Question

When initial concentration of a reactant is double in a reaction, its half-life period is not affected. the order of the reaction is:

• A. more then zero but less then first
• B. zero
• C. first
• D. second

Answer 1

The correct option is C first

For a zero order reaction $t_{\frac{1}{2}}$is directly proportional to the initial concentration of the reaction $\lceil R_O\rceil$

$t_{\frac{1}{2}}\alpha \left[R_O\right]$
For a first order reaction
$K=\frac{2.303}{t_{\frac{1}{2}}}log\frac{\left[R_O\right]}{\left[R\right]}at{t}_{\frac{1}{2}},\left[R\right]=\frac{\left[R_O\right]}{2}$
So the above equation becomes

$K=\frac{2.303}{t_{\frac{1}{2}}}log=\frac{\left[R_O\right]}{\frac{\left[R_O\right]}{2}}{t}_{\frac{1}{2}}=\frac{2.303}{K}=log2=\frac{2.303}{k}=0.3010$

$t_{\frac{1}{2}}=\frac{0.693}{K}$
this means that half life period is independent of initial concentration of a reactant.
conclusion: Hence the answer is first order