A: Molar conductivity of 0.1 M `NH_(4)OH` solution is less than that of 0.001 M `NH_(4)OH` solution.
R: Dilution increases the degree of ionisation of `NH_(4)OH`

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements then mark (4)

Answer

To solve the question regarding the assertion (A) and reason (R) about the molar conductivity of `NH₄OH`, we will analyze both statements step by step.

### Step 1: Understanding Molar Conductivity
Molar conductivity (Λ) is defined as the conductivity (κ) of an electrolyte solution divided by its molar concentration (C). It is expressed as:
\[ \Lambda = \frac{\kappa}{C} \]
For weak electrolytes like `NH₄OH`, molar conductivity depends on the degree of ionization (α) and the concentration of the solution.

### Step 2: Comparing Molar Conductivities
1. **0.1 M `NH₄OH`**: In this solution, the concentration is higher. Since `NH₄OH` is a weak electrolyte, it does not ionize completely. The degree of ionization (α) is relatively low due to the higher concentration, which means fewer ions are available to conduct electricity.

2. **0.001 M `NH₄OH`**: In this more dilute solution, the concentration is lower. The degree of ionization (α) increases as the concentration decreases, allowing more `NH₄⁺` and `OH⁻` ions to be present in the solution. This results in a higher molar conductivity.

### Step 3: Conclusion on Assertion
From the above analysis, we can conclude that the molar conductivity of the 0.1 M `NH₄OH` solution is indeed less than that of the 0.001 M `NH₄OH` solution. Therefore, Assertion (A) is true.

### Step 4: Understanding the Reason
The reason states that dilution increases the degree of ionization of `NH₄OH`. This is consistent with the behavior of weak electrolytes, where dilution leads to an increase in the degree of ionization due to the reduction in the concentration of the undissociated species. This relationship is described by Ostwald's dilution law.

### Step 5: Conclusion on Reason
Since dilution increases the degree of ionization for weak electrolytes like `NH₄OH`, Reason (R) is also true.

### Final Conclusion
Both the assertion (A) and reason (R) are true, and the reason correctly explains the assertion. Therefore, the answer is that both A and R are true, and R is the correct explanation of A.

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