changes happens, on average, over a measured time interval.

To find the mean rate, divide the quantity of reactant used up or product formed by the time taken:

For a reactant, calculate the quantity used up by subtracting the final quantity from the initial quantity. For a product, calculate the quantity formed by subtracting the initial quantity from the final quantity. Then divide the change by the elapsed time.

The rate unit must match the quantity measured. When time is measured in seconds, the units can be:

• $$\mathrm{g/s}$$ for mass in grams;
• $$\mathrm{cm^3/s}$$ for volume in cubic centimetres;
• $$\mathrm{mol/s}$$ for amount in moles, at Higher Tier.

Calculating a mean rate

Suppose the mass of a reactant decreases from $$2.4,\mathrm{g}$$ to $$0.9,\mathrm{g}$$ in $$30,\mathrm{s}$$. The mass used up is $$1.5,\mathrm{g}$$, so:

This means that, on average, $$0.05,\mathrm{g}$$ of the reactant was used up each second during those $$30,\mathrm{s}$$. The rate may have changed during the interval, so the mean rate does not necessarily give the rate at any one exact moment.

Rate at a specific time from a tangent

On a quantity–time graph, the gradient shows how quickly the quantity changes. If the graph is curved, its gradient changes with time, so a gradient measured across an interval gives a mean rate rather than the rate at one specific moment.

To find the rate at a chosen time, draw a tangent: a straight line that touches the curve at that point and follows the curve’s direction there. The gradient of the tangent gives the instantaneous rate at that time.

Calculating the tangent gradient

1. Find the chosen time on the horizontal axis and locate the corresponding point on the curve.
2. Draw a tangent at that point. Extend the line so that its gradient can be measured accurately.
3. Choose two well-separated points on the tangent line. They do not have to lie on the curve.
4. Divide the change in quantity between those points by the change in time:

For example, suppose a tangent drawn at $$30\ \mathrm{s}$$ passes through $$(20\ \mathrm{s}, 30\ \mathrm{cm^3})$$ and $$(40\ \mathrm{s}, 50\ \mathrm{cm^3})$$. Its gradient is:

The instantaneous rate at $$30\ \mathrm{s}$$ is therefore $$1.0\ \mathrm{cm^3,s^{-1}}$$. The two points were used to calculate the gradient of the tangent, not the mean rate along the curve between those times.

If the measured quantity decreases, the tangent has a negative gradient. The rate of disappearance is usually stated as a positive value: the magnitude of that gradient.

Reaction rate graphs

A reaction rate graph shows how the quantity of product formed or reactant used up changes as time passes. Its shape shows how quickly the reaction progresses at different stages.

Drawing a reaction rate graph

Put time on the horizontal axis and the measured quantity on the vertical axis. Label both axes with their units. Plot the measured quantity at each recorded time, then draw a suitable line or smooth curve through the points.

As product forms, the quantity of product increases. Similarly, the total quantity of reactant used up increases as the reaction proceeds.

Interpreting the graph

The steepness, or gradient, shows how quickly the measured quantity is changing:

• A steep section shows a faster reaction: the quantity changes by more in a given time.
• A less steep section shows a slower reaction: the quantity changes by less in the same time.
• A flat section shows that the quantity is no longer changing because the reaction has stopped.

The steepness can change along the graph, so the reaction may be faster at some times than at others. This lets the graph show changes in reaction progress that a single overall average rate would not reveal.