Question
Consider the reaction, $$2A + B →$$ 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.
$$L\,mo{l^{ - 1}}\,{s^{ - 1}}$$
C.
$${\text{no}}\,{\text{unit}}$$
D.
$$mol\,{L^{ - 1}}\,{s^{ - 1}}$$
Answer :
$$L\,mo{l^{ - 1}}\,{s^{ - 1}}$$
Solution :
For a first order reaction $${t_{\frac{1}{2}}} = \frac{{0.693}}{K}$$ i.e. for a first order reaction $${t_{\frac{1}{2}}}$$ does not depend up on the concentration. From the given data, we can say that order of reaction with respect to $$B = 1$$ because change in concentration of $$B$$ does not change half life. Order of reaction with respect to $$A = 1$$ because rate of reaction doubles when concentration of B is doubled keeping concentration of A constant.
∴ Order of reaction $$= 1 + 1 = 2$$ and units of second order reaction are $$L\,mo{l^{ - 1}}\,{\sec ^{ - 1}}.$$