Question

The rate of a gaseous reaction is given by the expression, r = k [A] [B]. If the volume of the reaction vessel is suddenly reduced to one fourth of the initial volume, the reaction rate relative to the original rate will be ______.

Options

• `1/10`

• `1/8`

• 8

• 16

Answer 1

The rate of a gaseous reaction is given by the expression, r = k [A] [B]. If the volume of the reaction vessel is suddenly reduced to one fourth of the initial volume, the reaction rate relative to the original rate will be 16.

Explanation:

Rate law: r = k [A] [B]

The reaction is first order in A and first order in B, so overall second order.

If volume `V/4`, the concentration increases 4 times because:

`"Concentration" prop 1/"Volume"`

So, 

New [A] = 4[A]

New [B] = 4[B]

Then the new rate becomes

r′ = k (4[A]) (4[B]) = 16 × k [A] [B] = 16 × r