In an experiment it is shown that `10 mL` of `0.05 M` solution of chloride required `10 mL` of `0.1 M` solution of `AgNO_(3)`, which of the following will be the formula of the chloride (X stands for the symbol of the element other than chlorine):

Options

A. (a)`X_(2)Cl`
B. (b)`X_(2)Cl_(2)`
C. (c )`XCl_(2)`
D. (d)`XCl_(4)`

Explanation

To determine the formula of the chloride (where X stands for the symbol of the element other than chlorine), we can follow these steps:

### Step 1: Calculate the moles of AgNO₃ used
We know the molarity (M) and volume (V) of the AgNO₃ solution. The formula to calculate moles (n) is:

\[ n = M \times V \]

Given:
- Molarity of AgNO₃ = 0.1 M
- Volume of AgNO₃ = 10 mL = 10 × 10⁻³ L

Calculating the moles of AgNO₃:

\[ n = 0.1 \, \text{mol/L} \times 10 \times 10^{-3} \, \text{L} = 0.001 \, \text{mol} \]

### Step 2: Calculate the moles of chloride
Similarly, we can calculate the moles of the chloride solution using its molarity and volume.

Given:
- Molarity of chloride = 0.05 M
- Volume of chloride = 10 mL = 10 × 10⁻³ L

Calculating the moles of chloride:

\[ n = 0.05 \, \text{mol/L} \times 10 \times 10^{-3} \, \text{L} = 0.0005 \, \text{mol} \]

### Step 3: Determine the mole ratio
From the reaction between AgNO₃ and chloride, we know that:

\[ \text{AgNO}_3 + \text{Cl}^- \rightarrow \text{AgCl} + \text{NO}_3^- \]

From the moles calculated:
- Moles of AgNO₃ = 0.001 mol
- Moles of chloride = 0.0005 mol

The mole ratio of AgNO₃ to chloride is:

\[ \text{Ratio} = \frac{0.001 \, \text{mol AgNO}_3}{0.0005 \, \text{mol chloride}} = 2 \]

This indicates that 2 moles of AgNO₃ react with 1 mole of chloride.

### Step 4: Write the formula of the chloride
Since 2 moles of AgNO₃ react with 1 mole of chloride, we can deduce that the chloride must contain 2 chlorine atoms. Therefore, the formula of the chloride can be represented as:

\[ \text{XCl}_2 \]

### Step 5: Identify the nitrate
The nitrate formed in the reaction will be:

\[ \text{X(NO}_3\text{)}_2 \]

This means that the overall reaction can be written as:

\[ \text{XCl}_2 + 2 \text{AgNO}_3 \rightarrow 2 \text{AgCl} + \text{X(NO}_3\text{)}_2 \]

### Conclusion
Thus, the formula of the chloride is:

\[ \text{XCl}_2 \]