10.78 g of `H_3 PO_4` in 550 ml solution is 0.40 N. Thus this acid:

Options

A. has been neutralized to `HPO_(4)^(2-)`
B. has been neutralized to `PO_(4)^(3-)`
C. has been reduced to `HPO_(3)^(2-)`
D. has been neutralized to `H_2 PO_(4)^(-)`

Answer

To solve the problem, we need to determine the equivalent weight of phosphoric acid (H₃PO₄) and its n-factor, and then identify the correct option based on the information provided.

### Step-by-Step Solution:

1. **Given Data:**
- Mass of H₃PO₄ = 10.78 g
- Volume of solution = 550 mL = 0.550 L (since 1 L = 1000 mL)
- Normality (N) = 0.40 N

2. **Using the Normality Formula:**
The formula for normality is given by:
\[ N = \frac{\text{Weight}}{\text{Equivalent Weight} \times \text{Volume in Liters}} \]
Rearranging this formula to find the equivalent weight:
\[ \text{Equivalent Weight} = \frac{\text{Weight}}{N \times \text{Volume in Liters}} \]

3. **Substituting the Values:**
Substitute the known values into the equation:
\[ \text{Equivalent Weight} = \frac{10.78 \, \text{g}}{0.40 \times 0.550 \, \text{L}} \]

4. **Calculating the Volume Contribution:**
Calculate the denominator:
\[ 0.40 \times 0.550 = 0.22 \]

5. **Calculating the Equivalent Weight:**
Now substitute this back into the equation:
\[ \text{Equivalent Weight} = \frac{10.78}{0.22} \approx 49 \, \text{g/equiv} \]

6. **Finding the Molar Mass of H₃PO₄:**
The molar mass of H₃PO₄ can be calculated as follows:
- Hydrogen (H) = 1 g/mol, so for 3 H: \(3 \times 1 = 3\)
- Phosphorus (P) = 31 g/mol
- Oxygen (O) = 16 g/mol, so for 4 O: \(4 \times 16 = 64\)

Therefore, the molar mass of H₃PO₄ is:
\[ 3 + 31 + 64 = 98 \, \text{g/mol} \]

7. **Finding the n-factor:**
The n-factor can be calculated using the formula:
\[ \text{n-factor} = \frac{\text{Molar Mass}}{\text{Equivalent Weight}} = \frac{98}{49} = 2 \]

8. **Conclusion:**
Since the n-factor is 2, it indicates that H₃PO₄ can donate 2 protons (H⁺ ions) in a reaction. Therefore, the correct option based on the information provided is that H₃PO₄ has been neutralized to HPO₄²⁻.

### Final Answer:
The acid H₃PO₄ has an equivalent weight of 49 g/equiv and an n-factor of 2.

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