Question

Consider the reaction, $2A+B\to$ Products. When concentration of $B$ alone was doubled, the half-life did not change. When the concentration of $A$ alone was doubled, the rate increased by two times. The unit of rate constant for this reaction is

• A. $s^{-1}$
• B. $Lmo{l}^{-1}{s}^{-1}$
• C. No unit
• D. $mol{L}^{-1}{s}^{-1}$

Answer 1

Answer: (B)

Rate $=k[A{]}^x[B{]}^y$
When $[B]$ is doubled, keeping $[A]$ constant half-life of the
reaction does not change.
Now, for a first order reaction $t_{1/2}=\frac{k}{0.693}$
i.e. $t_{1/2}$ is independent of the concentration of the reactant.
Hence the reaction is first order with respect to $B.$ Now
when $[A]$ is doubled, keeping $[B]$ constant, the rate also
doubles. Hence the reaction is first order with respect to $A.$
$\therefore Rate=[A{]}^1[B{]}^1\therefore order=2$
Now for $a{n}^{th}$ order reaction, unit of rate constant is
$(L{)}^{n-1}(mol{)}^{I-n}{s}^{-1}$ when $n=2$ , unit of rate constant is
$Lmo{l}^{-1}{s}^{-1}.$