Assertion (A): Molarity of 0.1 N solution of HCI is 0.1M.
Reason (R): Normality and molarity of a solution are always equal

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is True

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step 1: Understanding the Assertion
The assertion states that the molarity of a 0.1 N solution of HCl is 0.1 M.

- **Molarity (M)** is defined as the number of moles of solute per liter of solution.
- **Normality (N)** is defined as the number of equivalents of solute per liter of solution.

For HCl, which is a strong acid, it dissociates completely in water to give one hydrogen ion (H⁺) per molecule of HCl. Therefore, the equivalent factor (n-factor) for HCl is 1.

Since the normality of the solution is 0.1 N and the n-factor is 1, we can conclude that:
\[ \text{Normality (N)} = \text{n-factor} \times \text{Molarity (M)} \]
Thus,
\[ 0.1 N = 1 \times \text{Molarity (M)} \]
This implies:
\[ \text{Molarity (M)} = 0.1 M \]

**Conclusion for Assertion**: The assertion is true.

### Step 2: Understanding the Reason
The reason states that normality and molarity of a solution are always equal.

This statement is not universally true. Normality and molarity are equal only when the n-factor is 1, which is the case for HCl. However, for other acids, such as sulfuric acid (H₂SO₄), the n-factor is 2, and in that case, normality is twice the molarity.

For example:
- For H₂SO₄, if the molarity is 0.1 M, the normality would be:
\[ \text{Normality} = 2 \times \text{Molarity} = 2 \times 0.1 M = 0.2 N \]

**Conclusion for Reason**: The reason is false.

### Final Conclusion
- Assertion (A) is true.
- Reason (R) is false.

### Summary
- **Assertion (A)**: True (Molarity of 0.1 N solution of HCl is indeed 0.1 M).
- **Reason (R)**: False (Normality and molarity are not always equal; it depends on the n-factor).