Suppose a salt and a glucose solution are separated by a membrane that is permeable to water but not to the solutes. The NaCl solution has a concentration of 1.95 g per 250 mL (molecular weight = 58.5). The glucose solution has a concentration of 9.0 g per 250 mL (molecular weight = 180).

Question

Calculate the molality, millimolality, and milliosmolality of both solutions. State whether osmosis will occur and, if it will, in which direction. Explain your answer.

Answer 1

To calculate molality, we need to find the moles of solute per kilogram of solvent. Since water has a density of 1 g/mL, we can assume that there is 250 g of water in each 250 mL solution.

1. NaCl Solution:
Mass of NaCl = 1.95 g
Molecular weight of NaCl = 58.5 g/mol

Moles of NaCl = (mass of NaCl) / (molecular weight of NaCl) = 1.95 g / 58.5 g/mol ≈ 0.0333 mol

Molality (m) = moles of solute / kg of solvent = 0.0333 mol / 0.250 kg = 0.133 mol/kg

Millimolality (mm) = molality × 10^3 = 0.133 mol/kg × 10^3 = 133 mmol/kg

2. Glucose Solution:
Mass of glucose = 9.0 g
Molecular weight of glucose = 180 g/mol

Moles of glucose = (mass of glucose) / (molecular weight of glucose) = 9.0 g / 180 g/mol ≈ 0.050 mol

Molality (m) = moles of solute / kg of solvent = 0.050 mol / 0.250 kg = 0.200 mol/kg

Millimolality (mm) = molality × 10^3 = 0.200 mol/kg × 10^3 = 200 mmol/kg

Now, we will calculate the milliosmolality, which is a measure of the total concentration of all particles in the solution, taking into account that NaCl will dissociate into two particles (Na+ and Cl-) when dissolved in water.

3. NaCl Solution:
Milliosmolality (mosm) = millimolality × number of particles = 133 × 2 = 266 mosm/kg

4. Glucose Solution:
Milliosmolality (mosm) = millimolality × number of particles = 200 × 1 = 200 mosm/kg

Now, let's determine the direction of osmosis:

Osmosis occurs from solutions with a lower concentration of solute particles (higher water potential) to solutions with higher concentration of solute particles (lower water potential).
Here, the glucose solution has a milliosmolality of 200 mosm/kg, while the NaCl solution has a milliosmolality of 266 mosm/kg.

Therefore, osmosis will occur from the glucose solution to the NaCl solution, as water will move from a lower concentration of solute particles to a higher concentration.