The molecular weight of chloride of an element is 79. The `Ew` of the elements is 3.82. The atomic weight of the elements is

Options

A. 15.28
B. 7.64
C. 3.82
D. 11.46

Explanation

To find the atomic weight of the element from the given information, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Molecular weight of the chloride (MCl_x) = 79 g/mol
- Equivalent weight (Ew) of the element = 3.82 g/mol

2. **Set Up the Molecular Weight Equation:**
- The molecular weight of the chloride can be expressed as:
\[ \text{Molecular Weight} = \text{Atomic Weight of the element (M)} + x \times \text{Atomic Weight of Chlorine (Cl)} \]
- The atomic weight of chlorine (Cl) is approximately 35.5 g/mol.

3. **Express the Molecular Weight in Terms of Atomic Weight:**
- Thus, we can write:
\[ 79 = M + x \times 35.5 \]

4. **Relate the Molecular Weight to Equivalent Weight:**
- The molecular weight can also be expressed in terms of equivalent weight:
\[ \text{Molecular Weight} = \text{Ew} \times x \]
- Therefore:
\[ 79 = 3.82 \times x \]

5. **Solve for x (Valency of the Element):**
- Rearranging the equation gives:
\[ x = \frac{79}{3.82} \approx 20.68 \]
- Since valency must be a whole number, we round this to the nearest whole number, which is approximately 2.

6. **Calculate the Atomic Weight of the Element:**
- Now, we can find the atomic weight (M) using the value of x:
\[ M = 79 - x \times 35.5 \]
- Substituting x = 2:
\[ M = 79 - 2 \times 35.5 = 79 - 71 = 8 \]
- However, we can also calculate it using the equivalent weight:
\[ \text{Atomic Weight} = \text{Ew} \times x = 3.82 \times 2 = 7.64 \]

7. **Final Answer:**
- The atomic weight of the element is **7.64** g/mol.