If 9.55 g of CuS are dissolved in 500 ml `H_(2)O`. What will be the molarity of CuS in aqueous solution ? [Molar mass of CuS is 96.5 g]

Options

A. 0.02 M
B. 2 M
C. 0.2 M
D. 20 M

Answer

To find the molarity of CuS in an aqueous solution, we can follow these steps:

### Step 1: Calculate the number of moles of CuS
To find the number of moles of CuS, we use the formula:

\[ \text{Moles of solute} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]

Given:
- Mass of CuS = 9.55 g
- Molar mass of CuS = 96.5 g/mol

Substituting the values:

\[ \text{Moles of CuS} = \frac{9.55 \, \text{g}}{96.5 \, \text{g/mol}} \approx 0.0990 \, \text{moles} \]

### Step 2: Convert the volume of the solution from mL to L
The volume of the solution is given as 500 mL. To convert this to liters, we use the conversion factor:

\[ 1 \, \text{L} = 1000 \, \text{mL} \]

So,

\[ \text{Volume in L} = \frac{500 \, \text{mL}}{1000} = 0.5 \, \text{L} \]

### Step 3: Calculate the molarity of CuS
Molarity (M) is defined as the number of moles of solute per liter of solution:

\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in L}} \]

Substituting the values we calculated:

\[ \text{Molarity of CuS} = \frac{0.0990 \, \text{moles}}{0.5 \, \text{L}} = 0.198 \, \text{M} \]

Rounding to two decimal places, we get:

\[ \text{Molarity of CuS} \approx 0.20 \, \text{M} \]

### Final Answer:
The molarity of CuS in the aqueous solution is approximately **0.20 M**.

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