Question

A certain reaction obeys the rate equation (in the integrated form) $[C^{(1-n)}-C_0^{(1-n)}]=(n-1)$ kt where C${}_o$ is the initial concentration of C is the concentration after time, t. Then:

• A. the unit of k for n = 1 is sec${}^{-1}$
• B. the unit of k for n = 2 is litre mol${}^{-1}$ sec${}^{-1}$
• C. the unit of k for n = 3 is mol litre${}^{-1}$ sec${}^{-1}$
• D. the unit of k for n = 3 is litre${}^2$ mol${}^{-1}$ sec${}^{-1}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A the unit of k for n = 1 is sec${}^{-1}$
B the unit of k for n = 2 is litre mol${}^{-1}$ sec${}^{-1}$
D the unit of k for n = 3 is litre${}^2$ mol${}^{-1}$ sec${}^{-1}$

The expression for the unit of k is $k={\left(\frac{mol}{litre}\right)}^{1-n}\times s^{-1}$

For the first order reaction, n is 1:
The unit of k will be $k={\left(\frac{mol}{litre}\right)}^{1-1}\times s^{-1}=s^{-1}$

For the second-order reaction, n is 2:
The unit of k will be $k={\left(\frac{mol}{litre}\right)}^{1-2}\times s^{-1}={\left(\frac{mol}{litre}\right)}^{-1}\times s^{-1}$

For the third-order reaction, n is 3:
The unit of k will be $k={\left(\frac{mol}{litre}\right)}^{1-3}\times s^{-1}={\left(\frac{mol}{litre}\right)}^{-2}\times s^{-1}$

Hence, option A, B and D are correct.