Question

$A + B \longrightarrow \text { Product }$
For the above reaction following initial rates were given at various initial concentration

Initial conc. of $A\,ML^{-1}$	Initial conc. of $B$ in $ML^{-1}$	Rate in $ML^{-1}S^{-1}$
$0.1$	$0.1$	$0.05$
$0.2$	$0.1$	$0.1$
$0.1$	$0.2$	$0.05$

Determine the rate constant.

Answer 1

$R = K [ A ]^{ n }[ B ]^{ m }$
$0.05= K (0.1)^{ n }(0.1)^{ m }$ ...(i)
$0.1= K (0.2)^{ n }(0.1)^{ m }$ ...(ii)
$0.05= K (0.1)^{ n }(0.2)^{ m }$ ...(ii)
From eq. (ii) $\div$ (i)
$2=2^{n}$
$n=1$
From eq. (iii) $\div$ (i)
$1=2^{m}$
$m=0$
$\therefore $ Rate law : $R = K [ A ]$
and $K =\frac{ R }{[ A ]}=\frac{0.05}{0.1}=0.5\, s ^{-1}$
$K =0.5\, s ^{-1}$