What is the molecular weight of a polymer if 3.50 g are dissolved in enough water to give 252 mL of the solution and give a osmotic pressure of 28.52 mm Hg at 25°C? A) 6.49 × 10⁵ g/mol B) 9.05 × 10³ g/mol C) 2.63 × 10³ g/mol D) 28.5 g/mol E) 8.88 × 10⁴ g/mol

Question

Quizplus · Accepted Answer

We can use the Van't Hoff equation:

π = iMRT

where π is the osmotic pressure, i is the van't Hoff factor (which is assumed to be 1 for a non-electrolyte), M is the molar mass of the polymer, R is the gas constant, and T is the temperature in Kelvin.

We can first convert the osmotic pressure to atm:

28.52 mm Hg = 0.0376 atm

We also need to convert the volume to liters:

252 mL = 0.252 L

Substituting into the equation, we get:

0.0376 atm = (1)(M)(0.0821 L*atm/mol*K)(298 K) / (0.252 L)

Solving for M:

M = (0.0376 atm)(0.252 L) / (1)(0.0821 L*atm/mol*K)(298 K)

M = 90543 g/mol

Rounding to the appropriate number of significant figures, we get 9.05 × 10^4 g/mol, which corresponds to answer choice B.

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