Question

Write the unit of rate constant for first order of reaction and second order of reaction.

Hint:

The unit of rate constant depends on the order of the reaction, with higher order reactions having more complex units.

Answer 1

Step 1: Unit of rate constant for first order reaction.
For a first order reaction, the rate law is: \[ \text{Rate} = k[A] \] where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant. The unit of rate is mol/L·s, and the unit of concentration is mol/L. Thus, the unit of \( k \) for a first-order reaction is: \[ \text{Unit of } k = \frac{\text{mol}}{\text{L} \cdot \text{s}} \times \frac{\text{L}}{\text{mol}} = \frac{1}{\text{s}} \]

Step 2: Unit of rate constant for second order reaction.
For a second order reaction, the rate law is: \[ \text{Rate} = k[A]^2 \] where \( k \) is the rate constant and \( [A] \) is the concentration of the reactant. The unit of rate is mol/L·s, and the unit of concentration is mol/L. Thus, the unit of \( k \) for a second-order reaction is: \[ \text{Unit of } k = \frac{\text{mol}}{\text{L} \cdot \text{s}} \times \frac{1}{\left(\frac{\text{mol}}{\text{L}}\right)^2} = \frac{1}{\text{mol} \cdot \text{L} \cdot \text{s}} \]

Step 3: Conclusion.
Thus, the unit of rate constant for a first-order reaction is \( \frac{1}{\text{s}} \), and for a second-order reaction, it is \( \frac{1}{\text{mol} \cdot \text{L} \cdot \text{s}} \).