Question

The reaction $C{H}_3-C{H}_2-N{O}_2+O{H}^{-}\to C{H}_3-CH-N{O}_2+H_{2}O$ obeys the rate law for pseudo first order kinetics in the presence of a large excess of hydroxide ion. If 1 percent of nitro ethane undergoes reaction in half a minute when the reactant concentration is $0.002M$, the pseudo first order rate constant is :

• A. $2\times {10}^{-2}mi{n}^{-1}$
• B. $3\times {10}^{-2}mi{n}^{-1}$
• C. $5\times {10}^{-2}mi{n}^{-1}$
• D. $7\times {10}^{-2}mi{n}^{-1}$

Answer 1

The correct option is A $2\times {10}^{-2}mi{n}^{-1}$

1 percent of nitro ethane undergoes reaction in half a minute when the reactant concentration is $0.002M$.

Amount of nitroethane reacted = $\frac{0.002}{0.01}=0.00002$

The expression for the rate constant is $k=\frac{2.303}{t}\log \frac{a}{(a-x)}=\frac{2.303}{0.5}\log \frac{0.002}{(0.002-0.00002)}=2\times {10}^{-2}mi{n}^{-1}$.