A: In the reaction
`2NaOH + H_(3)PO_(4) to Na_(2)HPO_(4) + 2H_(2)O`
equivalent weight of `H_(3)PO_(4)` is `(M)/(2)` where M is its molecular weight.
R: `"Equivalent weight"= ("molecular weight")/("n-factor")`

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion
C. If Assertion is true statement but Reason is false
D. If both Assertion and Reason are false statements

Answer

To solve the question regarding the equivalent weight of \( H_3PO_4 \) in the reaction:

\[ 2NaOH + H_3PO_4 \rightarrow Na_2HPO_4 + 2H_2O \]

we will follow these steps:

### Step 1: Identify the Molecular Weight of \( H_3PO_4 \)
The molecular weight (M) of \( H_3PO_4 \) can be calculated by summing the atomic weights of its constituent elements:
- Hydrogen (H): 1 g/mol (3 H atoms)
- Phosphorus (P): 31 g/mol (1 P atom)
- Oxygen (O): 16 g/mol (4 O atoms)

Thus, the molecular weight \( M \) is calculated as:
\[ M = (3 \times 1) + (1 \times 31) + (4 \times 16) = 3 + 31 + 64 = 98 \text{ g/mol} \]

### Step 2: Determine the n-factor of \( H_3PO_4 \)
The n-factor of an acid is defined as the number of \( H^+ \) ions that can be donated by one molecule of the acid. In the reaction, \( H_3PO_4 \) donates 2 \( H^+ \) ions to form \( Na_2HPO_4 \) (since one \( H^+ \) remains in the product). Therefore, the n-factor for \( H_3PO_4 \) in this reaction is 2.

### Step 3: Calculate the Equivalent Weight of \( H_3PO_4 \)
The equivalent weight is given by the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{n-factor}} \]
Substituting the values we have:
\[ \text{Equivalent Weight} = \frac{M}{2} \]

### Conclusion
Thus, the assertion that the equivalent weight of \( H_3PO_4 \) is \( \frac{M}{2} \) is correct.

### Step 4: Verify the Reasoning
The reasoning states that "Equivalent weight = (molecular weight) / (n-factor)" is also correct. Since we have established that the n-factor for \( H_3PO_4 \) is 2, this confirms the reasoning.

### Final Answer
Both the assertion and reasoning are correct.

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