Question

When \(13.66 \mathrm{~g}\) of lactic acid, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3},\) are mixed with \(115 \mathrm{~g}\) of stearic acid, the mixture freezes at \(62.7^{\circ} \mathrm{C}\). The freezing point of pure stearic acid is \(69.4^{\circ} \mathrm{C}\). What is the freezing point constant of stearic acid?

Short answer

Answer: The freezing point constant (Kf) of stearic acid is approximately 5.08 °C/molkg.

Step-by-step solution

Calculate the change in freezing point ΔTf

To find the change in freezing point, subtract the freezing point of the mixture from the freezing point of pure stearic acid: ΔTf = 69.4 °C – 62.7 °C = 6.7 °C

Find the moles of lactic acid

To find the moles of lactic acid (C3H6O3), first we need to find its molar mass. The molar mass of lactic acid is: C3H6O3 = (3 * 12.01) + (6 * 1.01) + (3 * 16.00) = 36.03 + 6.06 + 48.00 = 90.09 g/mol Now, divide the mass of lactic acid by its molar mass to find the number of moles: moles of lactic acid = 13.66 g / 90.09 g/mol = 0.1517 mol

Find the molality of the solution

To find the molality of the solution, we need to know the mass of the solvent (stearic acid) in kilograms. Convert the mass of stearic acid to kg: mass of stearic acid = 115 g = 0.115 kg Now, divide the moles of lactic acid by the mass of stearic acid to find the molality of the solution: molality = 0.1517 mol / 0.115 kg = 1.3182 mol/kg

Calculate the freezing point constant (Kf) of stearic acid

Now we have all the information needed to find Kf. Use the formula for freezing point depression with i = 1 for lactic acid (non-electrolyte): ΔTf = Kf * molality Kf = ΔTf / molality Kf = 6.7 °C / 1.3182 mol/kg = 5.0807 °C/molkg The freezing point constant of stearic acid is approximately 5.08 °C/molkg.