Propylene glycol, C₃H₆(OH)₂, is sometimes used in automobile antifreeze solutions. If an aqueous solution has a mole fraction of c _C3H6(OH)2= 0.100, what is the molality of the propylene glycol in this solution?

Question

Quizplus · Accepted Answer

To find the molality of the solution, we need to first determine the moles of propylene glycol in the solution. We can use the mole fraction of propylene glycol to do this:

moles of propylene glycol = mole fraction of propylene glycol x total moles of solution

The total moles of solution can be calculated as:

total moles of solution = moles of water + moles of propylene glycol

Since water is the solvent, we can assume that its moles are equal to its mass in grams divided by its molar mass:

moles of water = mass of water / molar mass of water

Assuming 1 L of solution, with a density of 1 g/mL, and a mole fraction of propylene glycol of 0.100, we can calculate:

mass of propylene glycol = 0.100 x 1 L x 1.04 g/mL x 76.10 g/mol = 7.82 g
mass of water = (1 – 0.100) x 1 L x 1000 g/L = 900 g

moles of propylene glycol = 7.82 g / 76.10 g/mol = 0.103 mol
moles of water = 900 g / 18.015 g/mol = 49.97 mol
total moles of solution = 0.103 mol + 49.97 mol = 50.07 mol

Now we can calculate the molality of the solution:

molality = moles of propylene glycol / mass of water in kg

mass of water in kg = 900 g / 1000 g/kg = 0.900 kg

molality = 0.103 mol / 0.900 kg = 0.1144 mol/kg ≈ 6.17 m

Therefore, the answer is choice D, 6.17 m.

Propylene Glycol, C3H6(OH)2, Is Sometimes Used in Automobile Antifreeze Solutions

Propylene Glycol, C₃H₆(OH)₂, Is Sometimes Used in Automobile Antifreeze Solutions