Calculate the molality of a solution that contains 51.2g of naphthalene, (`C_(10)H_(8)`) in 500 mL of carbon tetrachloride. The density of `C Cl_(4)` is 1.60 g/m

Options

A. 0.250 m
B. 0.500 m
C. 0.750 m
D. 0.840 m

Explanation

To calculate the molality of a solution containing 51.2 g of naphthalene (C₁₀H₈) in 500 mL of carbon tetrachloride (CCl₄), we will follow these steps:

### Step 1: Calculate the mass of carbon tetrachloride (CCl₄)
We know that density is defined as mass per unit volume. Therefore, we can calculate the mass of CCl₄ using the formula:

\[ \text{Mass} = \text{Density} \times \text{Volume} \]

Given:
- Density of CCl₄ = 1.60 g/mL
- Volume of CCl₄ = 500 mL

Now, substituting the values:

\[ \text{Mass of CCl₄} = 1.60 \, \text{g/mL} \times 500 \, \text{mL} = 800 \, \text{g} \]

### Step 2: Calculate the moles of naphthalene (C₁₀H₈)
To find the number of moles of naphthalene, we use the formula:

\[ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} \]

First, we need to calculate the molar mass of naphthalene (C₁₀H₈):
- Molar mass of Carbon (C) = 12 g/mol
- Molar mass of Hydrogen (H) = 1 g/mol

Calculating the molar mass:

\[ \text{Molar Mass of C₁₀H₈} = (10 \times 12) + (8 \times 1) = 120 + 8 = 128 \, \text{g/mol} \]

Now, substituting the mass of naphthalene:

\[ \text{Moles of naphthalene} = \frac{51.2 \, \text{g}}{128 \, \text{g/mol}} = 0.4 \, \text{mol} \]

### Step 3: Calculate the mass of the solvent in kg
We have already calculated the mass of CCl₄ as 800 g. To convert this to kg:

\[ \text{Mass of CCl₄ in kg} = \frac{800 \, \text{g}}{1000} = 0.8 \, \text{kg} \]

### Step 4: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent:

\[ \text{Molality} = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} \]

Substituting the values we have:

\[ \text{Molality} = \frac{0.4 \, \text{mol}}{0.8 \, \text{kg}} = 0.5 \, \text{m} \]

### Final Answer
The molality of the solution is **0.5 m**.

---