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Chemical Kinetics

Question
CBSEENCH12010080

For the hydrolysis of methyl acetate in aqueous solution, the following results were obtained:

 

t/s

0

30

60

[CH3COOCH3] / mol L–1

0.60

0.30

0.15

 (i) Show that it follows pseudo-first order reaction, as the concentration of water remains constant.

(ii) Calculate the average rate of reaction between the time intervals 30 to 60 seconds.

 (Given log 2 = 0.3010, log 4 = 0.6021)

Solution

For the hydrolysis of methyl acetate to be a pseudo first-order reaction, the reaction should be first order with respect to ester when [H2O] is constant. The rate constant k for a first order reaction is given by:
K space equals fraction numerator 2.303 over denominator straight t end fraction l o g space fraction numerator left square bracket R right square bracket to the power of 0 over denominator left square bracket R right square bracket end fraction
Where,
[R]0 = intial concentration of reactant

[R] =final concentration of reactant

At =30s

 We have
: straight K subscript 1 space equals fraction numerator 2.303 over denominator straight t end fraction log fraction numerator 0.60 over denominator 0.30 end fraction space equals space 2.30 space straight x space 10 to the power of negative 2 end exponent straight s to the power of negative 1 end exponent

Or space at space space straight t equals space 15 straight s

straight K subscript 2 space equals space fraction numerator 2.303 over denominator straight t end fraction log space fraction numerator 0.60 over denominator 0.15 end fraction space equals 2.31 space straight x space 10 to the power of negative 2 end exponent straight s to the power of negative 1 end exponent

It can be seen that the rate constant k for the reaction has a constant value under any given time interval .Hence the given reaction follows pseudo-first order kinetics.

 

(ii) Average rate of reaction between the time interval 30-60 seconds is given by

 Average rate = negative increment open square brackets fraction numerator Ester over denominator increment straight t end fraction close square brackets space equals open square brackets fraction numerator 0.15 minus 0.60 over denominator 60 minus 30 end fraction close square brackets space equals fraction numerator 0.15 over denominator 30 end fraction space equals space 0.005 space mol space straight L to the power of negative 1 end exponent straight s to the power of negative 1 end exponent