Q13-107P - Chemistry: Molecular Nature Of Matter And Change

Question

In a study designed to prepare new gasoline-resistant coatings, a polymer chemist dissolves 6.053 g of poly (vinyl alcohol) in enough water to make 100.0mL of solution. At ,${25}^{\circ }C$the osmotic pressure of this solution is 0.272 atm. What is the molar mass of polymer sample?

Step-by-Step Solution

Answer

The molar mass of polymer is $5345.785g/mol$.

Step 1: Osmotic pressure

Osmotic pressure is defined as the pressure that must be applied to the solution side to stop fluid movement when a semi-permeable membrane separates a solution from pure water.

Step 2: Calculation of molar mass

In the question it is given that volume of solution is 100L, osmotic pressure 0.272atm, temperature 2${25}^{\circ }C$ and mass of poly (vinyl alcohol) is 6.053g.

So, we can calculate the molar mass from the equation n=MRT.

Where M is the molarity of solution, R gas constant $(0.082L.atm/molK.K)$ and T temperature.

 $$\begin{gathered} n=\frac{\left({\displaystyle \frac{mass of poly (vinyl alcohol) }{molar mass}}\right)}{volumw of solution\left(L\right)}RT \\ molar mass=\frac{\left({\displaystyle \frac{mass of poly (vinyl alcohol) }{n}}\right)}{volumw of solution\left(L\right)}RT \\ =\frac{\left({\displaystyle \frac{6.053g}{0.272atm}}\right)}{0.1L}\times 0.082L.atm/mol.K\times 298K \\ =5345.785g/mol \end{gathered}$$