Consider separate solutions of 0.500 M $$C_2H_5OH$$ (aq), 0.100 M $$Mg_3(PO_4)_2$$ (aq), 0.250 M KBr (aq) and 0.125 M $$Na_3PO_4$$ (aq) at 25 °C. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

We begin by recalling the van ’t Hoff equation for osmotic pressure. The formula is stated as

$$\pi \;=\; i\,M\,R\,T,$$

where $$\pi$$ is the osmotic pressure, $$i$$ is the van ’t Hoff factor (the total number of particles obtained per formula unit on complete dissolution), $$M$$ is the molarity of the solution, $$R$$ is the gas constant and $$T$$ is the absolute temperature. Because every solution in the question is at the same temperature $$\bigl(25^{\circ}\text{C}\bigr)$$ and $$R$$ is a constant, the factors $$R$$ and $$T$$ will be identical for all four solutions. Hence, to compare the osmotic pressures, we only need to compare the product $$iM$$ for each solution.

Now we determine $$i$$ for each solute by writing the dissociation (if any) in water.

1. For ethanol $$C_2H_5OH$$ we have no ionic dissociation because it is a molecular (nonelectrolyte) solute. Therefore

$$i_{\,C_2H_5OH}=1.$$

2. For potassium bromide $$KBr$$ (a strong electrolyte) the complete dissociation is

$$KBr \;\rightarrow\; K^+ + Br^-.$$

The number of ions produced is $$1 + 1 = 2,$$ so

$$i_{\,KBr}=2.$$

3. For sodium phosphate $$Na_3PO_4$$ (also a strong electrolyte) the dissociation is

$$Na_3PO_4 \;\rightarrow\; 3\,Na^+ + PO_4^{3-}.$$

The total particles are $$3 + 1 = 4,$$ giving

$$i_{\,Na_3PO_4}=4.$$

4. For magnesium phosphate $$Mg_3(PO_4)_2$$ (a strong electrolyte) the dissociation is

$$Mg_3(PO_4)_2 \;\rightarrow\; 3\,Mg^{2+} + 2\,PO_4^{3-}.$$

The number of ions equals $$3 + 2 = 5,$$ so

$$i_{\,Mg_3(PO_4)_2}=5.$$

With the van ’t Hoff factors in hand, we multiply each by its given molarity to obtain $$iM$$ for every solution.

Ethanol: $$iM = 1 \times 0.500 = 0.500$$

Potassium bromide: $$iM = 2 \times 0.250 = 0.500$$

Sodium phosphate: $$iM = 4 \times 0.125 = 0.500$$

Magnesium phosphate: $$iM = 5 \times 0.100 = 0.500$$

We see that each product $$iM$$ equals $$0.500$$. Because $$\pi = iMRT$$ and the factors $$R$$ and $$T$$ are the same for all the solutions, the osmotic pressure $$\pi$$ must likewise be identical for every one of the four solutions.

Therefore, the statement that correctly describes the situation is:

“They all have the same osmotic pressure.”

Hence, the correct answer is Option A.