A metal M (specific heat 0.16) forms a metal chloride with a 65% chlorine present in it. The formula of the metal chloride will be

Options

A. MCl
B. `MCl_(2)`
C. `MCl_(3)`
D. `MCl_(4)`

Explanation

To determine the formula of the metal chloride formed by metal M, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Specific Heat and Use Dulong-Petit Law**:
The specific heat of metal M is given as 0.16. According to Dulong-Petit Law, we can relate the atomic mass (M) of the metal to its specific heat (s) using the formula:
\[ M \times s = 6.4 \]
Substituting the specific heat value:
\[ M \times 0.16 = 6.4 \]

2. **Calculate the Atomic Mass of Metal M**:
Rearranging the equation to find M:
\[ M = \frac{6.4}{0.16} = 40 \]
Therefore, the approximate atomic mass of metal M is 40 g/mol.

3. **Determine the Composition of the Metal Chloride**:
We know that the metal chloride contains 65% chlorine by mass. Let the formula of the metal chloride be \(MCl_x\). The mass of chlorine in the compound can be expressed as:
\[ \text{Mass of Cl} = 35.5 \times x \]
The total mass of the metal chloride can be expressed as:
\[ \text{Total mass} = 40 + 35.5x \]
According to the problem, the percentage of chlorine is given by:
\[ \frac{35.5x}{40 + 35.5x} \times 100 = 65 \]

4. **Set Up the Equation**:
Rearranging the percentage equation gives:
\[ 35.5x = 0.65(40 + 35.5x) \]
Expanding the right side:
\[ 35.5x = 26 + 23.075x \]

5. **Solve for x**:
Rearranging gives:
\[ 35.5x - 23.075x = 26 \]
\[ 12.425x = 26 \]
\[ x = \frac{26}{12.425} \approx 2.09 \]
Rounding to the nearest whole number, we take \(x \approx 2\).

6. **Write the Formula of the Metal Chloride**:
Thus, the formula of the metal chloride is:
\[ MCl_2 \]

### Final Answer:
The formula of the metal chloride is \(MCl_2\).

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