Question

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).

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

Answers

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.

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