Question

For a reaction $A+B\to$ product, it was found that rate of reaction increases four times if concentration of ${}^{\prime }{A}^{\prime }$ is doubled, but the rate of reaction remains unaffected. If concentration of ${}^{\prime }{B}^{\prime }$ 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
$=K{\left[A\right]}^2{\left[B\right]}^{\circ }or=K{\left[A\right]}^2$