Rate of Reaction Calculations (Cambridge (CIE) AS Chemistry): Revision Note

Rate of Reaction Experimental Calculations

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

Concentrations of cyclopropane & propene results table

• 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

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 = $\frac{\mathbf{change}\mathbf{in}\mathbf{the}\mathbf{amount}\mathbf{of}\mathbf{reactants}\mathbf{or}\mathbf{products}\left(\mathrm{mol}{\mathrm{dm}}^{-3}\right)}{\mathbf{time}\left(s\right)}$ 

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

 Applying tangents to curves

• Rate of reaction = $\frac{\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{reactants}\mathrm{or}\mathrm{products}\left(\mathrm{mol}{\mathrm{dm}}^{-3}\right)}{\mathrm{time}\left(\mathrm{s}\right)}$ 

  • Rate of reaction =$\frac{0.27}{300}$

  • 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 = $\frac{\mathrm{change}\mathrm{in}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{reactants}\mathrm{or}\mathrm{products}\left(\mathrm{mol}{\mathrm{dm}}^{-3}\right)}{\mathrm{time}\left(\mathrm{s}\right)}$ 

  • Rate of reaction =$\frac{\left(0.83\right)-\left(0.68\right)}{\left(1200\right)-\left(900\right)}$

  • Rate of reaction = $\frac{0.14}{300}$

  • 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

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

• 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