Question

For the decomposition of a compound $AB$ at $600 \,K$. the following data were obtained .The order for the decomposition of $AB$ is

$[AB] mol \,dm ^{-3}$	Rate of decomposition of AB in mol $dm ^{-3} s ^{-1}$
0.20	$2.75\times 10^{-8}$
0.40	$11.0 \times 10^{-8}$
0.60	$24.75 \times 10^{-8}$

• A. 1
• B. 2
• C. 1.5
• D. 0

Answer 1

Answer: (B)

$A B\longrightarrow $ Product

Rate $=k[A B]^{n} $

$(\text { Rate })_{1}=k[0.20]^{n}=2.75 \times 10^{-8}\,\,\,\,\,\,\,\,\,...(i) $

$\text { (Rate) }_{2}=k[0.40]^{n}=11.0 \times 10^{-8}\,\,\,\,\,\,\,\,\,...(ii) $

Dividing Eq. (ii) by Eq. (i),

$\frac{(\text { Rate })_{2}}{(\text { Rate })_{1}}=\frac{k[0.40]^{n}}{k[0.20]^{n}}=\frac{11.0 \times 10^{-8}}{2.75 \times 10^{-8}}$

$2^{n}=4$

Or $\,\,\,\,\,\,2^{n}=2^{2}$

Hence, $\,\,\,\,\,n=2$