Question

For a reactions $A+B\to product$, 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:

$[MPPET/PMT1998;MPPMT2003]$

• 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)

$rate=k{\left[A\right]}^2$

Let the rate of reaction depends on $x$ power of $\left[A\right]$.

Then

$r_1=k{\left[A\right]}^x$ and $r_2=k{\left[2A\right]}^x$

$\therefore \frac{r_1}{r_2}=\frac{{\left[A\right]}^x}{{\left[2A\right]}^x}=\frac{1}{4}={\left(\frac{1}{2}\right)}^2(\because r_2=4r_1)$

$\therefore x=2$, As the reaction rate does not depend upon the concentration of $B$.

Hence, the correct rate law will be $rate=K{\left[A\right]}^2{\left[B\right]}^o$ or $=K{\left[A\right]}^2$