What mass of ethanol, C₂H₅OH a nonelectrolyte, must be added to 10.0 L of water to give a solution that freezes at -10.0°C? Assume the density of water is 1.0 g/mL. K_f of water is 1.86°C/m. A)85.7 kg B)24.8 kg C)5.38 kg D)2.48 kg E)1.17 kg

Question

Quizplus · Accepted Answer

The correct answer is D.The freezing point depression is given by the equation:$$\Delta T_f = K_f 	imes m$$where:$$\Delta T_f$$ is the change in freezing point$$K_f$$ is the freezing point depression constant for the solvent$$m$$ is the molality of the solutionWe are given that the freezing point of the solution is -10.0°C, which is 10.0°C lower than the freezing point of pure water (0.0°C). We are also given that the freezing point depression constant for water is 1.86°C/m. Therefore, we can solve for the molality of the solution:$$10.0°C = 1.86°C/m 	imes m$$$$m = 5.38 mol/kg$$We are also given that the density of water is 1.0 g/mL, which means that 10.0 L of water has a mass of 10.0 kg. Therefore, the mass of ethanol that must be added to the water is:$$5.38 mol/kg 	imes 10.0 kg = 53.8 mol$$The molar mass of ethanol is 46.07 g/mol, so the mass of ethanol that must be added is:$$53.8 mol 	imes 46.07 g/mol = 2.48 kg$$

What Mass of Ethanol, C2H5OH a Nonelectrolyte, Must Be Added

What Mass of Ethanol, C₂H₅OH a Nonelectrolyte, Must Be Added