Which solution has the lower freezing point in each of the following pairs? (a) 11.0 g of CH3OH in 100. g of H2O or 22.0 g of CH3CH2OH in 200. g of H2O? CH3OH/H2O CH3CH2OH/H2O Both solutions have the same freezing point. (b) 20.0 g of H2O in 1.00 kg of CH3OH or 20.0 g of CH3CH2OH in 1.00 kg of CH3OH? H2O/CH3OH CH3CH2OH/CH3OH Both solutions have the same freezing point.

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Explanation:

(a)

From the data provided;

Mass of methanol =11.0 g

Mass of solvent (H2O) =100 g = 0.1 kg

Molar mass of CH3OH =32.04 g/mol

Number of moles of solute = 0.343 mol

molality(m) of methanol = 3.43 m

Also,

Mass of ethanol =22.0 g

Mass of solvent (H2O) =200 g = 0.2 kg

Molar mass of C2H5OH =46.068 g/mol

Number of moles of solute = 0.477 mol

molality(m) of ethanol= 2.38 m

The greater the concentration of a solution, the higher the freezing point of solvent will be depressed. Therefore, higher molality, leader to a greater decrease of the freezing point.

Therefore, the freezing point of methanol CH3OH/H2O is lower than the freezing point of ethanol.

b)

Mass of solvent = 1 kg

Mass of water = 20g or 0.02 Kg

Molar mass of water = 18 gmol-1

Number of moles of solute = 20g/18 gmol-1 = 1.11 moles

Molality= 1.11 moles/1 kg = 1.11 m

Also;

Mass of ethanol = 20 g = 0.02 kg

Mass of solvent = 1.00 Kg

Molar mass of solute = 46 gmol-1

Number of moles of solute = 20g/ 46 gmol-1 = 0.43 moles

Molality= 0.43 moles/ 1 kg = 0.43 m

The greater the concentration of a solution, the higher the freezing point of solvent will be depressed. Therefore, higher molality, leader to a greater decrease of the freezing point.

Therefore, the freezing point of water H2O/CH3OH is lower than the freezing point of ethanol.

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