During the kinetic study of the reaction , the following results were obtained, Based on above data, overall order of the reaction is

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Solution

Q.
During the kinetic study of the reaction $2 A + B \to C + D$ , the following results were obtained:

A[M] B[M] initial rate of formation of D

I 0.1 0.1 $6.0 \times 10^{- 3}$

II 0.3 0.2 $7.2 \times 10^{- 2}$

III 0.3 0.4 $2.88 \times 10^{- 1}$

IV 0.4 0.1 $2.40 \times 10^{- 2}$

Based on above data, overall order of the reaction is _______ . [2024]

Ans.
(3)

$2 A + B \to C + D$

$r = - \frac{1}{2} \frac{d [A]}{d t} = - \frac{d [B]}{d t} = \frac{d [C]}{d t} = \frac{d [D]}{d t} = k {[A]}^{p} {[B]}^{q}$

From observation II and III

$\frac{r_{3}}{r_{2}} = \frac{k \times {(0.3)}^{p} \times {(0.4)}^{q}}{k \times {(0.3)}^{p} \times {(0.2)}^{q}} = \frac{2.88 \times 10^{- 1}}{7.2 \times 10^{- 2}}$

$2^{q} = 4, q = 2$

From observation I and IV

$\frac{r_{4}}{r_{1}} = \frac{k \times {(0.4)}^{p} \times {(0.1)}^{q}}{k \times {(0.1)}^{p} \times {(0.1)}^{q}} = \frac{2.40 \times 10^{- 2}}{6.0 \times 10^{- 3}}$

$4^{p} = 4, p = 1$

$r = k {[A]}^{1} {[B]}^{2}$

$O r d e r = 1 + 2 = 3$

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