Question

If a first order reaction takes $40$ minutes for $75\%$ completion, then time required for $50\%$ completion is

• A. $5 \,min$
• B. $10\, min$
• C. $15\, min$
• D. $20\, min$

Answer 1

Answer: (D)

$20\, min$

Answer 2

$k=\frac{2.303}{t} log \frac{a}{a-x}$ $= \frac{2.303}{40} log \left(\frac{100}{25}\right) \quad\left(log 4 = 0.60206\right)$ $k = 0.035\, min^{-1}$ Time for $50\%$ completion $\left(t_{1/2} \right) = \frac{0.693}{k}$ $t_{1/2} = \frac{0.693}{0.035} = 19.8 \approx 20\, min$