Question

For a first order reaction (at constant temperature)
$A\to P$
Which of the following is correct?

• A. Half life increases as the reaction progresses.
• B. Half life decreases as the reaction progresses.
• C. Half life is constant as the reaction progresses.
• D. None of the above

Answer 1

The correct option is C Half life is constant as the reaction progresses.

Since $\left[A\right]=[A{]}_0{e}^{-kt}$
Here
$[A{]}_0$ is the intial concentration.
$\left[A\right]$ is the concentration at time t
Now, at $t=t_{\frac{1}{2}},\left[A\right]=\frac{[A{]}_0}{2}$
Putting the value in equation:
$\frac{[A{]}_0}{2}=[A{]}_0{e}^{-k{t}_{\frac{1}{2}}}$
Solving,
$t_{\frac{1}{2}}=\frac{\ln 2}{k}$
So half life for first order does not depend on the concentration of the reactants and is a constant value until the temperatureis kept constant.