Question

'A' decomposes to give 'X' by a first order process with a rate constant of $6.93\times {10}^{-2}mi{n}^{-1}$. The reactant 'A' in the presence of a catalyst gives 'Y' via a second order mechanism that has a rate constant of $0.2M^{-1}mi{n}^{-1}$. If both the half-lives are the same, what would the initial concentration of A be?

Answer 1

A first order reaction's half-life is independant of the initial concentration.
For a first order reaction,
$t_{\frac{1}{2}}=\frac{0.693}{k}$
Therefore, $t_{\frac{1}{2}}$= 10 minutes
$t_{\frac{1}{2}}$ for a second order reaction $=\frac{1}{k\times a_0}$
$10=\frac{1}{0.2\times a_0}$
$a_0=0.5M$