A metallic chloride contain 47.22% metal. Calculate the equivalent weight of metal.

Options

A. 39.68
B. 31.76
C. 36.35
D. 33.46

Explanation

To find the equivalent weight of the metal in the metallic chloride that contains 47.22% metal, we can follow these steps:

### Step 1: Assume the total weight of the metallic chloride
Let's assume the total weight of the metallic chloride (MCl) is 100 grams.

### Step 2: Calculate the weight of the metal
Since the metallic chloride contains 47.22% metal, we can calculate the weight of the metal in the compound:
\[ \text{Weight of Metal} = 47.22\% \text{ of } 100 \text{ grams} = 47.22 \text{ grams} \]

### Step 3: Calculate the weight of chlorine
To find the weight of chlorine in the metallic chloride, we subtract the weight of the metal from the total weight:
\[ \text{Weight of Cl} = 100 \text{ grams} - 47.22 \text{ grams} = 52.78 \text{ grams} \]

### Step 4: Determine the molar mass of chlorine
The molar mass of chlorine (Cl) is approximately 35.5 g/mol.

### Step 5: Calculate the number of moles of chlorine
Using the weight of chlorine, we can calculate the number of moles of chlorine:
\[ \text{Moles of Cl} = \frac{\text{Weight of Cl}}{\text{Molar mass of Cl}} = \frac{52.78 \text{ grams}}{35.5 \text{ g/mol}} \approx 1.487 \text{ moles} \]

### Step 6: Determine the moles of metal
Assuming the metal chloride has the formula MCl_x, where x is the number of chlorine atoms, we can say that the number of moles of metal (M) is equal to the number of moles of chlorine (since each metal atom combines with one chlorine atom):
\[ \text{Moles of M} = \text{Moles of Cl} \approx 1.487 \text{ moles} \]

### Step 7: Calculate the molar mass of the metal
Now, we can calculate the molar mass of the metal using the weight of the metal and the number of moles:
\[ \text{Molar mass of M} = \frac{\text{Weight of Metal}}{\text{Moles of M}} = \frac{47.22 \text{ grams}}{1.487 \text{ moles}} \approx 31.7 \text{ g/mol} \]

### Step 8: Calculate the equivalent weight of the metal
The equivalent weight of a metal is calculated as the molar mass divided by the valency (assuming the valency of the metal is 1 for simplicity):
\[ \text{Equivalent weight of M} = \frac{\text{Molar mass of M}}{\text{Valency}} = \frac{31.7 \text{ g/mol}}{1} = 31.7 \text{ g/equiv} \]

Thus, the equivalent weight of the metal is approximately **31.7 g/equiv**.

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