Question

The reaction A$+$B$\to$ products is first order in each of the reactants. How does the rate of reaction change if the concentration of A is increased by factor $3$?

Answer 1

Since, the reaction is first order in each reactant, the rate law expression is rate $=k\left[A\right]\left[B\right]$.....( 1)

The concentration of A is increased by a factor of 3.

$[A{]}^{\prime }=3[A]$.....( 2)

rate' $=k\left[A{]}^{\prime }\right[B]$.....( 3)

Substitute equation (2) in equation (3)

rate' $=k\left(3\right[A\left]\right)\left[B\right]$.....( 4)

Divide equation (4) with equation (1)

$\frac{{\text{rate}}^{\prime }}{\text{rate}}=\frac{k\left(3\right[A\left]\right)\left[B\right]}{k\left[A\right]\left[B\right]}=3$
Hence, the rate will increase by a factor of 3.