The molar mass of a compound expresses the ratio of mass to moles: molar mass=ma

Question

The molar mass of a compound expresses the ratio of mass to moles:

molar mass=mass in gramsnumber of moles

This quantity can be determined experimentally by accurately measuring the mass of the sample and determining the corresponding number of moles based on some property of the sample. Freezing-point depression and osmotic pressure measurements are frequently used to calculate the number of moles in solution for this type of determination.

Freezing-point depression is equal to

Tf=Kfm

where T is the change in temperature, Kf is the molal freezing-point-depression constant, and m is the molality in moles of solute per mass of solvent.

Osmotic pressure is equal to

=MRT

where is the osmotic pressure, R=0.08206 Latm/(Kmol), T is temperature, and M is molarity in moles per liter of solution.

Part A

tert-Butyl alcohol is a solvent with a Kf of 9.10 C/m and a freezing point of 25.5 C. When 0.807 gof an unknown colorless liquid was dissolved in 11.6 g of tert-butyl alcohol, the solution froze at 15.3 C.

Which of the following is most likely the identity of this unknown liquid?

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Correct

PART B

A protein subunit from an enzyme is part of a research study and needs to be characterized. A total of 0.160 g of this subunit was dissolved in enough water to produce 2.00 mL of solution. At 28 C the osmotic pressure produced by the solution was 0.138 atm. What is the molar mass of the protein?

ethylene glycol (molar mass = 62.07 g/mol) 1-octanol (molar mass = 130.22 g/mol) glycerol (molar mass = 92.09 g/mol) 2-pentanone (molar mass = 86.13 g/mol) 1-butanol (molar mass = 74.12 g/mol)

Explanation / Answer

Part A.

molality = moles of solute/kg of solvent

moles = g/molar mass

solvent = 11.6 g = 0.0116 kg

solute = 0.807 g

Using formula,

dTf = mKf

where, m = molality of solution

(25.5 - 15.3) = m x 9.10

m = moles/0.0116 = 1.121 m

moles of solute = 0.013 mols

molar mass of solute = 62.07 g/mol

So, the correct answer would be, the unknown liquid is ethylene glycol (molar mass = 62.07 g/mol)

Part B.

osmotic pressure = MRT

where,

M = molarity of solution = moles/L of solution = g/molar mass x L of solution

volume of solution = 2 ml = 0.002 L

mass of solute = 0.160 g

T = 28 oC = 28 + 273 = 301 K

Feed values,

M = 0.138/0.08206 x 301 = 5.587 x 10^-3 M

molar mass of the protein = 0.160/5.587 x 10^-3 x 0.002 = 14318.95 g/mol

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