Question

A substance, 'A' decomposes by a first order reaction. Starting initially with [A] = $2.00M$, after $200min$, [A] $=0.250M$. The $t_{1/2}$ and rate constant for the reaction, are respectively:

• A. $66.63s$ and $0.0104s^{-1}$
• B. $66.63min$ and $0.0104mi{n}^{-1}$
• C. $99.93min$ and $0.0347mi{n}^{-1}$
• D. None of these

Answer 1

The correct option is B $66.63min$ and $0.0104mi{n}^{-1}$

For a first order reaction, rate law equation is as follows:
$k=\frac{2.303}{t}lo{g}_{10}\frac{a}{a-x}$
Here, if $t=200min,(a-x)=0.250M,a=$ initial concentration $=2.0M$
So, $k=\frac{2.303}{200}lo{g}_{10}\frac{2.00}{0.25}$
$=\frac{2.303}{200}lo{g}_{10}8$
$=0.0104mi{n}^{-1}$
For first order reaction, half life,
$t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.0104}$
$=66.63min$
Hence, (b) is the correct option.