Mole fraction of A in `H_(2)O` is 0.2. The molality of A in `H_(2)O` is:

Options

A. 13.9
B. 15.5
C. 14.5
D. 16.8

Answer

To find the molality of A in H₂O when the mole fraction of A is given as 0.2, we can follow these steps:

### Step 1: Understand the relationship between mole fraction and molality
The formula to relate mole fraction (xA) and molality (m) is given by:

\[ m = \frac{x_A \times 1000}{(1 - x_A) \times M} \]

Where:
- \( m \) = molality
- \( x_A \) = mole fraction of solute A
- \( M \) = molar mass of the solvent (in this case, water)

### Step 2: Identify the values
From the problem, we know:
- \( x_A = 0.2 \) (mole fraction of A)
- Molar mass of water (H₂O) = 18 g/mol

### Step 3: Substitute the values into the formula
Now we substitute the known values into the formula:

\[ m = \frac{0.2 \times 1000}{(1 - 0.2) \times 18} \]

### Step 4: Calculate the denominator
First, calculate \( (1 - x_A) \):

\[ 1 - 0.2 = 0.8 \]

Now substitute this back into the formula:

\[ m = \frac{0.2 \times 1000}{0.8 \times 18} \]

### Step 5: Calculate the numerator
Calculate the numerator:

\[ 0.2 \times 1000 = 200 \]

### Step 6: Calculate the denominator
Now calculate the denominator:

\[ 0.8 \times 18 = 14.4 \]

### Step 7: Divide the numerator by the denominator
Now, we can calculate molality:

\[ m = \frac{200}{14.4} \]

### Step 8: Perform the division
Now, perform the division:

\[ m \approx 13.8889 \]

### Step 9: Round off the result
Rounding off gives us:

\[ m \approx 13.9 \]

### Final Answer
Thus, the molality of A in H₂O is approximately **13.9**.