A 33.6 g sample of a nonelectrolyte was dissolved is 670. g of water. The solution's freezing point was -2.74°

Question

What is the molar mass of the compound?

Answer 1

The principle at work here is the fact that when you dissolve something in water the freezing point of the resulting solution is lowered.
The amount by which the freezing point is lowered is a function of the concentration of the solute dissolved in terms of molality.

(Delta T) = m * k
Where m is the molality of the solution and k is the freezing point depression of the solvent (in this case, water, k = 1.858 °C per molality)

Molality = moles of solute / kg of solvent

We are told the mass of the water (which acts as the solvent) = 670 grams = .670 kg.
We are not told the number of moles of solute (actually, we are indirectly asked to find this), but we are told the freezing point depression.

The freezing point of pure water is 0°C, but the solution in the question freezes at -2.74 °C, meaning that the freezing point went down 2.74 °C, which is out value for (delta T).

Plugging into the equation,
(2.74 °C) = m * (1.858 °C per molality)
Solving for the concentration, m, we get,
m = (2.74 °C) / (1.858 °C per molality)
m = 1.475 molality

We now know the concentration of the solution in terms of molality. From this, we can find the number of moles of the solute and then the molar mass.

Remember,
Molality = moles of solute / kg of solvent
We know the kg of solvent = .670 kg. We know the molality = 1.475 molality. All we need do now is solve for moles of solute.

Moles of solute = molality * kg solvent
Moles of solute = (1.475 molality) * (.670 kg)
Moles - .988 moles

We are told in the question that 33.6 grams of the non-electrolyte dissolved in solution, so .988 moles of the solute has a mass of 33.6 grams.
Molar mass = mass / moles
Mass = 33.6 g
Moles = .988 moles

Molar mass = 33.6 g / .988moles
Molar mass = 34.01 grams per mole

So the molar mass of the non-electrolyte solute dissolved in the water to lower its freezing point to 2.74 °C is 34.01 grams / mole.

Answer 2

DeltaTf = 0.0 - (-2.74°C) = 2.74°C
kf = 1.86°C kg mol-1 (look up in tables)
m = DeltaTf/kf = 2.74°C/1.86°C kg mol-1=1.473mol kg^-1
1.473mol nonelectrolyte/1000g *670g = 0.987mol nonelectrolyte
33.6g nonelectrolyte/0.987mol nonelectrolyte = 34.042g mol^-1
This is only the approximate molar mass of the nonelectrolyte since this technique is not very accurate (only 2 or three sig figs in this problem).

PS: Wanna chat???

Answer 3

The cryoscopic constant of water is 1.858 K/m.

So the depression is 2.74 degrees, giving you 2.74/1.858=1.47 molal solution, assuming the solute has an activity of 1 and does not dissociate in anyway.

From there, you just back it out:

1.47 molal * 0.670Kg = 0.985 moles of solute.
33.6g/0.985 moles = 34.1 g/mole for the molecular weight.

Answer 4

I'm thinking the same as guy above me, and you didn't specify degrees what.

Answer 5

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