The rate of a reaction, which may also be called its velocity or speed, can be defined with relation to the concentration of any of the reacting substances, or to that of any product of the reaction. If the species chosen is a reactant which has a concentration c at time t the rate is - dc/dt, while the rate with reference to a product having a concentration x at time t is dx/dt. Any concentration units may be used for expressing the rate, thus, if moles per liter are employed for concentration and seconds for the time, the units for the rate are moles `"liter"^(-1) sec^(-1)`. For gas reactions pressure units are sometimes used in place of concentrations, so that legitimate units for the rate would be (mm. Hg) `sec^(-1)` and atm. `sec^(-1)`
The order of a reaction concerns the dependence of the rate upon the concentrations of reacting substances, thus, if the rate is found experimentally to be proportional to the `alpha^(th)` power of the concentration of one of the reactants A, to the `beta^(th)` power of the concentration of a second reactant B, and so forth, via.,
rate `kC_(A)^(alpha) C_(B)^(beta)" " (1)`
the over-all order of the reaction is simply
`n = alpha +beta + ` ---------(2)
Such a reaction is said to be of the `alpha^(th)` order with respect to the substance A, the `beta^(th)` order with respect to B and so on...
(Laidler, K. J., & Glasstone, S. (1948). Rate, order and molecularity in chemical kinetics. Journal of Chemical Education, 25(7), 383.)
In the following questions, a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices on the basis of the above passage.
Assertion: The unit of k is independent of order of reaction.
Reason: The unit of k is moles `L^(-1)s^(-1)`.

Options

A. Assertion and reason both are correct statements and reason is correct explanation for assertion.
B. Assertion and reason both are correct statements but reason is not correct explanation for assertion.
C. Assertion is correct statement but reason is wrong statement.
D. Assertion is wrong statement but reason is correct statement.

Answer

To solve the question, we need to analyze the assertion and reason statements provided regarding the unit of the rate constant \( k \) in relation to the order of a reaction.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states, "The unit of \( k \) is independent of the order of reaction."
- This implies that no matter the order of the reaction, the unit of the rate constant \( k \) remains the same.

2. **Understanding the Reason**:
- The reason states, "The unit of \( k \) is moles \( L^{-1} s^{-1} \)."
- This suggests a specific unit for the rate constant, which may or may not hold true for all orders of reactions.

3. **Analyzing the Rate Law Expression**:
- For a general reaction \( aA + bB \rightarrow cC + dD \), the rate law can be expressed as:
\[ \text{Rate} = k [A]^x [B]^y \]
- Here, \( x \) and \( y \) are the orders with respect to reactants \( A \) and \( B \), respectively, and \( n = x + y \) is the overall order of the reaction.

4. **Determining the Unit of \( k \)**:
- The unit of rate is typically expressed as concentration per time, which can be in moles per liter per second (mol \( L^{-1} s^{-1} \)).
- The unit of concentration is moles per liter (mol \( L^{-1} \)).
- Therefore, the unit of \( k \) can be derived from the rate law:
\[ k = \frac{\text{Rate}}{[A]^x [B]^y} \]
- Substituting the units:
\[ k = \frac{\text{mol} \, L^{-1} \, s^{-1}}{(\text{mol} \, L^{-1})^x (\text{mol} \, L^{-1})^y} = \frac{\text{mol} \, L^{-1} \, s^{-1}}{(\text{mol} \, L^{-1})^{x+y}} = \text{mol}^{1-n} \, L^{-(1-n)} \, s^{-1} \]
- This shows that the unit of \( k \) depends on the overall order \( n \) of the reaction.

5. **Conclusion**:
- Since the unit of \( k \) changes with different orders of reactions (e.g., zero-order, first-order, second-order), the assertion that "the unit of \( k \) is independent of the order of reaction" is **false**.
- The reason, stating that "the unit of \( k \) is moles \( L^{-1} s^{-1} \)," is **true** for zero-order reactions but not universally applicable.

### Final Answer:
- The assertion is **false** and the reason is **true**. Therefore, the correct choice is that the assertion is wrong but the reason is correct.