09-214 Physical Chemistry Name__________KEY________________

Quiz 6 March 7, 2001

1 atm = 760 torr

R = 8.314 J/K mol

= 0.0821 L atm/K mol

(12 points) In January 2001, an experiment was performed in which exactly 3.00 grams of the protein carnegiemellonine were dissolved in 100 mL of water. The osmotic pressure of the solution was measured to be 180 torr at 25^oC. Estimate the molecular weight of the protein.

Let M = molecular wt = g/mol

= cRT = 180 torr/760 torr atm^-1 = 0.237 atm (3 pts)

0.237 atm = (3.00 g/M g/mol)(0.0821 L atm/K mol)(298 K)/0.100 L (7 pts)

M = 3093 g/mol (2 pts)

(3 points) In February 2001, a more detailed experiment exploring the osmotic pressure of solutions of carnegiemellonine as a function of its concentration demonstrated that the activity coefficient for the protein in the January experiment was 0.91. Show a reasonable method for estimating the corrected molecular weight.

Replace the concentration of protein, c, in the above equation, with an "effective concentration", c

0.237 atm = (0.91)(3.00 g/M g/mol)(0.0821 L atm/K mol)(298 K)/0.100 L

M = 2815 g/mol

(Note: you can't use ln a_A --> ln x_A because that's for the solvent, not the solute)