Question

For an elementary reaction $2A+B_2\to 2AB$, if the volume of the vessel is reduced to one-third of its original volume, then the rate of the reaction will:

• A. increase by 27 times
• B. decrease by 27 times
• C. increase by 32 times
• D. decrease by 32 times

Answer 1

The correct option is A increase by 27 times

When the volume is reduced to one third, the pressure is increased to three times.
$rate=k{P}_A^2{P}_{B_2}$
Let a and b be the initial pressures of A and $B_2$ respectively.
After volume change, the pressures of A and $B_2$ are 3a and 3b respectively.
$r_0=k{a}^{2}b$ ...... (1)
$r=k(3a{)}^{2}3b$ ...... (2)
Divide (2) by (1)
$\frac{r}{r_0}=\frac{k(3a{)}^{2}3b}{k{a}^{2}b}=\frac{27}{1}$
Thus, the rate increases 27 times.