I am confused about why this is the answer to a practice problem I was given. (answer is c). Could someone explain why/why not for each answer?

2) Solution A is made from 1 L of water and 0.1 moles of Na(CH3COO), and Solution B is made
from 1 L of water and 0.1 moles of Na2(SO4). Assuming both salts completely dissolve and
behave ideally, which of the following is a TRUE statement?
a) Solution A has a higher osmotic pressure than Solution B
b) Solution A has a lower vapor pressure than Solution B
c) Solution A has a higher freezing point than Solution B
d) Solution A has a higher boiling point than Solution B
e) None of the above.

It all has to do with the number of particles in solution.

Solution A is sodium acetate and will have two particles in solutio for every mole of the salt.
Solution B is sodium sulfate and will have 3 particles in solution for every mole of the salt. Can you take it from here or do you want me to draw you a picture? c is the only true statement.

I see how there are the numbers of particles in solution, I am a little confused on how that relates to these properties. My text is pretty brief over this section.

a) Solution A has a higher osmotic pressure than Solution B

pi = MRT. Effective molarity A is 0.2, effective molarity B is 0.3 so A will give a smaller osmotic pressure than B.

b) Solution A has a lower vapor pressure than Solution B
Psolution = Xsolvent*Pnormal solvent. Since there are 0.2 mol for A and 0.3 mol for B, that means the water is a SMALLER mole fraction for B which means B will have a lower vp.

c) Solution A has a higher freezing point than Solution B
delta T = i*Kf*molality.
i is the van't Hoff factor which is the number of particles. i is smaller for A which means delta T is smaller than for B. A smaller value for A means the lowering of T is less and freezing point is higher.True statement


d) Solution A has a higher boiling point than Solution B.
delta T = i*Kb*m
i is larger for B so delta T will be larger for B and the boiling point will be larger for B and that makes this statement false.


e) None of the above.
Since (c) is the only correct one, (e) can't be true.

To determine which statement is true, we need to consider the colligative properties of the solutions, which depend on the number of solute particles relative to the solvent particles.

1. Osmotic pressure: The osmotic pressure of a solution depends on the concentration of solute particles. In this case, both solutions have the same number of solute particles since they both contain 0.1 moles of solute per liter. Therefore, their osmotic pressures would be the same. So, option a) is not true.

2. Vapor pressure: The vapor pressure of a solution decreases as the concentration of solute particles increases. Solution B has two moles of solute particles (Na2SO4) per liter, whereas Solution A has only one mole of solute particles (Na(CH3COO)) per liter. Therefore, Solution B would have a lower vapor pressure compared to Solution A. Hence, option b) is true.

3. Freezing point: The freezing point depression depends on the concentration of solute particles. A solution with more solute particles will have a lower freezing point compared to a solution with fewer solute particles. Since Solution B has two moles of solute particles (Na2SO4) per liter, and Solution A has only one mole of solute particles (Na(CH3COO)) per liter, Solution A would have a higher freezing point compared to Solution B. Thus, option c) is true.

4. Boiling point: The boiling point elevation also depends on the concentration of solute particles. A solution with more solute particles will have a higher boiling point compared to a solution with fewer solute particles. Since Solution B has two moles of solute particles (Na2SO4) per liter, and Solution A has only one mole of solute particles (Na(CH3COO)) per liter, Solution B would have a higher boiling point compared to Solution A. Therefore, option d) is not true.

Based on our analysis, the correct answer is option c) Solution A has a higher freezing point than Solution B.