Question

It takes $1h$ for a first order reaction to go to $50$ completion. The to ta l time required for the same reaction to reach $87.5$ completion will be

• A. 1.75 h
• B. 6.00 h
• C. 3.50 h
• D. 3.00 h

Answer 1

Answer: (D)

For Ist order reaction
$t_{1/2}=\frac{0.693}{k}$
$1=\frac{0.693}{k}$
$\therefore k=\frac{0.693}{1}$
Also, $t=\frac{2.303}{k}log\frac{a}{a-x}$
For $87.5\%$ completion
$t=\frac{2.303}{k}log\frac{a}{a-0.875}$
$=\frac{2.303}{0.693}$ log 8
$=\frac{2.303}{0.693}\times 3\times 0.3010=3h$