Question

For a reaction $A + B \to$ product, it was found that rate of reaction increases four times if concentration of $'A'$ is doubled, but the rate of reaction remains unaffected. If concentration of $'B'$ is doubled. Hence, the rate law for the reaction is

• A. $rate=k\left[A\right]\left[B\right]$
• B. $rate=k\left[A\right]^{2}$
• C. $rate=k\left[A\right]^{2}\left[B\right]^{1}$
• D. $rate=k\left[A\right]^{2}\left[B\right]^{2}$

Answer 1

Answer: (B)

Let the rate of reaction depends on $x^{th}$ power o f $\left[A\right]$. Then
$r_{1}=k\left[A\right]^{x}$ and $r_{2}=k\left[2A\right]^{x}$
$\therefore \frac{r_{1}}{r_{2}}=\frac{\left[A\right]^{x}}{\left[2A\right]^{x}}=\frac{1}{4}=\left(\frac{1}{2}\right)^{2} \left(\because r_{2}=4r_{1}\right)$
$\therefore x=2.$As the reaction rate does not depend upon the concentration of $B.$ Hence, the correct rate law will be rate
$=K\left[A\right]^{2}\left[B\right]^{\circ} or =K\left[A\right]^{2}$