What is the formula mass of the polymer?

Question

A 250 mL solution containing 25.4 g of polymer in toluene had an osmotic pressure of 0.155 atm at 28 degree Celsius. What is the formula mass of the polymer?

Answer 1

Let's start with the equation for osmotic pressure:

π = MiRT

Let's make some substitutions

First, we know the definition of molarity

M = n*V^-1

Next, let us find a way to get moles (n) into a value of something we already know: mass

MW = mass*n^-1 => n = mass*MW^-1

Now, let us substitute this equation for moles into our molarity definition

M = n*V^-1 = (mass*MW^-1)*V^-1 = mass

MW*V

Then, let us substitute this into our original equation for osmotic pressure

π = (mass*MW^-1*V^-1)iRT = mass*iRT

MW*V

Let us rearrange using algebra and solve for the MW

MW = mass*iRT

π*V

=> i = 1 because we told this is a polymer in toluene; toluene is a highly nonpolar solvent, so it is unlikely that this dissociates at any appreciable level

MW = mass*RT

π*V

<=> (25.4g)(0.08205 L*atm*K^-1*mol^-1)(301K)

(0.155atm)(0.250L)

MW = 1.6x10⁴ g*mol^-1