25 g of `MCl_(4)` contains 0.5 mole chlorine then its gram molecular weight is

Options

A. `"100 g mol"^(-1)`
B. `"200 g mol"^(-1)`
C. `"150 g mol"^(-1)`
D. `"400 g mol"^(-1)`

Explanation

To find the gram molecular weight (molar mass) of MCl₄ given that 25 g of MCl₄ contains 0.5 moles of chlorine, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the relationship between moles of chlorine and moles of MCl₄**:
- In one mole of MCl₄, there are 4 moles of chlorine (Cl).
- Therefore, the relationship is:
\[ 1 \text{ mole of MCl}_4 \rightarrow 4 \text{ moles of Cl} \]

2. **Determine the moles of MCl₄ corresponding to the given moles of chlorine**:
- Since we have 0.5 moles of chlorine, we can find the moles of MCl₄ that would produce this amount of chlorine:
\[ \text{Moles of MCl}_4 = \frac{0.5 \text{ moles of Cl}}{4} = 0.125 \text{ moles of MCl}_4 \]

3. **Use the mass of MCl₄ to find its molar mass**:
- We know that the mass of MCl₄ is given as 25 g. We can use the formula for molar mass:
\[ \text{Molar Mass} = \frac{\text{mass}}{\text{moles}} \]
- Plugging in the values:
\[ \text{Molar Mass of MCl}_4 = \frac{25 \text{ g}}{0.125 \text{ moles}} = 200 \text{ g/mol} \]

4. **Conclusion**:
- The gram molecular weight (molar mass) of MCl₄ is 200 g/mol.

### Summary:
The molar mass of MCl₄ is calculated to be 200 g/mol based on the given information.