Question

The rate constant of third order reaction is:
(A) \[{\text{mol li}}{{\text{t}}^{ - 1}}{\text{ }}{{\text{s}}^{ - 1}}\]
(B) \[{\text{mo}}{{\text{l}}^{ - 2}}{\text{ }}{{\text{L}}^2}{\text{ }}{{\text{T}}^{ - 1}}\]
(C) \[{\text{mo}}{{\text{l}}^{ - 1}}{\text{ lit }}{{\text{s}}^{ - 1}}\]
(D) \[{\text{mo}}{{\text{l}}^{ - 2}}{\text{ li}}{{\text{t}}^{ - 1}}{\text{ }}{{\text{s}}^{ - 1}}\]

Answer 1

Hint: Use the following formula for the units of the rate constant of nth order reaction.
\[{\text{Unit}} = {\left( {{\text{mol li}}{{\text{t}}^{ - 1}}} \right)^{1 - n}}{\text{ }}{{\text{s}}^{ - 1}}\]
In the above formula, substitute 3 for the value of n and obtain the units of the rate constant for third order reaction.

Complete step by step answer:
A rate law expression is the relationship between the rate of the reaction, the rate constant of the reaction and the specific reaction rate.
For nth order reaction, the rate law expression is, \[{\text{rate }} = k \times {\left[ {{\text{reactant}}} \right]^n}\] .
Here, k is the rate constant or specific reaction rate.
For nth order reaction, the rate of the reaction is proportional to the nth order of the reactant concentration.
Thus, for the first order reaction, \[{\text{rate }} = k \times {\left[ {{\text{reactant}}} \right]^1}\].
Thus, for the second order reaction, \[{\text{rate }} = k \times {\left[ {{\text{reactant}}} \right]^2}\].
Thus, for the third order reaction, \[{\text{rate }} = k \times {\left[ {{\text{reactant}}} \right]^3}\].
Obtain the units of the rate constant for third order reaction.
\[{\text{Unit}} = {\left( {{\text{mol li}}{{\text{t}}^{ - 1}}} \right)^{1 - n}}{\text{ }}{{\text{s}}^{ - 1}} \\
{\text{Unit}} = {\left( {{\text{mol li}}{{\text{t}}^{ - 1}}} \right)^{1 - 3}}{\text{ }}{{\text{s}}^{ - 1}} \\
{\text{Unit}} = {\left( {{\text{mol li}}{{\text{t}}^{ - 1}}} \right)^{ - 2}}{\text{ }}{{\text{s}}^{ - 1}} \\
{\text{Unit}} = {\text{mo}}{{\text{l}}^{ - 2}}{\text{ li}}{{\text{t}}^2}{\text{ }}{{\text{s}}^{ - 1}} \]
\[{\text{Unit}} = {\text{mo}}{{\text{l}}^{ - 2}}{\text{ li}}{{\text{t}}^2}{\text{ }}{{\text{T}}^{ - 1}}\]
Here, the second is replaced with T for the unit of time.
The unit for the rate constant of third order reaction is \[{\text{mo}}{{\text{l}}^{ - 2}}{\text{ }}{{\text{L}}^2}{\text{ }}{{\text{T}}^{ - 1}}\] :
You can also write the unit for the rate constant of third order reaction as \[{{\text{M}}^{ - 2}}{\text{ }}{{\text{T}}^{ - 1}}\] :
Here, M represents the molarity or molar concentration. The unit of molarity is moles per litre.

So, the correct option is the option (B).

Note: You can use the following alternate approach to obtain units of the rate constant for the third order reaction.
\[{\text{rate }} = k \times {\left[ {{\text{reactant}}} \right]^3}\]
Rearrange the above equation. Substitute the units of rate and the reactant concentration
\[k = \dfrac{{{\text{rate}}}}{{{{\left[ {{\text{reactant}}} \right]}^3}}}{\text{ }} \\
k = \dfrac{{{\text{mol li}}{{\text{t}}^{ - 1}}{\text{ }}{{\text{T}}^{ - 1}}}}{{{{\left( {{\text{mol li}}{{\text{t}}^{ - 1}}} \right)}^3}}}{\text{ }} \\
k = {\text{mo}}{{\text{l}}^{ - 2}}{\text{ li}}{{\text{t}}^2}{\text{ }}{{\text{T}}^{ - 1}}\]