Assertion: When a solution is separated from the pure solvent by a semipermeable membrane, the solvent molecul

NCERT Exemplar · Q54

Q. Assertion: When a solution is separated from the pure solvent by a semipermeable membrane, the solvent molecules pass through it from pure solvent side to the solution side. Reason: Diffusion of solvent occurs from a region of high concentration solution to a region of low concentration solution. Choose the correct option:

(i) Assertion and reason both are correct statements and reason is correct explanation for assertion.

(ii) Assertion and reason both are correct statements but reason is not correct explanation for assertion.

(iii) Assertion is correct statement but reason is wrong statement.

(iv) Assertion and reason both are incorrect statements.

(v) Assertion is wrong statement but reason is correct statement.

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Concept understanding — Osmosis

Osmotic Pressure and Molar Mass: From Intuition to Formula

Imagine you have a glass of pure water, and you carefully place a tea bag into it. After a while, the water turns brown. The tea molecules have moved from the bag into the water. That's simple diffusion. But now imagine a different setup: you have a U-shaped tube with a special membrane at the bottom that only lets water molecules pass through — not larger molecules like sugar. On one side you put pure water, on the other side you put a sugar solution. What happens?

Water will spontaneously move from the pure water side into the sugar solution side, pushing the liquid level higher on the sugar side. That rising column of liquid is a direct physical effect — it's osmotic pressure trying to equalise concentrations. The taller the column gets, the more hydrostatic pressure it exerts back. Eventually, that back-pressure exactly balances the "pull" of the sugar, and the system stops.

That balancing pressure — the pressure you would need to apply to the solution side to prevent the water from moving — is the osmotic pressure ( $\Pi$ ).

The Intuition Behind Molar Mass from Osmotic Pressure

Here's the key insight: the osmotic pressure depends only on the number of solute particles in a given volume of solution, not on what those particles are. A big protein molecule and a tiny sugar molecule, if present in the same number per litre, produce the same osmotic pressure.

This is incredibly useful. If you dissolve an unknown substance (say, a polymer or a protein) in water and measure the osmotic pressure, you can work backwards to find how many moles of it are present. And if you know the mass you dissolved, you can calculate the molar mass:

\text{Molar mass} = \frac{\text{mass of solute (g)}}{\text{number of moles}}

So osmotic pressure becomes a direct window into the molecular weight of substances that are too large or too fragile to vaporise (like proteins, polymers, or enzymes).

The Precise Statement

For dilute solutions, osmotic pressure follows a law that looks exactly like the ideal gas law:

\Pi V = nRT

This is the van't Hoff equation for osmotic pressure. It tells you that osmotic pressure is directly proportional to the molar concentration of the solute:

\Pi = \frac{n}{V}RT = cRT

where $c$ is the molar concentration (mol/L).

From Osmotic Pressure to Molar Mass

If you dissolve a known mass $w$ (in grams) of an unknown substance in a volume $V$ of solvent, and measure the osmotic pressure $\Pi$ at temperature $T$ , you can find the molar mass $M$ as follows:

From $\Pi V = nRT$ , we get $n = \frac{\Pi V}{RT}$
But $n = \frac{w}{M}$ (mass divided by molar mass)
Equating: $\frac{w}{M} = \frac{\Pi V}{RT}$
Rearranging:

M = \frac{wRT}{\Pi V}

This is the working formula. Every quantity on the right is measurable in the lab.

Why This Method is Special

Osmotic pressure measurements are extraordinarily sensitive. For a substance with a very large molar mass (say, 100,000 g/mol), the freezing point depression or boiling point elevation would be too tiny to measure accurately. But osmotic pressure can still give a measurable reading because it's a colligative property that depends only on particle count, and the effect is large even at low concentrations.

Important

Osmotic pressure is the most sensitive colligative property for determining molar masses of macromolecules. It can detect concentrations as low as $10^{-4}$ M, which is 100–1000 times more sensitive than freezing point depression.

A Worked Example

Problem: 0.50 g of a protein is dissolved in enough water to make 100 mL of solution at 25°C. The osmotic pressure is measured as 0.012 atm. Find the molar mass of the protein.

Solution:

Given: …

Why this formula?

Osmosis: Why the Key Formulas Hold

Osmosis is the net movement of solvent molecules (usually water) across a semipermeable membrane from a region of lower solute concentration to higher solute concentration. The membrane allows solvent to pass but blocks solute.

Let’s build the reasoning step-by-step — from the physical picture to the formulas.

1. The Physical Picture: Why Does Water Move?

Imagine a U-shaped tube divided by a semipermeable membrane. Left side: pure water. Right side: water + dissolved sugar.

Water molecules on both sides are in constant random motion.
On the pure water side, every molecule hitting the membrane can pass through (if it fits the pore).
On the sugar side, sugar molecules block some water molecules from reaching the membrane — effectively reducing the number of water molecules that can cross per second.

Result: More water molecules cross from pure side to sugar side than the reverse. This net flow continues until equilibrium is reached.

Key insight: The driving force is the difference in chemical potential of water across the membrane — not a "desire" to dilute the sugar.

2. Chemical Potential: The Real Driver

For an ideal dilute solution, the chemical potential of water ( $\mu_w$ ) is:

\mu_w = \mu_w^0 + RT \ln x_w

Where:

$\mu_w^0$ = chemical potential of pure water
$x_w$ = mole fraction of water
$R$ = gas constant
$T$ = absolute temperature

Since $x_w < 1$ in a solution, $\ln x_w < 0$ , so $\mu_w$ is lower in the solution than in pure water.

Water flows spontaneously from higher $\mu_w$ (pure side) to lower $\mu_w$ (solution side) — this is the fundamental thermodynamic reason.

3. Osmotic Pressure: The Formula $\Pi = iCRT$

What is osmotic pressure ( $\Pi$ )?

It is the external pressure that must be applied to the solution side to prevent net water flow into it — i.e., to make the chemical potential of water equal on both sides.

Derivation sketch:

At equilibrium under applied pressure $\Pi$ :

\mu_w^{\text{pure}}(P) = \mu_w^{\text{solution}}(P + \Pi)

For the solution side, we have two contributions:

Dilution effect (lower mole fraction): $RT \ln x_w$
Pressure effect: $V_w \cdot \Pi$ (where $V_w$ = partial molar volume of water)

So:

\mu_w^0(P) = \mu_w^0(P) + RT \ln x_w + V_w \Pi

Cancel $\mu_w^0(P)$ from both sides:

0 = RT \ln x_w + V_w \Pi

\Pi = -\frac{RT}{V_w} \ln x_w

For dilute solutions:

$x_w \approx 1 - x_{\text{solute}}$ (where $x_{\text{solute}}$ is small)
$\ln(1 - x_{\text{solute}}) \approx -x_{\text{solute}}$ (using Taylor expansion)

Thus:

\Pi \approx \frac{RT}{V_w} \cdot x_{\text{solute}}

Now, $x_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{water}}} \approx \frac{n_{\text{solute}}}{n_{\text{water}}}$ for dilute solutions.

And $n_{\text{water}} \cdot V_w \approx V$ (total volume of solution).

So:

\Pi \approx \frac{RT}{V} \cdot n_{\text{solute}} = CRT

Where $C = \frac{n_{\text{solute}}}{V}$ = molar concentration. …

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The assertion is correct — solvent moves from the pure solvent side to the solution side across a semipermeable membrane. But the reason, as literally worded, describes solvent diffusing from a region of high concentration solution to a region of low concentration solution — that is, from the more concentrated (solute-rich) side to the less concentrated side. That is the OPPOSITE of what actually happens in osmosis, so the reason is a wrong statement. The correct option is (iii).

Getting the direction right

Osmosis is the net movement of solvent molecules across a semipermeable membrane. The membrane lets solvent (e.g., water) pass but blocks the solute. The key question is: which way does the solvent move?

What the assertion says. Solvent moves from the pure solvent side into the solution side. This is the textbook definition of osmosis, and it is correct: pure solvent has the highest concentration of solvent molecules (100%), so the solvent has a natural tendency to move toward the side where its own concentration is lower — inside the solution, where some of the volume is occupied by solute.
What the reason says, read literally. "Diffusion of solvent occurs from a region of high concentration solution to a region of low concentration solution." In standard usage, "concentration of a solution" refers to how much solute is dissolved in it — a "high concentration solution" is one with more solute (pure solvent, with zero solute, is the lowest concentration solution possible). Read this way, the reason claims that solvent moves FROM the more concentrated (solute-rich) side TO the less concentrated (dilute/pure-solvent) side.

But that is exactly backwards from real osmosis, where solvent moves from the less concentrated (or pure) side INTO the more concentrated solution. If the reason's claimed direction were correct, water would flow OUT of a salty solution into pure water — the opposite of what is observed when, say, a cell is placed in salt water (the cell shrinks because water leaves it, moving toward the higher-solute-concentration external solution, not away from it). …

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Here’s a breakdown of the common mistakes students make with this osmosis-based assertion-reason question, and how to avoid each.

Mistake 1: Misinterpreting the direction of solvent flow in the Assertion

The mistake:

Students think solvent moves from the solution side to the pure solvent side (i.e., they reverse the direction). They confuse osmosis with reverse osmosis or think “higher concentration of solute” means “higher concentration of solvent.”

Why it happens:

They focus on solute concentration instead of solvent concentration. In osmosis, the solvent (usually water) moves from a region of higher solvent concentration (pure solvent) to a region of lower solvent concentration (solution). The solution has solute particles dissolved in it, so its solvent concentration is lower.

How to avoid:

Always ask: Where is the solvent more concentrated?
- Pure solvent → 100% solvent molecules.
- Solution → some solvent molecules replaced by solute → lower % of solvent.
Remember the mnemonic: Solvent flows from “pure” to “solution” (not the other way).
The Assertion here is correct.

Mistake 2: Misreading the Reason — confusing “high concentration solution” with “high concentration of solvent”

The mistake:

Students read “high concentration solution” and think it means “high concentration of solute.” They then conclude the Reason is correct because “diffusion occurs from high to low concentration.” But the Reason actually says:

“Diffusion of solvent occurs from a region of high concentration solution to a region of low concentration solution.”

This is wrong — it should say “from a region of high solvent concentration to a region of low solvent concentration.” The phrase “high concentration solution” is ambiguous and, in standard terminology, means a solution with a high solute concentration (i.e., low solvent concentration).

How to avoid:

In osmosis, always specify: solvent concentration, not just “concentration.”
If a statement says “high concentration solution,” ask: High in what? If it’s solute, the solvent concentration is low.
The correct phrasing: Solvent diffuses from a region of high solvent concentration (or low solute concentration) to a region of low solvent concentration (or high solute concentration).
The Reason here is incorrect.

Mistake 3: Choosing option (i) — thinking both are correct and Reason explains Assertion

The mistake:

Students see that the Assertion is correct and the Reason sounds like a general diffusion principle, so they assume it’s a valid explanation. They don’t catch the subtle error in the Reason’s wording.

Why it happens:

They memorise “diffusion is from high to low concentration” without applying it specifically to solvent in osmosis. They also don’t notice the phrase “high concentration solution” is the opposite of what it should be.

How to avoid:

Read the Reason word by word.
Replace “solution” with “solvent” mentally:
- Original: “high concentration solution” → means high solute → low solvent.
- Correct: “high concentration of solvent” → means pure solvent side.
If the Reason contradicts the Assertion’s direction, it cannot be the correct explanation. …

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Concept understanding — Osmosis

Osmotic Pressure and Molar Mass: From Intuition to Formula

The Intuition Behind Molar Mass from Osmotic Pressure

The Precise Statement

From Osmotic Pressure to Molar Mass

Why This Method is Special

A Worked Example

Why this formula?

Osmosis: Why the Key Formulas Hold

1. The Physical Picture: Why Does Water Move?

2. Chemical Potential: The Real Driver

3. Osmotic Pressure: The Formula $\Pi = iCRT$

What is osmotic pressure ( $\Pi$ )?

Derivation sketch:

For dilute solutions:

Getting the direction right

Concept: Osmosis and Concentration Gradients

Method: Concept Verification by Definition

Mistake 1: Misinterpreting the direction of solvent flow in the Assertion

Mistake 2: Misreading the Reason — confusing “high concentration solution” with “high concentration of solvent”

Mistake 3: Choosing option (i) — thinking both are correct and Reason explains Assertion

Getting the direction right

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