Q.At a given temperature, osmotic pressure of a concentrated solution of a substance _____________.

The key idea is that osmotic pressure ($\pi$) is a colligative property — it depends only on the number of solute particles per unit volume, not on their identity. For a non-electrolyte, $\pi = iCRT$, where $C$ is the molar concentration.

1. For a given temperature, $R$ and $T$ are constant.
2. A concentrated solution has a higher molar concentration ($C$) than a dilute solution. …

Osmotic pressure is a colligative property — it depends only on the number of solute particles, not on their identity or chemical nature. The classic formula that governs this is van’t Hoff’s law for dilute solutions:

where $\Pi$ is osmotic pressure, $i$ is the van’t Hoff factor (number of particles per formula unit), $C$ is molar concentration (mol/L), $R$ is the gas constant, and $T$ is absolute temperature.

At a fixed temperature, $R$ and $T$ are constants. So $\Pi$ is directly proportional to $C$. A concentrated solution has a higher molar concentration than a dilute solution — more solute molecules or ions per unit volume. That means more collisions with the semipermeable membrane per second, and a greater tendency to pull solvent across the membrane. The result: a higher osmotic pressure.

Now let’s walk through the reasoning step by step.

1. Recall the definition. Osmotic pressure is the extra pressure needed to stop the net flow of solvent into a solution across a semipermeable membrane. It measures how strongly the solution “pulls” solvent.

2. Identify the controlling variable. For dilute solutions, van’t Hoff’s law says $\Pi = iCRT$. At a given temperature, $R$ and $T$ are fixed. For a non-electrolyte, $i = 1$; for an electrolyte, $i$ is constant for that substance. So $\Pi$ is directly proportional to $C$. …

Concept: Osmotic Pressure and Concentration

Method: Direct Application of van't Hoff Law for Osmotic Pressure

Steps:

1. Recall the van't Hoff equation for osmotic pressure ($\pi$):

where:

• $i$ = van't Hoff factor (number of particles per formula unit)
• $C$ = molar concentration (mol/L)
• $R$ = universal gas constant
• $T$ = absolute temperature (constant here)

2. Identify the key variable: At a fixed temperature, $R$ and $T$ are constants. For the same substance, $i$ is also constant. Therefore:

Osmotic pressure is directly proportional to concentration.

3. Compare concentrated vs. dilute solution: …

Here’s a breakdown of the common mistakes students make on this concept and how to avoid each.

The Core Concept

Osmotic pressure ($\pi$) is given by the van’t Hoff equation:

where:

• $i$ = van’t Hoff factor (number of particles per formula unit)
• $C$ = molar concentration (mol/L)
• $R$ = gas constant
• $T$ = absolute temperature

At a fixed temperature, $\pi$ is directly proportional to $C$. Therefore, a concentrated solution (higher $C$) has higher osmotic pressure than a dilute solution (lower $C$).

Correct answer: (i)

Common Mistake #1: Confusing Osmotic Pressure with Vapor Pressure or Boiling Point

• What students do: They think “concentrated solution has lower vapor pressure, so it must have lower osmotic pressure too.”
• Why it’s wrong: Osmotic pressure is not the same as vapor pressure lowering. In fact, all colligative properties (vapor pressure lowering, boiling point elevation, freezing point depression, osmotic pressure) increase with concentration — but osmotic pressure is the most sensitive because it depends directly on molarity, not mole fraction.
• How to avoid: Memorise the formula $\pi = iCRT$. If $C$ increases, $\pi$ increases. Don’t mix up the direction of different colligative properties.

Common Mistake #2: Thinking “Concentrated” Means “Non-Ideal” or “Cannot Compare”

• What students do: They choose option (iv) — “cannot be compared” — because they recall that van’t Hoff’s law is valid only for dilute solutions.
• Why it’s wrong: While it’s true that the equation $\pi = iCRT$ is strictly valid for ideal dilute solutions, the qualitative trend still holds: at the same temperature, a more concentrated solution exerts a higher osmotic pressure than a less concentrated one, even if the exact value deviates from the ideal prediction. The question asks for a comparison, not an exact calculation.
• How to avoid: Distinguish between “exact formula limitation” and “qualitative trend.” For comparison questions, always apply the direct proportionality — unless the question explicitly mentions non-ideality or dissociation/association effects.

Common Mistake #3: Forgetting the van’t Hoff Factor ($i$)

• What students do: They assume concentration alone decides osmotic pressure, ignoring that electrolytes dissociate.
• Why it’s wrong: If the concentrated solution is of a non-electrolyte (e.g., glucose) and the dilute solution is of a strong electrolyte (e.g., NaCl, $i=2$), the dilute solution could have higher osmotic pressure despite lower molarity. But the question does not specify different solutes — it says “a substance,” implying the same solute.
• How to avoid: Always check if the solute is the same. If the same substance is used, $i$ is constant, so $\pi \propto C$. If different solutes are involved, compare $iC$ values. …