Question

A solution contains 4 g of NaOH and 16.2 g of water. The mole fraction solute and solvent are respectively

• A. 0.1, 0.9
• B. 0.2, 0.8
• C. 0.5, 0.5
• D. 0.4, 0.6

Answer 1

The Correct Option is A

Answer (A) 0.1, 0.9 

To calculate the mole fraction of a solute and solvent in a solution, we need to determine the number of moles of each component.

Given:

• Mass of NaOH = 4 g
• Mass of water = 16.2 g

Step 1: To find the number of moles of NaOH, we divide the given mass by the molar mass of NaOH. The molar mass of NaOH is:

Molar mass of NaOH = 22.99 g/mol (for Na) + 16.00 g/mol (for O) + 1.01 g/mol (for H) = 39.99 g/mol

Number of moles of NaOH = \( \frac{4\ \text{g}}{39.99\ \text{g/mol}} \) ≈ 0.1 mol

Step 2: To find the number of moles of water, we divide the given mass by the molar mass of water. The molar mass of water (H₂O) is:

Molar mass of H₂O = 1.01 g/mol (for H) + 1.01 g/mol (for H) + 16.00 g/mol (for O) = 18.02 g/mol

Number of moles of water = \( \frac{16.2\ \text{g}}{18.02\ \text{g/mol}} \) ≈ 0.9 mol

Step 3: Now, we can calculate the mole fraction of solute (NaOH) and solvent (water):

Mole fraction of solute (NaOH) = \( \frac{\text{Moles of NaOH}}{\text{Total moles}} = \frac{0.1\ \text{mol}}{(0.1\ \text{mol} + 0.9\ \text{mol})} = 0.1 \)

Mole fraction of solvent (water) = \( \frac{\text{Moles of water}}{\text{Total moles}} = \frac{0.9\ \text{mol}}{(0.1\ \text{mol} + 0.9\ \text{mol})} = 0.9 \)

Therefore, the mole fraction of solute (NaOH) and solvent (water) in the given solution are approximately 0.1 and 0.9, respectively. So the correct option is 0.1, 0.9.