An element A forms a chloride which contains 29.34% by weight of chloride and is isomorphous with KCl. The atomic weight of A is

Options

A. 85.49
B. 40
C. 23
D. 137.5

Answer

To find the atomic weight of element A that forms a chloride with 29.34% by weight of chlorine and is isomorphous with KCl, we can follow these steps:

### Step 1: Understand the Composition
Since the compound is isomorphous with KCl, we can assume the formula of the chloride is ACl, where A is the unknown element and Cl is chlorine.

### Step 2: Set Up the Equation for Percentage Composition
The percentage by weight of chlorine in ACl can be expressed as:
\[ \text{Percentage of Cl} = \frac{\text{mass of Cl}}{\text{molar mass of ACl}} \times 100 \]
Given that the atomic mass of chlorine (Cl) is approximately 35.5 g/mol, we can write:
\[ \text{Percentage of Cl} = \frac{35.5}{m + 35.5} \times 100 \]
where \( m \) is the atomic mass of element A.

### Step 3: Set Up the Equation Using Given Percentage
According to the problem, the percentage of chlorine is 29.34%. Therefore, we can set up the equation:
\[ \frac{35.5}{m + 35.5} \times 100 = 29.34 \]

### Step 4: Cross-Multiply to Solve for m
Cross-multiplying gives:
\[ 35.5 \times 100 = 29.34 \times (m + 35.5) \]
This simplifies to:
\[ 3550 = 29.34m + 1041.57 \]

### Step 5: Rearrange the Equation
Now, rearranging the equation to isolate \( m \):
\[ 29.34m = 3550 - 1041.57 \]
Calculating the right side:
\[ 29.34m = 2508.43 \]

### Step 6: Solve for m
Now, divide both sides by 29.34 to find \( m \):
\[ m = \frac{2508.43}{29.34} \approx 85.49 \]

### Conclusion
The atomic weight of element A is approximately **85.49 g/mol**.

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