A different student investigated how the concentration of sulfuric acid affected the rate of the reaction. The student did a different experiment using sulfuric acid of concentration 0.40 mol/dm³. The student calculated the number of moles of hydrogen collected after every 20 seconds. Figure 12 shows the results.

Determine the rate of reaction at 45 seconds. You should draw a tangent on Figure 12. Give your answer in standard form.

The rate of reaction at a particular instant in time is represented by the gradient (steepness) of the curve at that point. Since the graph is a curve, the gradient is constantly changing. To find the gradient at a specific point (t = 45 s), we must draw a tangent. 1. A tangent is a straight line that touches the curve at a single point without crossing it, and which has the same slope as the curve at that point. 2. Once the tangent is drawn, we can calculate its gradient, which is equal to the rate of reaction. The gradient is calculated as the change in the y-axis value divided by the change in the x-axis value (Δy/Δx). 3. We pick two points on the tangent line that are far apart to minimise reading errors. For example, using the points (20 s, 0.004 mol) and (80 s, 0.012 mol): Δy = 0.012 - 0.004 = 0.008 mol Δx = 80 - 20 = 60 s Rate = Δy / Δx = 0.008 / 60 = 0.000133... mol/s. 4. To express this in standard form, we move the decimal point four places to the right, so the exponent is -4. Rate = 1.33 x 10⁻⁴ mol/s.