A sugar syrup of weight 214.2 grams contains 34.2 grams of sugar. The molal concentration is-

Options

A. 0.55
B. 5.5
C. 55
D. 0.1

Answer

To find the molal concentration (molality) of the sugar syrup, we will follow these steps:

### Step 1: Identify the given data
- Weight of the sugar syrup (solution) = 214.2 grams
- Weight of sugar (solute) = 34.2 grams

### Step 2: Calculate the weight of the solvent
The weight of the solvent can be calculated by subtracting the weight of the solute from the total weight of the solution.

\[ \text{Weight of solvent} = \text{Weight of solution} - \text{Weight of solute} = 214.2 \, \text{g} - 34.2 \, \text{g} = 180 \, \text{g} \]

### Step 3: Convert the weight of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert the weight of the solvent from grams to kilograms.

\[ \text{Weight of solvent in kg} = \frac{180 \, \text{g}}{1000} = 0.180 \, \text{kg} \]

### Step 4: Calculate the number of moles of solute (sugar)
To find the number of moles of sugar, we need the molecular mass of sugar (sucrose, C₁₂H₂₂O₁₁).

The molecular mass of sucrose is calculated as follows:
- Carbon (C): 12 atoms × 12 g/mol = 144 g/mol
- Hydrogen (H): 22 atoms × 1 g/mol = 22 g/mol
- Oxygen (O): 11 atoms × 16 g/mol = 176 g/mol

Adding these together gives:
\[ \text{Molecular mass of sucrose} = 144 + 22 + 176 = 342 \, \text{g/mol} \]

Now, we can calculate the number of moles of sugar:
\[ \text{Number of moles of sugar} = \frac{\text{Weight of sugar}}{\text{Molecular mass of sugar}} = \frac{34.2 \, \text{g}}{342 \, \text{g/mol}} \approx 0.100 \, \text{mol} \]

### Step 5: Calculate the molality
Now we can calculate the molality (m) using the formula:
\[ m = \frac{\text{Number of moles of solute}}{\text{Weight of solvent in kg}} = \frac{0.100 \, \text{mol}}{0.180 \, \text{kg}} \approx 0.555 \, \text{mol/kg} \]

### Final Result
Thus, the molal concentration (molality) of the sugar syrup is approximately:
\[ \text{Molality} \approx 0.555 \, \text{mol/kg} \]