A solution is made by dissolving 5.61 g of a new polymer in enough water to make 260 mL of solution. At 25.0 oC, the osmotic pressure of the solution is 0.174 atm. What is the molar mass of the polymer in g/mol?

3030.2 g/mol is the molar mass for our polymer

Explanation:

Formula for Osmotic pressure → π = M. R. T

where π is pressure (atm)

M is molarity mol/L

R, the Universal Gases Constant (0.082 L. atm/mol. K)

T, Absolute T° (T°C + 273)

25°C + 273 = 298 K

Let's replace the values

0.174 atm = M. 0.082l. atm/mol. K. 298K

0.174 atm / (0.082l. atm/mol. K. 298K) = M

7.12*10⁻³ mol/L

As molarity is mol/L, and we have the volume of solution (in mL we must convert to L) we can find out the moles of our polymer that corresponds to the mass we used.

260mL. 1L/1000mL = 0.260L

7.12*10⁻³ mol/L = mol / 0.260L

7.12*10⁻³ mol. 0.260 = mol → 1.85*10⁻³

These moles refers to te 5.61 g of solute, to if we want to determine the molar mass, we should do:

g/mol → 5.61 g / 1.85*10⁻³ mol = 3030.2 g/mol