Question

Calculate the number of moles of nonvolatile solute dissolved in 0.5 kg solvent if molal elevation constant for solvent is 2 kg K mol$^{-1}$ [$\Delta T_b = 0.8$ K].

• A. 0.1
• B. 0.2
• C. 0.3
• D. 0.4

Hint:

Always ensure the mass of the solvent is in kilograms when using the molality equation. If it is given in grams, divide by 1000 before substituting into the formula.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the boiling point elevation ($\Delta T_b$), the molal elevation constant ($K_b$), and the mass of the solvent. We need to calculate the number of moles of the dissolved solute.

Step 2: Key Formula or Approach:
The elevation in boiling point is directly proportional to the molality ($m$) of the solution:
$$\Delta T_b = K_b \times m$$
Molality ($m$) is defined as the number of moles of solute ($n$) divided by the mass of the solvent in kilograms ($W_{solvent}$):
$$m = \frac{n}{W_{solvent}}$$

Step 3: Detailed Explanation:
1. First, find the molality of the solution using the elevation formula:
$$0.8 = 2 \times m$$
$$m = \frac{0.8}{2} = 0.4 \text{ mol kg}^{-1}$$
2. Next, use the molality definition to find the number of moles ($n$):
Given mass of solvent $W_{solvent} = 0.5 \text{ kg}$.
$$0.4 = \frac{n}{0.5}$$
$$n = 0.4 \times 0.5$$
$$n = 0.2 \text{ moles}$$

Step 4: Final Answer:
The number of moles of solute is 0.2, matching option (b).