What is the mass percent of ethylene glycol (HOCH₂CH₂OH)in a solution of ethylene glycol in water that has a freezing point of -17.8°C? (K_f for water is 1.858°C/m.)

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Quizplus · Accepted Answer

The freezing point depression formula is ΔTf = iKf * m, where ΔTf is the change in freezing point, i is the van't Hoff factor (which is 1 for ethylene glycol since it does not ionize in solution), Kf is the cryoscopic constant of the solvent (water in this case, 1.858°C/m), and m is the molality of the solution. Given ΔTf = -17.8°C (since water's normal freezing point is 0°C and it's now -17.8°C), we can solve for m (molality). First, rearrange the formula to solve for m: m = ΔTf / (i*Kf) = -17.8°C / (1*1.858°C/m) = -9.58 mol/kg. The negative sign indicates freezing point depression, but we consider the absolute value for calculations.Next, to find the mass percent, we need the mass of ethylene glycol and the total mass of the solution. The molar mass of ethylene glycol (HOCH2CH2OH) is approximately 62.07 g/mol. If we have 9.58 mol of ethylene glycol in 1 kg of water, the mass of ethylene glycol is 9.58 mol * 62.07 g/mol = 594.7 g. The total mass of the solution is the mass of ethylene glycol plus the mass of water (1000 g), which equals 1594.7 g. The mass percent of ethylene glycol is then (594.7 g / 1594.7 g) * 100% = 37.3%. The closest answer provided is 37.2%, which is due to rounding differences in the calculation.

What Is the Mass Percent of Ethylene Glycol (HOCH2CH2OH)in a Solution

What Is the Mass Percent of Ethylene Glycol (HOCH₂CH₂OH)in a Solution