Calculate the molality of solution containing 3 g glucose dissolved in 30 g of water . (molar mass of glucose = 180)

Options

A. 0.50 m
B. 0.56 m
C. 0.091 m
D. 0.05 m

Answer

To calculate the molality of a solution containing 3 g of glucose dissolved in 30 g of water, we will follow these steps:

### Step 1: Identify the given data
- Mass of glucose (solute) = 3 g
- Mass of water (solvent) = 30 g
- Molar mass of glucose = 180 g/mol

### Step 2: Convert the mass of the solvent from grams to kilograms
Since molality is defined as the number of moles of solute per kilogram of solvent, we need to convert the mass of water from grams to kilograms.

\[ \text{Mass of water in kg} = \frac{30 \text{ g}}{1000} = 0.03 \text{ kg} \]

### Step 3: Calculate the number of moles of glucose
To find the number of moles of glucose, we use the formula:

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

Substituting the values:

\[ \text{Number of moles of glucose} = \frac{3 \text{ g}}{180 \text{ g/mol}} = 0.01667 \text{ moles} \]

### Step 4: Calculate the molality of the solution
Now that we have the number of moles of glucose and the mass of the solvent in kilograms, we can calculate the molality using the formula:

\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]

Substituting the values:

\[ \text{Molality} = \frac{0.01667 \text{ moles}}{0.03 \text{ kg}} = 0.5557 \text{ mol/kg} \]

Rounding to two decimal places, we get:

\[ \text{Molality} \approx 0.56 \text{ mol/kg} \]

### Final Answer:
The molality of the solution is approximately **0.56 mol/kg**.

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