Question

The dimensions of rate constant of a second order reaction involve:
A.Neither time nor concentration
B.Only time
C.Time and concentration
D.Time square and concentration

Answer 1

Hint: The unit of rate constants changes with change in order. For a second order reaction, the rate is directly proportional to the square of concentration of reactant. Rearranging the formula and putting units of respective known variables we will get the answer.
Formula used:
\[{\text{Rate}} = {\text{ Rate constant}} \times {[{\text{A}}]^{{\text{order}}}}\]

Complete step by step answer:
The unit of rate constant changes as the order of reaction changes because the unit of rate is always constant that is \[{\text{mol}}{{\text{L}}^{ - 1}}{{\text{s}}^{ - 1}}\] .
Substituting the value of units for rate and concentration for a second order reaction we will get,
\[{\text{Rate}} = {\text{ Rate constant}} \times {[{\text{A}}]^{\text{2}}}\]
\[\dfrac{{{\text{mol}}{{\text{L}}^{ - 1}}{{\text{s}}^{ - 1}}}}{{{{{\text{(mol}}{{\text{L}}^{ - 1}})}^2}}} = {\text{ Rate constant}}\]
We will get the unit of rate constant as,
\[{\text{Rate constant}} = {\text{mo}}{{\text{l}}^{ - 1}}{\text{L}}{{\text{s}}^{ - 1}}\]
We can rewrite it as: \[{{\text{(mol}}{{\text{L}}^{ - 1}}{\text{)}}^{ - 1}}{{\text{s}}^{ - 1}}\]
 Hence it involves a second which is a unit of time and \[{\text{mol}}{{\text{L}}^{ - 1}}\] which is a unit of concentration. So the rate constant involves time and concentration.

Hence the correct option is C.

Additional information:
 Rate of the reaction is defined as the change in concentration of reactant or product per unit time. As the reaction proceeds the concentration of the reactant decreases and the concentration of product increases. The rate of reaction is always positive. We generally study zero to third order reactions. For a zero order reaction the unit of rate and rate constant is the same.

Note:
Rate constant is a constant of proportionality. It depends upon the nature of reaction and temperature. At a constant temperature and at a particular reaction rate constant remain fixed. The units of rate constant can be calculated from the formula ${\left( {{\text{mol L}}} \right)^{1 - {\text{n}}}}{{\text{s}}^{ - 1}}$, where n is the order of the reaction.