Determine the equivalent weight of each given below, if formula weight of these compounds are `X,Y` and `Z` respectively:
(i) `Na_(2)SO_(4)`, (ii) `Na_(3)PO_(4). 12H_(2)O`
(iii) `Ca_(3)(PO_(4))_(2)`

Options

A. `(X)/(2),(Y)/(3),(Z)/(6)`
B. `(X)/(2),Y ,(Z)/(3)`
C. `X,(Y)/(3),(Z)/(3)`
D. `X,Y,Z`

Answer

To determine the equivalent weight of the given compounds, we will use the formula for equivalent weight of salts, which is:

\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight (or Formula Weight)}}{\text{Net Charge on Cation or Anion}} \]

Now, let's calculate the equivalent weight for each compound step by step.

### (i) For `Na₂SO₄`:

1. **Identify the charges**:
- Sodium (Na) has a charge of +1.
- Sulfate (SO₄) has a charge of -2.
- There are 2 sodium ions, contributing a total charge of +2.

2. **Calculate the net charge**:
- The net charge on the cation (Na) is +2.

3. **Formula weight**:
- Let the formula weight of `Na₂SO₄` be `X`.

4. **Calculate the equivalent weight**:
\[ \text{Equivalent Weight} = \frac{X}{2} \]

### (ii) For `Na₃PO₄.12H₂O`:

1. **Identify the charges**:
- Sodium (Na) has a charge of +1.
- Phosphate (PO₄) has a charge of -3.
- There are 3 sodium ions, contributing a total charge of +3.

2. **Calculate the net charge**:
- The net charge on the cation (Na) is +3.

3. **Formula weight**:
- Let the formula weight of `Na₃PO₄.12H₂O` be `Y`.

4. **Calculate the equivalent weight**:
\[ \text{Equivalent Weight} = \frac{Y}{3} \]

### (iii) For `Ca₃(PO₄)₂`:

1. **Identify the charges**:
- Calcium (Ca) has a charge of +2.
- Phosphate (PO₄) has a charge of -3.
- There are 3 calcium ions, contributing a total charge of +6.

2. **Calculate the net charge**:
- The net charge on the cation (Ca) is +6.

3. **Formula weight**:
- Let the formula weight of `Ca₃(PO₄)₂` be `Z`.

4. **Calculate the equivalent weight**:
\[ \text{Equivalent Weight} = \frac{Z}{6} \]

### Summary of Equivalent Weights:
- For `Na₂SO₄`: \(\frac{X}{2}\)
- For `Na₃PO₄.12H₂O`: \(\frac{Y}{3}\)
- For `Ca₃(PO₄)₂`: \(\frac{Z}{6}\)