The equivalent weight of an element is `4`. Its chloride has a vapour density `59.25`. Find the valency of element.

Options

A. 4
B. 3
C. 2
D. 1

Answer

To solve the problem step by step, we will follow the information given in the question and apply the relevant formulas.

### Step 1: Understand the given data
- Equivalent weight of the element = 4 g/equiv
- Vapor density of the chloride = 59.25

### Step 2: Calculate the molecular mass of the chloride
The formula for vapor density (VD) is given by:
\[ \text{Vapor Density} = \frac{\text{Molecular Mass}}{2} \]
From the question, we can rearrange this to find the molecular mass (MM) of the chloride:
\[ \text{Molecular Mass} = \text{Vapor Density} \times 2 \]
Substituting the given vapor density:
\[ \text{Molecular Mass} = 59.25 \times 2 = 118.5 \text{ g/mol} \]

### Step 3: Calculate the equivalent weight of the chloride
The equivalent weight of the chloride can be calculated as:
\[ \text{Equivalent Weight of Chloride} = \text{Equivalent Weight of Element} + \text{Equivalent Weight of Chlorine} \]
The equivalent weight of chlorine (Cl) is approximately 35.5 g/equiv. Therefore:
\[ \text{Equivalent Weight of Chloride} = 4 + 35.5 = 39.5 \text{ g/equiv} \]

### Step 4: Use the equivalent weight to find the valency of the element
The relationship between molecular weight (MW), equivalent weight (EW), and valency (n) is given by:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{Valency}} \]
Rearranging this gives:
\[ \text{Valency} = \frac{\text{Molecular Weight}}{\text{Equivalent Weight}} \]
Substituting the values we have:
\[ \text{Valency} = \frac{118.5}{39.5} \]
Calculating this gives:
\[ \text{Valency} \approx 3 \]

### Conclusion
The valency of the element is **3**.

---