Question

A substance A decomposes by a first order reaction starting initially with $[A]=2.00m$ and after $200\min ,[A]$ becomes $0.15m$. 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)

$[A{]}_0=2.0m,[A]=0.15m,t=200\min$
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, $t_{1/2}=\frac{0.6932}{k}$
$=\frac{0.6932}{0.01295}$
$=53.50\min$