Question

For a first-order reaction, $A⟶B$, with initial concentration $=a$, which of the following relations are correct?

• A. $t_{1/2}=\frac{k}{a}$
• B. $t_{3/4}=2t_{1/2}$
• C. $t_{1/2}=\frac{0.693}{k}$
• D. $t_{1/2}=k\times 0.693$

Answer 1

Answer: (B), (C)

$t_{3/4}=2t_{1/2}$
$t_{1/2}=\frac{0.693}{k}$

For first order, $t=\frac{1}{k}In\frac{a_0}{a_t}$

At $t=t_{1/2}$, $a_t=\frac{a_0}{2}$

$t_{1/2}=\frac{In2}{k}$

At $t=t_{3/4}$, $a_t=a_0-\frac{3a_0}{4}=\frac{a_0}{4}$

$t_{3/4}=\frac{1}{k}.In4=\frac{2In2}{k}$

or $t_{3/4}=2t_{1/2}$