7.5 - Interpreting reaction-rate graphs

Axes and quantities

A reaction-rate graph usually has time on the horizontal axis. The vertical axis shows a measured quantity related to a reactant or product.

Always read the axis label before deciding what the curve means. A product graph often rises because more product is formed. A reactant graph often falls because reactant is used up. A mass graph can rise or fall depending on what mass is being measured. For example, the mass of a product may increase, but the mass of an open reaction flask may decrease if a gas escapes.

For this lesson, "amount" means the measured graph quantity, such as volume, mass or concentration. A graph of volume of gas against time can therefore give a rate in $\mathrm{cm}^{3}/\mathrm{s}$. A graph of concentration against time can give a rate in mol dm-3 s-1 if concentration is measured in mol dm-3 and time is measured in seconds.

Gradient as rate

The gradient of an amount-against-time graph tells you the rate of change of that amount. The gradient is the change in the vertical-axis quantity divided by the change in time.

For a straight section of graph, use two points on that section. For a curve, a tangent can be drawn at the time you are interested in, and the gradient of the tangent gives the rate at that time. Choose two well-separated points on the tangent, not on the curve, when calculating its gradient.

[DIAGRAM: asset_name: product_graph_gradient: Product graph showing gradient, tangent and plateau - diagram 1; asset_slug: 167_7_5_interpreting_reaction_rate_graphs_diagram1; file: 167_7_5_interpreting_reaction_rate_graphs_diagram1_corrected.png; recommended_method: deterministic_drawn; description: Exact monochrome graph of volume of gas produced against time. The x-axis is labelled time / s and the y-axis is labelled volume of gas / cm3. A single curve rises steeply from 0, becomes shallower, then plateaus at about 80 cm3. The graph includes a tangent at 40 s, a gradient triangle labelled change in volume and change in time, and labels for faster initial rate, slower later rate and plateau: rate = 0. Assessed graph visual; deterministic drawing is used because axes, curve shape, tangent and gradient labels must be exact.]

Worked example: a reaction produces $42\,\mathrm{cm}^{3}$ of gas in the first 30 s.

That is a mean rate for the first 30 s. It does not mean the rate was exactly $1.4\,\mathrm{cm}^{3}/\mathrm{s}$ at every moment during those 30 s; the curve may be steeper at the start and less steep later.

For a falling reactant graph, the mathematical gradient is negative because the y-value decreases. In chemistry, the rate of using up the reactant is usually reported as a positive value by using the size of the decrease.

Example: the concentration of a reactant decreases from 0.80 mol dm-3 to 0.50 mol dm-3 in 60 s.

The next check uses the same gradient idea for a reactant graph, where the reported rate uses the positive size of the decrease.

Steepness and plateau

The shape of a reaction-rate graph is part of the answer. Use the words steeper, shallower, horizontal, constant, plateau and gradient carefully.

For a product graph:

For a reactant graph: