MCQ
For the reaction $2A + B \to C$,the values of initial rate at different reactant concentrations are given in the table below: The rate law for the reaction is

$[A] (mol\,L^{-1})$ $[B] (mol\,L^{-1})$ Initial Rate $(mol\, L^{-1}\,s^{-1} )$
$0.05$ $0.05$ $0.045$
$0.10$ $0.05$ $0.090$
$0.20$ $0.10$ $0.72$

 

  • A
    Rate $= k[A]^2[B]^2$
  • Rate $= k[A][B]^2$
  • C
    Rate $= k[A][B]$
  • D
    Rate $= k[A]^2[B]$

Answer

Correct option: B.
Rate $= k[A][B]^2$
b
$r\, = \,K{[A]^x}\,{[B]^y}$

$0.045\, = \,K{(0.05)^x}{(0.05)^y}$  ...... $(1)$

$0.090\, = \,K{(0.10)^x}{(0.05)^y}$   .......$(2)$

$0.72\, = \,K{(0.20)^x}{(0.10)^y}$     ........$(3)$  

Diving $(1)$ by $(2)$ We get

$\frac{{0.045}}{{0.090}}\, = \,{\left( {\frac{{0.05}}{{0.10}}} \right)^x}\, \Rightarrow \,x = 1$

Diving $(2)$ by $(3)$

$\frac{{0.090}}{{0.720}}\, = \,{\left( {\frac{{0.10}}{{0.20}}} \right)^x}\,{\left( {\frac{{0.05}}{{0.10}}} \right)^y}\, \Rightarrow \,y = 2\,$

Hence, $r\, = \,K[A]\,{[B]^2}$

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