Question

Choose the correct statement(s) regarding a first order reaction :
Here,
$t_{\frac{1}{2}}\text{is the half life period for first order reaction}$
$k\text{is the first order rate constant}$

• A. The graph between $t_{\frac{1}{2}}$ (y-axis) and initial concentration of reactant (x-axis) is a straight line parallel to x-axis
• B. The graph between $t_{\frac{1}{2}}$ y-axis) and initial concentration of reactant (x-axis) is a rectangular hyperbola
• C. $t_{\frac{1}{2}}=\frac{\ln 2}{k}$
• D. $t_{\frac{1}{2}}=\frac{[A{]}_0}{2k}$

Answer 1

Answer: (A), (C)

$t_{\frac{1}{2}}=\frac{\ln 2}{k}$

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,
$t_{\frac{1}{2}}=\frac{\ln 2}{k}$

The graph between $t_{\frac{1}{2}}(y-axis)$and concentration of reactant (x-axis )is a straight line parallel to x axis as shown: