1. Use the osmotic pressure formula

For dilute solutions, $\pi = iMRT$ where:

• $\pi$ = osmotic pressure
• $i$ = van't Hoff factor
• $M$ = molarity
• $R$ = gas constant
• $T$ = temperature

Since all solutions are at the same temperature ($25^\circ$C), and $R,T$ are constant, we only need to compare $iM$.

2. Find $i$ for each solute

(a) $0.500\,M\; C_2H_5OH$

Ethanol is a non-electrolyte, so it does not dissociate. $i=1$ Thus, $iM = 1 \times 0.500 = 0.500$

(b) $0.100\,M\; Mg_3(PO_4)_2$

Assuming complete dissociation: $Mg_3(PO_4)_2 \rightarrow 3Mg^{2+} + 2PO_4^{3-}$ Total ions $= 3+2=5$, so $i=5$ Thus, $iM = 5 \times 0.100 = 0.500$

(c) $0.250\,M\; KBr$

Strong electrolyte: $KBr \rightarrow K^+ + Br^-$ Total ions $=2$, so $i=2$ Thus, $iM = 2 \times 0.250 = 0.500$

(d) $0.125\,M\; Na_3PO_4$

Strong electrolyte: $Na_3PO_4 \rightarrow 3Na^+ + PO_4^{3-}$ Total ions $=4$, so $i=4$ Thus, $iM = 4 \times 0.125 = 0.500$

3. Compare osmotic pressures

For all four solutions, $iM = 0.500$ So, $\pi = iMRT$ will be the same for all.

4. Evaluate options

• A: False
• B: False
• C: True
• D: False

So the correct option is: $\boxed{C}$

5. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They agree.