Question

A medical technology instrument called the "Osmette S" uses the freezing point depression technique to measure the molality of aqueous solutions. It can be used to measure the molecular weight of water-soluble polymers. The minimum molality that the instrument can measure is 1 mmol/kg. Suppose you make up a polymer of concentration 25 mg/ml. What is the maximum polymer molecular weight that can be measured with this instrument?

Answer 1

We know:

Molality = moles of solute/Mass of solvent in kgs

Moles = Mass/Molecular mass

Mostly, solvent is water with density = 1 g/mL

The conc of the given solution is:

C = 25 mg/mL = 25 g/L

We also assume that density of this solution = Density of water = 1 g/mL

So,

Mass of 1 L solution = 1 kg

Now, 1 L of this solution contains 25 g solute.

So, mass of solvent water = 1000-25 = 975 g = 0.975 kg

Assume that MW of solute is 'x'

So, for this 1 L solution:

Moles of solute = 25/x

So,

Molality = Moles/Mass of solvent in kgs = (25/x)/0.975 = 25.64/x mol/kg

Given that lowest possible molality value = 1 mmol/kg = 0.001 mol/kg

So,

25.64/x = 0.001

x = 25640

So, Maximum polymer MW that can be measured = 25640 g