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For the non-stoicheometric reaction : $2 A + B \to C + D$ , the following kinetic data were obtained in three separate experiments, all at 298k.

Initial
concentration[A] Initial Conc[B] Initial rate of
formation of C [mol L^-1S^-1]
0.1 M 0.1 M 1.2 x10^-3
0.1 M 0.2M 1.2 x10^-3
0.2M 0.1 M 2.4 x10^-3
The rate law for the formation of C is

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$\frac{dc}{dt} = k [A]$

$\frac{dc}{dt} = k [A] [B]$

$\frac{dc}{dt} = k [A]^{2} [B]$

$\frac{dc}{dt} = k [A] [B]^{2}$

answer is A.

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Detailed Solution

Let order wrt A, B are a,b respectively
$∴ \frac{dc}{dt} = K \cdot [A]^{a} [B]^{b}$
$\begin{array}{l} 1 .2 \times 10^{- 3} = K [0 .1]^{a} [0 .1]^{b} ⟶ (1) 1 .2 \times 10^{- 3} = K [0 .1]^{a} [0 .2]^{b} ⟶ (2) \\ 2 .4 \times 10^{- 3} = K [0 .2]^{a} [0 .1]^{b} ⟶ (3) \frac{(2)}{(1)} \Rightarrow {(\frac{0 .2}{0 .1})}^{b} = 1 (2)^{b} = 1 \Rightarrow b = 0 \frac{(3)}{(1)} \Rightarrow {(\frac{0 .2}{0 .1})}^{a} = 2 \end{array}$ $(2)^{a} = 2 \Rightarrow a = 1 ∴ Rate law will be \frac{dc}{dt} = K [A]$

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