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. $L mol^{-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
$L \,mol^{-1}\, s^{-1} .$