Question

Consider the reaction, $2A+B\to \text{products}$. When the concentration of 'B' alone was doubled, the half-life did not change. When the concentration of 'A' alone was doubled the rate increased by two times. The unit rate of constant for this reaction is

• A. $s^{-1}$
• B. $mo{l}^{-1}{L}^1{s}^{-1}$
• C. No unit
• D. $mol{L}^{-1}{s}^{-1}$

Answer 1

The correct option is B $mo{l}^{-1}{L}^1{s}^{-1}$

Consider the reaction,
$2A+B\to \text{products}$.
When the concentration of B alone was doubled, the half-life did not change. When the concentration of A alone was doubled the rate increased by tow times.
We know that for a first order reaction
$t_{1/2}=\frac{0.693}{K}$
Half-life does not depend on the concentration of reactants.
Hence the order of 'B' will be one.


By initial rate method,

$\frac{r_1}{r_2}={\left(\frac{[A_o{]}_1}{[A_o{]}_2}\right)}^p$

For reactant 'A'

$\frac{R}{2R}={\left(\frac{A}{2A}\right)}^a$

$\frac{1}{2}={\left(\frac{1}{2}\right)}^a$

Thus, an order of reaction with respect to A is also one.

Hence, $\text{Total order}=1+1=2$
The unit rate of constant for reaction is
$mo{l}^{1-n}{L}^{n-1}tim{e}^{-1}$
where n is order of the reaction

When $n=2$
The unit rate of constant for reaction is
$mo{l}^{-1}{L}^1{s}^{-1}$
Thus, option B is correct