Question

In first order reaction the concentration of reactant is reduced to 1/8 of the initial concentration in 75 minutes at 298K. what is the half-life period of the reaction in minutes?

• A. 50 min.
• B. 15 min
• C. 30 min.
• D. 25 min

Answer 1

Answer: (D)

25 min

Answer 2

Let a = 1, a-x = 1/8, t = 75 min.

$k = \frac{2.303}{t}\log\frac{a}{a - x} = \frac{2.303}{75}\log\frac{1}{1/8} = \frac{2.303 \times 0.903}{75}\min^{- 1}{}$ For first order reaction,

$t_{1/2} = \frac{0.693}{k} = \frac{0.693 \times 75}{2.303 \times 0.903} = 25\min$