Question

The rate constant data of the following reactions are as given below:

I. $aA\to Products,k=amol{e}^{-1}Lmi{n}^{-1}$

II. $bB\to Products,k=bmi{n}^{-1}$

The half-lives of both the reactions are the same and equal to 1 hour when molar concentration of reactant is equal to $1.0mol{L}^{-1}$ in each case. If these reactions are carried out simultaneously taking 1 M of the reactant in each case, the ratio $\frac{\left[A\right]}{\left[B\right]}$ after a lapse of 3 hours will be :

• A. 2
• B. 0.5
• C. 4
• D. 1

Answer 1

The correct option is A 2

$aA\to Product$

From the unit of the reaction we can identify that it is a $2^{nd}$ order reaction.

$\because k=amol{e}^{-1}ltmi{n}^{-1}$

$bB\to Product$

$k=bmi{n}^{-1}$

From the unit of the reaction, we can identify that it is a $I^{st}$ order reaction.

$t_{\frac{1}{2}}=\frac{0.693}{k}$; for $I^{st}$ order reaction

$t_{\frac{1}{2}}=\frac{1}{k{A}_0}$; for $I{I}^{nd}$ order reaction

$\frac{\left[A\right]}{\left[B\right]}=\frac{1/4}{1/8}=2$

Hence, the correct option is B.