Question

For the first - order reaction $T_{av}$ (average life), $T_{50}$ , and $T_{75}$ in the increasing order are :

• A. $T_{50}<T_{av}<T_{75}$
• B. $T_{50}<T_{75}<T_{av}$
• C. $T_{av}<T_{50}<T_{75}$
• D. $T_{av}=T_{50}<T_{75}$

Answer 1

The correct option is A $T_{50}<T_{av}<T_{75}$

For first order reaction

$T_{50}=\frac{0.693}{k}$
$T_{av}=1.44\times T_{50}$

$T_{75}=\frac{2.303}{k}\log \frac{100}{100-75}$
$⟹\frac{2.303}{k}\log 4$
$⟹\frac{2\times 0.693}{k}=2\times T_{50}$

Hence $T_{50}<T_{av}<T_{75}$