Final answer:
To find the freezing point of the solution with ethyl alcohol, calculate the moles of ethyl alcohol, determine the molality, and then use the formula ΔTf = i * Kf * m to find the freezing point depression. The calculated freezing point of the solution is -1.37°C.
Step-by-step explanation:
The question asks to determine the freezing point of a solution consisting of ethyl alcohol (C2H5OH) dissolved in water. To answer, we should use the freezing point depression concept, which is a colligative property. This property depends on the number of particles of solute in the solution and not on their identity. The freezing point depression (ΔTf) is given by ΔTf = i * Kf * m, where i is the can't Hoff factor for the solute (in this case, i = 1 for non-electrolyte ethyl alcohol), Kf is the freezing point depression constant for the solvent (water in this case, which is given as 1.86°C/m), and m is the molality of the solution. First, we must calculate the moles of ethyl alcohol using the equation: moles = mass (g) / molar mass (g/mol). Moles of C2H5OH = 20g / 46g/mol = 0.435 moles. Then, the molality (m) is calculated using moles of solute per kilogram of solvent. Molality = moles of C2H5OH / kilograms of water = 0.435 moles / 0.590 kg = 0.737 mol/kg. Finally, we calculate the freezing point depression. ΔTf = 1 * 1.86°C/m * 0.737 mol/kg = 1.37°C. The freezing point of the solution = freezing point of pure water - ΔTf = 0°C - 1.37°C = -1.37°C.