A solution of `0*1` M of a metal chloride `MCl_(x)` requires 500 mL of `0*6` M `AgNO_(3)` solution for complete precipitation. The value of x is

Options

A. `1`
B. `2`
C. `4`
D. `3`

Explanation

To solve the problem step by step, we need to find the value of \( x \) in the metal chloride \( MCl_x \) based on the given information.

### Step 1: Identify the Reaction
The metal chloride \( MCl_x \) reacts with silver nitrate \( AgNO_3 \) to form silver chloride \( AgCl \) and another product. The balanced reaction can be written as:
\[ MCl_x + x \, AgNO_3 \rightarrow M(NO_3)_x + x \, AgCl \]

### Step 2: Calculate Moles of \( AgNO_3 \)
Given that the concentration of \( AgNO_3 \) is \( 0.6 \, M \) and the volume used is \( 500 \, mL \) (which is \( 0.5 \, L \)), we can calculate the number of moles of \( AgNO_3 \) used:
\[ \text{Moles of } AgNO_3 = \text{Molarity} \times \text{Volume} = 0.6 \, \text{mol/L} \times 0.5 \, \text{L} = 0.3 \, \text{mol} \]

### Step 3: Relate Moles of \( AgCl \) to Moles of \( MCl_x \)
From the balanced equation, we see that 1 mole of \( MCl_x \) produces \( x \) moles of \( AgCl \). Therefore, if \( 0.3 \, \text{mol} \) of \( AgNO_3 \) is used, it will produce \( 0.3 \, \text{mol} \) of \( AgCl \):
\[ \text{Moles of } AgCl = 0.3 \, \text{mol} \]

### Step 4: Calculate Moles of \( MCl_x \)
Since \( 1 \, \text{mol} \) of \( MCl_x \) produces \( x \, \text{mol} \) of \( AgCl \), we can set up the equation:
\[ \text{Moles of } MCl_x = \frac{\text{Moles of } AgCl}{x} = \frac{0.3}{x} \]

### Step 5: Use the Given Concentration of \( MCl_x \)
We know that the concentration of \( MCl_x \) is \( 0.1 \, M \). The number of moles of \( MCl_x \) can also be expressed as:
\[ \text{Moles of } MCl_x = \text{Molarity} \times \text{Volume} = 0.1 \, \text{mol/L} \times 1 \, \text{L} = 0.1 \, \text{mol} \]

### Step 6: Set Up the Equation
Equating the two expressions for moles of \( MCl_x \):
\[ \frac{0.3}{x} = 0.1 \]

### Step 7: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ 0.3 = 0.1x \]
\[ x = \frac{0.3}{0.1} = 3 \]

### Conclusion
Thus, the value of \( x \) is \( 3 \).