Question

For a reaction $2 A+B \rightarrow P$, when concentration of $B$ alone is doubled, $t_{1 / 2}$ does not change and when concentrations of both $A$ and $B$ is doubled, rate increases by a factor of $4$ . The unit of rate constant is,

• A. $s ^{-1}$
• B. $L \,mol ^{-1} \,s ^{-1}$
• C. $mol \,L ^{-1} \,s ^{-1}$
• D. $L ^{2} \,mol ^{-2} \,s ^{-1}$

Answer 1

Answer: (B)

Rate law: $r=k[A]^{\alpha}[B]^{\beta}, B $follows first order kinetics.
$\therefore \beta=1$
$\frac{r_{2}}{r_{1}}=\frac{[2 A]^{\alpha}[2 B]^{\beta}}{[A]^{\alpha}[B]^{\beta}}$
or, $4=2^{\alpha+\beta}$
or, $\alpha+\beta=2$
or, $\alpha=1$
$\therefore $ overall order of reaction $=2$
Hence unit of rate constant $= L. mol ^{-1} \,.S ^{-1}$