Question

A substance A decomposes by a first order reaction starting initially with $[A] = 2.00 \,m$ and after $200 \min, [A]$ becomes $0.15\, m$. For this reaction $t_{1/2}$ is

• A. 53.49 min
• B. 50.49 min
• C. 48.45 min
• D. 46.45 min

Answer 1

Answer: (A)

$[A]_0 = 2.0 \, m, [A] = 0.15 \,m, t = 200 \min$
For first order reaction
$A_0$ = Initial concentration
$A = $ Final concentration
Rate constant, $k=\frac{2.303}{t} \, \log \frac{[A]_0}{[A]}$
$=\frac{2.303}{200} \, \log \frac{2.0}{0.15}$
$=\frac{2.303}{200} \, (\log \, 200 -\log \, 15)$
$=\frac{2.303}{200} \times (2.3010 -1.1761)$
$=\frac{2.303 \times 1.1249}{200}$
$=0.01295 \, \min^{-1}$
Now, half life, $t_{1/2}=\frac{0.6932}{k}$
$=\frac{0.6932}{0.01295}$
$=53.50 \min$