Question

The rate of a first order reaction is $0.4\, mol\, L^{-1} sec^{-1} $ at $10$ minutes and $0.04\, mol\, L^{-1 } sec^{-1} $ at $20 $ minutes after initiation. The half-life of the reaction is

• A. $2\, minutes$
• B. $6.9\, minutes $
• C. $3.0\, minutes$
• D. $3.3\, minutes.$

Answer 1

Answer: (C)

Let the reaction starting at $ 10$ minutes
$k=\frac{2.303}{t} log \frac{a}{a-x} , \left(Time = 20 - 10 = 10\, minutes\right) $
$=\frac{2.303}{10} log \frac{0,4}{0.04} =\frac{2.303}{10 } $
$t_{1/ 2} =\frac{0.693}{k} =\frac{0.693\times10}{2.303} 3.0\, minutes$