In a study designed to prepare new gasoline-resistant coatings, a polymer chemist dissolves 6.143 g poly(vinyl alcohol) in enough water to make 100.0 mL of solution. At 25°C, the osmotic pressure of this solution is 0.272 atm. What is the molar mass of the polymer sample?

MM = 5,521.54 g/mol

Explanation:

To solve this, we need to use the expression for osmotic pressure which is the following:

π = MRT (1)

Where:

M: Concentration of the solution

R: gas constant (0.082 L atm/ mol K

T: temperature in K

25 °C in Kelvin is: 25 + 273.15 = 298.15 K

Now, we do not have the concentration of the solution, but we do have the mass. and the concentration can be expressed in terms of mass, molar mass and volume:

Concentration (M) is:

M = n/V (2)

and n (moles) is:

n = m/MM (3)

Therefore, if we replace (2) and (3) in (1) we have:

π = mRT/V*MM

Solving for MM we have:

MM = mRT/πV (4)

All we have to do now, is replace the given data and we should get the value of the molar mass:

MM = 6.143 * 0.082 * 298.15 / 0.1 * 0.272

MM = 150.1859 / 0.0272

MM = 5,521.54 g/mol

This is the molar mass.

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