If a 3.90 m solution boils at 103.45 °C, what is the actual value of the van't Hoff factor, i, given that the boiling point of pure water is 100.00 °C and the ebullioscopic constant (Kb) is 0.512 °C/m?

• A. 3.0
• B. 2.5
• C. 2.0
• D. 1.5

Answer: (C)

Verified step by step guidance

1. Identify the formula for boiling point elevation: ΔT_b = i * K_b * m, where ΔT_b is the boiling point elevation, i is the van't Hoff factor, K_b is the ebullioscopic constant, and m is the molality of the solution.
2. Calculate the boiling point elevation (ΔT_b) by subtracting the boiling point of pure water from the boiling point of the solution: ΔT_b = 103.45 °C - 100.00 °C.
3. Substitute the known values into the boiling point elevation formula: ΔT_b = i * 0.512 °C/m * 3.90 m.
4. Rearrange the formula to solve for the van't Hoff factor, i: i = ΔT_b / (K_b * m).
5. Substitute the calculated value of ΔT_b and the given values of K_b and m into the rearranged formula to find the actual value of i.