Question
For the reaction system : $$2NO\left( g \right) + {O_2}\left( g \right) \to 2\,N{O_2}\left( g \right)$$ volume is
suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order
with respect to $${O_2}$$ and second order with respect to $$NO,$$ the rate of reaction will
A.
diminish to one-eighth of its initial value
B.
increase to eight times of its initial value
C.
increase to four times of its initial value
D.
diminish to one-fourth of its initial value
Answer :
increase to eight times of its initial value
Solution :
$$r = k\left[ {{O_2}} \right]{\left[ {NO} \right]^2}.$$ When the volume is reduced to $$\frac{1}{2},$$ the $$conc.$$ will double
∴ New rate $$ = k\left[ {2{O_2}} \right]{\left[ {2NO} \right]^2} = 8\,k\left[ {{O_2}} \right]{\left[ {NO} \right]^2}$$
The new rate increases to eight times of its initial.