Graphs for Rates (Higher Tier)

Interpreting Reaction Rate Graphs

Graphs are a key way to understand how fast a chemical reaction happens. Two common types of graphs used to show rates of reaction are:

• Concentration vs time graphs: These show how the concentration of a reactant or product changes as the reaction proceeds.
• Volume of gas vs time graphs: These show how much gas is produced over time if the reaction releases a gas.

The initial rate of reaction is the rate right at the start, when the reaction begins. On a graph, this is the steepness (gradient) of the curve at time zero.

The shape of the curve tells us how the rate changes:

• At the start, the curve is usually steep because the reactants are at their highest concentration, so the reaction is fastest.
• As the reaction continues, the curve becomes less steep because reactants are used up and the rate slows down.
• Eventually, the curve flattens out when the reaction finishes 1 no more reactants remain or the reaction has reached completion.

For example, a concentration-time graph for a reaction that uses up a reactant will start high and decrease over time, flattening as the reactant runs out.

The volume of gas-time graph will start at zero and increase as gas is produced, then level off when the reaction stops producing gas.

For instance, if magnesium reacts with hydrochloric acid, the volume of hydrogen gas produced will increase quickly at first, then slow down as the magnesium is used up.

Calculating Rate from Graphs

The rate of reaction at any point on a graph is the gradient (steepness) of the curve at that point.

To find the rate at a specific time:

• Draw a tangent to the curve at that point (a straight line that just touches the curve).
• Calculate the gradient of the tangent using the formula:

Rate = $\frac{\text{change in y}}{\text{change in x}}$

For concentration-time graphs, the rate units are usually mol/dm8/s or g/dm8/s, depending on what is measured.

For volume of gas-time graphs, the rate units are cm8/s or dm8/s.

Comparing rates from different graphs means comparing their gradients at the same time point (usually at the start).

For example, if one reactions graph has a steeper initial tangent than another, it means the first reaction is faster initially.

For instance, if a concentration-time graph shows concentration dropping from 0.50 mol/dm8 to 0.30 mol/dm8 in 20 seconds, the average rate over that time is:

$\text{Rate} = \frac{0.50 - 0.30}{20} = \frac{0.20}{20} = 0.01 \text{ mol/dm}^3/\text{s}$

Effect of Concentration on Graphs

Increasing the concentration of reactants increases the rate of reaction.

On concentration-time or volume-time graphs, this is seen as a steeper initial gradient because the reaction starts faster.

Higher concentration means more particles in the same volume, so more frequent collisions occur, speeding up the reaction (see Collision Theory in another topic).

The shape of the graph changes with concentration:

• Higher concentration graphs start steeper and reach completion faster.
• Lower concentration graphs have gentler slopes and take longer to finish.

For example, if hydrochloric acid concentration is increased in a reaction with magnesium, the volume of hydrogen gas produced rises more quickly and levels off sooner.

For instance, comparing two volume-time graphs for the same reaction but different acid concentrations, the graph with higher concentration will have a steeper initial slope and finish earlier.

Effect of Temperature on Graphs

Increasing temperature increases the rate of reaction.

On graphs, this is seen as a steeper initial gradient because particles move faster and collide more energetically.

The graph shape changes with temperature:

• Higher temperature graphs rise more quickly and finish sooner.
• Lower temperature graphs have gentler slopes and take longer to complete.

For example, a volume-time graph for magnesium and acid at 406C will show gas produced faster than at 206C.

For instance, comparing two concentration-time graphs for the same reaction at different temperatures, the higher temperature graph has a steeper initial slope and reaches completion earlier.