Animated Solution for Chemistry - Solutions: Consider the separate solution of $0.500\text{ M}$ ${\text{C}}_2{\text{H}}_5\text{OH}\text{ (aq)}$, $0.100\text{ M}$ ${\text{Mg}}_3({\text{PO}}_4{)}_2\text{ (aq)}$, $0.250\text{ M}$ $\text{KBr}\text{ (aq)}$ and $0.125\text{ M}$ ${\text{Na}}_3{\text{PO}}_4\text{ (aq)}$ at $25^{\circ }\text{C}$. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

When we look at a lineup of different chemical solutions, our first instinct is often to judge their properties based purely on their stated molarity. A $0.500\text{ M}$ solution must surely exert a higher osmotic pressure than a $0.100\text{ M}$ solution, right? Well, not quite. This is where the magic of the van't Hoff factor ($i$) comes into play, revealing that the true 'effective concentration' is what really matters.

Osmotic pressure ($\pi$) is a colligative property, meaning it depends strictly on the number of solute particles in a given volume of solvent, not on their chemical identity. The governing equation is:

Here, $C$ is the molarity, $R$ is the universal gas constant, and $T$ is the absolute temperature. Since all our solutions are at the same temperature ($25^{\circ }\text{C}$), $R$ and $T$ are constants. Therefore, the osmotic pressure is directly proportional to the product of the van't Hoff factor and the molarity:

This product, $i\times C$, is often referred to as the osmolarity or the effective concentration of particles.

Let's break down each solution to find its true particle concentration:

1. Ethanol (${\text{C}}_2{\text{H}}_5\text{OH}$): Ethanol is a covalent compound and a non-electrolyte. It dissolves in water but does not dissociate into ions. Thus, one molecule of ethanol yields one particle in solution.

2. Magnesium Phosphate (${\text{Mg}}_3({\text{PO}}_4{)}_2$): This is a strong electrolyte. Upon dissolving, one formula unit shatters into three magnesium ions (${\text{Mg}}^{2+}$) and two phosphate ions (${\text{PO}}_4^{3-}$).

3. Potassium Bromide ($\text{KBr}$): Another strong electrolyte, it splits cleanly into one potassium ion (${\text{K}}^{+}$) and one bromide ion (${\text{Br}}^{-}$).

4. Sodium Phosphate (${\text{Na}}_3{\text{PO}}_4$): This salt dissociates into three sodium ions (${\text{Na}}^{+}$) and one phosphate ion (${\text{PO}}_4^{3-}$).

Despite having wildly different initial molarities ranging from $0.100\text{ M}$ to $0.500\text{ M}$, the dissociation of the electrolytes perfectly balances the scales. Every single solution produces an effective particle concentration of exactly $0.500\text{ M}$.

Because their effective concentrations are identical, they will all exert the exact same osmotic pressure. Solutions that share the same osmotic pressure are known as isotonic solutions. This problem beautifully illustrates why we must always account for electrolytic dissociation when dealing with colligative properties!