What is the molality of a solution in which 18 g of glucose (mol. wt. = 180) is dissolved in 500g of `H_2O` ?

Options

A. 0.5 m
B. 0.2 m
C. 2 m
D. 1 m

Answer

To find the molality of the solution, we can follow these steps:

### Step 1: Understand the formula for molality
The formula for molality (m) is given by:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

### Step 2: Calculate the moles of glucose
First, we need to calculate the number of moles of glucose. The formula to calculate moles is:
\[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given:
- Mass of glucose = 18 g
- Molar mass of glucose = 180 g/mol

Calculating the moles of glucose:
\[ \text{moles of glucose} = \frac{18 \text{ g}}{180 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 3: Convert the mass of solvent to kilograms
The mass of the solvent (water) is given as 500 g. To convert grams to kilograms:
\[ \text{mass of solvent in kg} = \frac{500 \text{ g}}{1000} = 0.5 \text{ kg} \]

### Step 4: Calculate the molality
Now we can substitute the values into the molality formula:
\[ m = \frac{0.1 \text{ moles}}{0.5 \text{ kg}} = 0.2 \text{ molal} \]

### Final Answer
The molality of the solution is **0.2 molal**.

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