256 14 · SPEED OF CHEMICAL REACTIONS
Example 14.4
The reaction of benzaldehyde with cyanide ions (as catalyst) at
50 °C was studied by the initial rates method:CN(aq)
2C 6 H 5 CHO(aq) ——C 6 H 5 CH(OH)COC 6 H 5 (aq)The results were:
Initial concentration/mol dm^3 Initial rate of reaction
Experiment number [C 6 H 5 CHO(aq)] 0 [CN(aq)] 0 /mol dm (^3) s 1
1 0.500 0.500 1.00 10 ^4
2 1.00 0.500 4.01 10 ^4
3 1.00 1.00 7.98 10 ^4
What is the overall order of reaction? What is the rate constant
at this temperature?
Answer
The rate expression is:
rate of reaction k[C 6 H 5 CHO(aq)]x[CN(aq)]y
Experiment 1 is used as a ‘norm’. Doubling the concentration of benzaldehyde
(experiment 2) quadruples the initial rate. This means that x2.
Doubling the concentration of cyanide ions (experiment 3) produces an initial
rate which is double that of experiment 2. Therefore, y1 so that
overall order x y 2 1 3
The reaction is third order overall and the rate expression becomes
rate of reaction k[C 6 H 5 CHO(aq)]^2 [CN(aq)]
Rearranging this equation and considering the initial rate:
initial rate
k
[C 6 H 5 CHO(aq)] 02 [CN(aq)] 0
For experiment 1,
1.00 10 ^4
k
[0.500]^2 [0.500]
8.00 10 ^4 mol^2 dm^6 s^1
For experiment 2,
4.01 10 ^4
k
[1.00]^2 [0.500]
8.02 10 ^4 mol^2 dm^6 s^1
For experiment 3,
7.98 10 ^4
k
[1.00]^2 [1.00]
7.98 10 ^4 mol^2 dm^6 s^1
The average rate constant at 50 °C is
k
(8.008.027.98) 10 ^4
8.00 10 ^4 mol^2 dm^6 s^1
3