What is the molal boiling point constant for a solvent that has a boiling point elevation of 2.5°C when 10.0 g of a solute of molar mass 72.0 g/mol is dissolved in 0.314 kg of the solvent?
A)5.7 °C/m
B)18 °C/m
C)0.25 °C/m
D)0.035 °C/m
E)8.0 °C/m

Question

Quizplus · Accepted Answer

The molal boiling point constant (Kb) can be calculated using the formula ΔTb = i * Kb * m, where ΔTb is the boiling point elevation, i is the van't Hoff factor (which is 1 for non-electrolytes, and not given here, so we assume it to be 1), Kb is the molal boiling point constant, and m is the molality of the solution. Given ΔTb = 2.5°C, the mass of solute = 10.0 g, the molar mass of solute = 72.0 g/mol, and the mass of solvent = 0.314 kg, we first find the molality (m) of the solution: m = moles of solute / kg of solvent = (10.0 g / 72.0 g/mol) / 0.314 kg = 0.439 mol / 0.314 kg = 1.397 mol/kg. Then, we solve for Kb: 2.5°C = 1 * Kb * 1.397, so Kb = 2.5°C / 1.397 ≈ 1.79°C/m. However, since none of the provided options exactly match this calculation, it seems there was a mistake in my calculation. Correcting for the calculation error and using the correct approach to find the molal boiling point constant that matches one of the provided options, the correct calculation should align with the given options. Given the discrepancy, let's re-evaluate the approach:To find the molal boiling point constant (Kb), we use the formula for boiling point elevation: ΔTb = Kb * m, where ΔTb is the boiling point elevation and m is the molality of the solution. The molality (m) is calculated as the number of moles of solute per kilogram of solvent. First, calculate the number of moles of solute: moles of solute = mass of solute / molar mass of solute = 10.0 g / 72.0 g/mol = 0.1389 mol.Next, calculate the molality (m): molality (m) = moles of solute / mass of solvent in kg = 0.1389 mol / 0.314 kg = 0.442 mol/kg.Finally, solve for Kb using the boiling point elevation formula: ΔTb = Kb * m, so Kb = ΔTb / m = 2.5°C / 0.442 mol/kg = 5.65°C/m, which rounds to 5.7°C/m, matching option A. The initial explanation contained a calculation error; the corrected approach accurately matches the given data to option A.

What Is the Molal Boiling Point Constant for a Solvent