Question

Rate constant does not depend upon unit of concentration for reaction whose order is –
(A) zero
(B) first
(C) fractional
(D) infinite

Answer 1

Hint: units of k(Rate constant) depends upon the unit of r(rate of the reaction) and the concentration of the reactant as per the value of x(order of the reaction) according to $k=\dfrac{r}{{{\text{ }\!\![\!\!\text{ reactant }\!\!]\!\!\text{ }}^{\text{x}}}}$. The unit of r(rate of the reaction) is $\dfrac{mol}{L.\sec }$ and of [reactant] (concentration of reactant ) is $\dfrac{mol}{L}$.

Complete answer:
As we know that the representation of rate of reaction (r) in terms of concentration of the reactants is known as the rate law which is also called as rate equation for rate expression. Mathematically it can be expressed as-
     \[\begin{align}
  & r\propto {{[\text{reactant}]}^{x}} \\
 & r=k\times {{[\text{reactant}]}^{x}} \\
\end{align}\]
Where k is the proportionality constant, also known as the rate constant and x is the order of the reaction.
Order - The sum of powers of the concentration of the reactants in the rate law expression of a chemical reaction is called the order of that chemical reaction. The value of Order of a reaction can be 0, 1, 2, 3 and even a fraction.
As $k=\dfrac{r}{{{\text{ }\!\![\!\!\text{ reactant }\!\!]\!\!\text{ }}^{\text{x}}}}$ , units of k depends upon the unit of r(rate of the reaction) and the concentration of the reactant as per the value of x(order of the reaction). We know that the unit of r(rate of the reaction) is $\dfrac{mol}{L.\sec }$ and of [reactant] (concentration of reactant ) is $\dfrac{mol}{L}$ , So the unit of k will vary with the value of x(order of the reaction).
For zero order reaction, the unit of k is \[\dfrac{mol}{L.\sec }\times {{[\dfrac{L}{mol}]}^{0}}=mol.{{L}^{-1}}.{{\sec }^{-1}}\]
For first order reaction, unit of k is \[\dfrac{mol}{L.\sec }\times {{[\dfrac{L}{mol}]}^{1}}={{\sec }^{-1}}\]
Evidently, the Rate constant does not depend upon the unit of concentration for reaction of first order.

Hence, the correct option is (B) first.

Additional information:
Other names for rate constant (k) are
-velocity constant
-speed constant
-reaction rate constant

Note:
Rate of the reaction(r) is change in concentration with respect to time.
     \[r=\dfrac{\text{change in concentration}}{time}\]
Hence its unit is $\dfrac{mol}{L.\sec }$.
Alternatively, the general formula to determine the unit of k(rate constant) for ${{n}^{th}}$ order reaction is $mo{{l}^{(1-n)}}{{L}^{(n-1)}}{{\sec }^{-1}}$ .