Sarthaks Test
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a). A first order reaction takes 40 minutes for 30 % decomposition. Calculate 1/2

b). The following results have been obtained during the kinetics of the reaction: 

2A + B → C + D

Experiment No.   [A][B]Initial Rate of formation of D
10.1 M0.1 M6.0 × 10−3 M min−1
20.3 M0.2 M7.2× 10−2  M min−1
30.3 M0.4 M2.88 × 10−1 M min−1
40.4 M0.1 M2.4 × 10−2 M min −1

Determine the Rate law and the rate constant for the reaction:

1 Answer

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(a) k = \(\frac{2.303}{t}\) log \(\frac{[A]_o}{[A]}\) 

Substituting the values, we have

k = \(\frac{2.303}{40}\) log \(\frac{100}{70}\) 

or k = \(\frac{2.303}{40}\) x 0.159 = 0.0089 min-1 

t1/2 \(\frac{0.693}{k}\) = \(\frac{0.693}{0.0089}\) = 77.86 minutes

(b) Suppose order w.r.t A is a and w.r.t B is b Rate = k [A]a [B]b 

Rate law expression is: Rate = k[A][B]2.

k can be calculated as in the first method.

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