Rate of Reaction Calculations (CIE AS Chemistry)

• During a reaction, the reactants are used up and changed into the products
• This means that as the reaction proceeds, the concentration of reactants decreases and the concentration of products increases
• Therefore, the rate of the reaction is not the same throughout the reaction but changes
• The rate of reaction during the reaction can be calculated from a concentration-time graph.
• The isomerisation of cyclopropane to propene will be taken as an example:

Isomerisation of cyclopropane

The reactant cyclopropane isomerises to form propene

• The concentrations of reactant (cyclopropane) and product (propene) over time can be experimentally obtained

Concentrations of cyclopropane & propene results table

Time (min)	[cyclopropane] (mol dm-3)	[propene] (mol dm-3)
0	1.50	0.00
5	1.23	0.27
10	1.00	0.50
15	0.82	0.68
20	0.67	0.83
25	0.55	0.95
30	0.45	1.05
35	0.37	1.13
40	0.33	1.17

• When taking the measurements, the temperature should be kept the same at all times as a change in temperature will change the rate of reaction
• A concentration-time graph for the concentration of propene as well as cyclopropane can be obtained from the above results
  • As an example, the concentration-time graph for propene is shown below:

Concentration-time graph for propene

The graph shows that the concentration of propene increases with time

Calculating the rate at the start of a reaction

• At the start of the reaction, the concentration-time curve looks almost linear
• The rate at this point can therefore be found by treating the curve as a linear line and by using:

Rate of reaction =  

• Using the graph, the average rate of the reaction over the first 5 minutes for propene is:

 Applying tangents to curves

Line (a) shows the average rate over the first five minutes whereas line (b) shows the actual initial rate found by drawing a tangent at the start of the curve. The calculated rates are very similar for both methods.

 

• Rate of reaction =  
  • Rate of reaction =
  • Rate of reaction = 0.0009 mol dm^-3 s^-1 

Calculating the rate as the reaction proceeds

• The curve becomes shallower with time which means that the rate decreases with time
• The rate of reaction can be calculated by taking short time intervals
  • For example, the rate of reaction from 15 to 20 mins
  • During this time, the concentration of propene increases from 0.68 to 0.83 mol dm^-3:

• Rate of reaction =  
  • Rate of reaction =
  • Rate of reaction = 
  • Rate of reaction = 0.0005 mol dm^-3 s^-1 

• The smaller the time intervals, the more accurate the reaction rate value is
• Even more accurate is to find the rate of reaction at different concentrations of reactant or product at particular time points
• This can be done by drawing tangents at several points on the graph
  • As an example, the rates of reaction at different concentrations of cyclopropane are calculated by drawing the appropriate tangents:

Calculating rate as a reaction progresses

The rate of reaction at 3 different concentrations of cyclopropane is calculated by drawing tangents at those points in the graph

Rate-concentration graph

• The calculated rates can then be summarised in a table to show how the rate of reaction changes with changing concentration of the reactants or products

Change in rate with decreasing concentration of cyclopropane table

[cyclopropane] (mol dm-3)	Rate (10–3 mol dm-3 s-1)
0.5	0.33
1.0	0.67
1.5	1.0

• This data can then be used to plot a rate-concentration graph
• The graph shows that the rate is directly proportional to the concentration of cyclopropane
  • If you double the concentration of cyclopropane the rate of reaction will double too

 Rate-concentration graph

The graph shows a directly proportional correlation between the concentration of cyclopropane and the rate of reaction