- Often a curved graph is obtained or a graph which starts out as a straight line but then curves to form a horizontal line as the reaction peters out, usually due to one of the reactants running out
- The curved section signifies that the relationship between rate and the factor being measured is not directly proportional, so the rate of reaction is different along each point of the curve
- For a curve graph a tangent must be drawn to calculate the change in x and y so the rate of reaction at a particular point during the reaction can be calculated
- Place a ruler on the point being studied and adjust its position so the space on either side of the point between the ruler and curve are equal:
Drawing a tangent to a curve using a ruler
- Use the tangent to calculate the rate of reaction as shown below:Obtaining a tangent on a curve
- The gradient at that point is
GRADIENT = ∆ (PRODUCT) ÷ ∆(TIME)
- You can use this formula to calculate the gradient at any particular point in the curve or you can find the mean rate of reaction by taking the difference between two points on the curve as shown in the following example:
A student analysed the reaction between HCl and Mg by measuring the volume of hydrogen gas given off at regular intervals. The equation for the reaction is:
Mg + 2HCl ⟶ MgCl2 + H2
A graph of the results was plotted shown below:
Calculate the mean rate of reaction between 10s and 40s
- Using a ruler draw two lines upwards from the x-axis at 10 seconds and 40 seconds.
- At the points these lines meet the curve extend two horizontal lines to meet the y-axis and read the values.
- From the graph, the mean rate of reaction between 10 and 40 seconds is found by calculating the total change in the y valued and dividing it by the total time taken:
Total change in volume = 19- 9.5 = 9.5 cm3
Time taken 40-10 = 30 s
Mean rate of reaction = 9.5 ÷ 30 = 0.317 cm3 s-1
When drawing tangents, the line should be extended as far as is convenient for you to perform the calculations. Extending the tangent in this way decreases the amount of uncertainty.