Question

A first order reactions: $A\to$ Product and a second order reaction: $2R\to Products$; both have halt-time of 20 minutes when they are carried out taking 4 mole $L^{-1}$ of their respective reactants. Number of mole per litre of A and R remaining unreacted after 60 minutes from the start of the reaction, will be respectively:

• A. 1 and 0.5
• B. 0.5 and negligible
• C. 0.5 and 1
• D. 1 and 0.25

Answer 1

The correct option is C 0.5 and 1

In the case of first order reaction $t_{\frac{1}{2}}$ will remain constant as it is independent of initial concentration so.
$4mole{L}^{-1}\stackrel{20min}{\to }2mole{L}^{-1}\stackrel{20min}{\to }1mole{L}^{-1}\stackrel{20min}{\to }0.5mole{L}^{-1}$.
That is, after 60 minutes 0.5 mole $L^{-1}$ of A will be left unreacted.
In the case of second order reaction $t_{\frac{1}{2}}$ is inversely proportional to initial concentration of reactant i.e., $t_{\frac{1}{2}}$ will go on doubling as concentration of reactant will go on getting half.
$4mole{L}^{-1}\stackrel{20min}{\to }2mole{L}^{-1}\stackrel{40min}{\to }1mole{L}^{-1}$.
That is, after 60 minutes, the concentration of R remaining unreacted will be 1 mole $l^{-1}$.