Question

4. (10 points) (i) calculate the osmotic pressure of 20 g/l glucose water solution against pure water through a semipermeable membrane at 298.15 k temperature. the semipermeable membrane is not permeable to glucose molecules and is permeable to water molecules. glucose molecular weight is 180.156 g/mol. report the result in [bar]. (ii) adding some sodium chloride (nacl) powder into the glucose solution and it fully dissolved. assuming the semipermeable membrane is permeable to na and clions. will this process change the osmotic pressure value in (i)? briefly explain your answer. (iii) calculate the osmotic pressure of 1 mm glucose water solution against pure water. report the result in [pa].

Answer 1

The osmotic pressure of a 20 g/L glucose solution at 298.15 K is 2.74 bar. Adding NaCl to the solution increases the osmotic pressure. For a 1 mM glucose solution, the osmotic pressure is 247.57 Pa.

Step-by-step explanation:

To calculate the osmotic pressure (Π) of a 20 g/L glucose solution at 298.15 K, we use the formula Π = iMRT, where i is the van't Hoff factor which is 1 for glucose, M is the molarity, R is the gas constant (0.0831 L·bar/K·mol), and T is the temperature in Kelvin. The molarity (M) is calculated by dividing the mass of glucose (20 g) by its molecular weight (180.156 g/mol) and then by the volume of solution in liters (1 L), resulting in a molarity of 0.111 mol/L. The osmotic pressure is then Π = (1)(0.111 mol/L)(0.0831 L·bar/K·mol)(298.15 K) = 2.74 bar.

Adding sodium chloride (NaCl) to the glucose solution will change the osmotic pressure because NaCl dissociates into Na+ and Cl- ions, increasing the number of particles in solution and thus the osmotic pressure.

For a 1 mM glucose solution, we repeat the osmotic pressure calculation with the new molarity of 1 mM which is 0.001 mol/L. The osmotic pressure, in this case, converts to Pascals using the conversion 1 bar = 100,000 Pa. So the osmotic pressure is Π = (1)(0.001 mol/L)(0.0831 L·bar/K·mol)(298.15 K) × 100,000 Pa/bar = 247.57 Pa.