Question

For a first order reaction $A\to$ product with initial concentration $x{\text{molL}}^{-1},$as half life period of $2.5$ hours. For the same reaction with initial concentration $\frac{x}{2}{\text{molL}}^{-1}$, the half life is:

• A.
  $(2.5\times 2)\text{hours}$
• B.
  $\frac{2.5}{2}\text{hours}$
• C.
  $2.5\text{hours}$
• D.
  Without knowing the rate constant , $t_{1/2}$ cannot be determined from the given data

Answer 1

The correct option is C

$2.5\text{hours}$
For a first order reaction
$t_{1/2}=\frac{0.693}{k}$
Where, $k=\text{rate constant}$
Thus $t_{1/2}$ does not depend on the initial concentration and it remains constant, whatever may be the initial concentration.
So, $t_{1/2}=2.5hrs.$