Question

The specific rate of a reaction is $1.51\times {10}^{-4}$ lit mole${}^{-1}$ sec${}^{-1}$. If the reaction is commenced with 0.2 mole lit${}^{-1}$ of the reactant, the initial rate of the reaction in mole lit${}^{-1}$ sec${}^{-1}$ is:

• A. $1.5\times {10}^{-4}$
• B. $3\times {10}^{-5}$
• C. $6\times {10}^{-6}$
• D. $6\times {10}^{-5}$

Answer 1

The correct option is C $6\times {10}^{-6}$

For a general reaction of order $n$, the units of rate constant is given as $(mol/litre{)}^{1-n}se{c}^{-1}$.
So for our question, the unit of rate constant is $(mol/litre{)}^{-1}se{c}^{-1}$ so $1-n=-1$.

So, the value of $n=2$, so the reaction is of second order.

The rate is given as $r=k[A{]}^2$. Specific rate of equation is the rate for concentration of 1 $mol/litre$.

From this, the value of k is $1.51\times 10^{-4}$.
$r=1.51\times {10}^{-4}[A{]}^2$.
[A] = $0.2mol/litre$.

Initial rate is $6\times 10^{-6}$.

Hence, option C is correct.