The following questions are case-based questions. Each question has an internal choice and carries 4 (2+1+1) m

Question

Q. The following questions are case-based questions. Each question has an internal choice and carries 4 (2+1+1) marks each. Read the passage carefully and answer the questions that follow : Osmosis is a process by which the molecules of a solvent pass from a solution of low solute concentration to a solution of high solute concentration through a semi-permeable membrane. Osmotic pressure is a colligative property. When the applied pressure on a solution exceeds its osmotic pressure, reverse osmosis occurs. When two solutions are separated by a semipermeable membrane and they have same osmotic pressure they are said to be isotonic. Of the two solutions separated by a semipermeable membrane, if one is a lower osmotic pressure, it is said to be hypotonic relative to the second solution. If it has a higher osmotic pressure, than the second solution, it is said to be hypertonic relative to the second solution. The osmotic pressure associated with the fluid inside the blood cell is equivalent to that of 0.9% (mass/volume) sodium chloride solution called normal saline solution and it is safe to inject intravenously. Osmotic pressure is vital in daily life and nature. It helps in explain, why IV fluids match blood's osmotic pressure, its also the principle behind food preservation using salt or sugar.

(a) Calculate the amount of

CaCl_2

(i = 2.59) dissolved in 2.46 litre of water such that its osmotic pressure is 0.70 atm at 27°C. [Given : R = 0.082 L atm K

^{-1}

mol

^{-1}

, molar mass of

CaCl_2

= 111 g mol

^{-1}

]

(b) When raisins are kept in water, they get swollen. Name the phenomenon involved in this process.

(OR)

(b) Why osmotic pressure is more advantageous than other colligative properties ?

CBSECBSE Class XII Board 2026Subjective· 4mImportance★★★★★

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Part (a)Concept understanding — Osmotic Pressure

Osmotic Pressure: The Push of Pure Solvent

Imagine you have a U-shaped tube with a special membrane at the bottom that only lets water molecules pass through — not sugar molecules. On one side you put pure water, on the other side you put a sugar solution. What happens?

Water moves from the pure side into the solution side. The solution level rises. This is osmosis — the spontaneous net movement of solvent across a semipermeable membrane from a region of lower solute concentration to higher solute concentration.

But here's the key question: what if you don't want that level to rise? What if you want to keep the solution side exactly where it is?

You would have to push down on the solution side with extra pressure — just enough to stop the water from coming in. That extra pressure is osmotic pressure.

Note

Osmotic pressure is not a pressure the solution "has" inside it. It is the external pressure you must apply to prevent osmosis. Think of it as the "resistance pressure" that exactly balances the tendency of solvent to dilute the solution.

The Precise Definition

Osmotic pressure ( $\Pi$ ) is the minimum excess pressure that must be applied to a solution to prevent the inward flow of solvent across a semipermeable membrane.

The membrane must be permeable only to solvent molecules, not to solute particles. This is the defining condition — if the membrane leaks solute, you don't get true osmotic pressure.

The van't Hoff Equation

For dilute solutions, osmotic pressure follows a beautifully simple law:

\Pi = CRT

Where:

$\Pi$ = osmotic pressure (in atm or Pa)
$C$ = molar concentration of solute (mol/L or mol/m³)
$R$ = universal gas constant
$T$ = absolute temperature (K)

This is van't Hoff's law of osmotic pressure. It looks exactly like the ideal gas law ( $PV = nRT$ rearranged as $P = (n/V)RT$ ), and that's no coincidence — van't Hoff noticed that solute particles in dilute solution behave like gas molecules bouncing around, creating a "pressure" against the membrane.

Watch out

This equation works only for non-electrolyte solutions at low concentrations. For electrolytes, you must include the van't Hoff factor $i$ : $\Pi = iCRT$ . A 0.1 M NaCl solution gives nearly twice the osmotic pressure of a 0.1 M glucose solution because NaCl dissociates into two ions.

Why It Matters for Macromolecules

Here's where osmotic pressure becomes a powerful tool. Suppose you have a protein — say, hemoglobin — and you want to know its molar mass. You can't easily measure its concentration in mol/L because you don't know the molar mass yet. But you can measure:

The mass of protein dissolved (say, $w$ grams in $V$ liters)
The osmotic pressure $\Pi$ of that solution

Since $C = n/V = (w/M)/V$ , where $M$ is the molar mass:

\Pi = \frac{wRT}{MV}

Rearrange:

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

Tip

| Property | Why osmotic pressure wins |

|----------|---------------------------|

| Boiling point elevation | Very small for macromolecules — hard to measure |

| Freezing point depression | Very small — same problem | …

Part (b)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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Part (a): $\pi = iCRT$ gives $n = 0.027$ mol → mass of $CaCl_2 = 3.0$ g; raisins swell by osmosis (endosmosis).

Part (b): osmotic pressure is measurable even for dilute/macromolecular solutions; sea-water desalination uses reverse osmosis.

Part (a)

CaCl $_2$ needed for $\pi = 0.70$ atm

$CaCl_2$ is an electrolyte, so use the van't Hoff factor: $\pi = i\dfrac{n}{V}RT$ .

n = \frac{\pi V}{iRT} = \frac{0.70\times2.46}{2.59\times0.082\times300}

Denominator $= 2.59\times0.082\times300 = 63.71$ ; numerator $= 1.722$ , so $n = 0.0270$ mol.

\text{mass} = n\times M = 0.0270\times111 = 3.0\ \text{g}

Raisins swelling …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 37 on this concept.

CBSE 2026Set DZ1 markMCQ
$Q. Which formula is used to calculate osmotic pressure?$
(a) $\pi = CRT$
(b) $\pi = VRT$
(c) $\pi = PVT$
(d) $\pi = nRT$
›Reveal solutionSolution

Osmotic pressure is a colligative property given by $\pi = CRT$ , so option (a) is correct.

Osmotic pressure ( $\pi$ ) is the extra pressure that must be applied on the solution side of a semipermeable membrane to just stop the net flow of solvent into the solution. For a dilute solution it depends only on the number of solute particles per unit volume, i.e. the molar concentration $C = n/V$ .

The van't Hoff equation for osmotic pressure is:

$\pi = CRT = \dfrac{n}{V}RT$ …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Isotonic solutions have the same:$
(a) Normality
(b) Molarity
(c) Osmotic pressure
(d) Formality
›Reveal solutionSolution

Isotonic solutions have equal osmotic pressure, which is why cells neither swell nor shrink when placed in an isotonic medium.

Osmotic pressure (π) of a solution is given by π = CRT, where C is the molar concentration of solute particles. Two solutions are said to be isotonic with respect to each other when they exhibit the SAME osmotic pressure at the same temperature. When such solutions are separated by a semipermeable membrane, there is no net flow of solvent from one to the other — this is why isotonic saline (0.9% NaCl) is used for intravenous drips, since it matches the osmotic pressure of blood plasma and doesn't cause red blood cells to swell (hypotonic) or shrink (hypertonic).

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. A plant cell shrinks when it is kept in a$
(a) Hypotonic solution
(b) Hypertonic solution
(c) Isotonic solution
(d) Pure water
›Reveal solutionSolution

A plant cell placed in a hypertonic solution loses water to its surroundings by osmosis and shrinks; this is called plasmolysis.

A solution is hypertonic relative to the cell sap if it has a higher solute concentration (higher osmotic pressure) than the cell's interior. Water always moves from a region of lower solute concentration (higher water potential) to higher solute concentration (lower water potential) across the semi-permeable cell membrane.

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q. Sea water is converted into fresh water based upon the phenomenon of:$
(a) Diffusion
(b) Osmosis
(c) Plasmolysis
(d) Reverse Osmosis
›Reveal solutionSolution

Desalination of sea water to get fresh water uses reverse osmosis.

In normal osmosis, solvent flows from a dilute solution to a concentrated solution through a semipermeable membrane. If a pressure greater than the osmotic pressure of the sea water is applied on the sea-water side, the flow of solvent is reversed — pure water is forced from the concentrated (saline) side through the membrane to the dilute side, leav …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. The pressure of solution that just prevents the flow of solvent is called:$
(a) Vapour Pressure
(b) Osmotic Pressure
(c) Partial Pressure
(d) Gas pressure
›Reveal solutionSolution

The pressure that just stops solvent flow (osmosis) is the osmotic pressure.

When a solution is separated from pure solvent by a semipermeable membrane, solvent flows into the solution (osmosis). The excess pressure that must be applied on the solution side to just prevent this net inflow of solvent is …

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CBSE 2025Set D1 markMCQ
$Q. Isotonic solutions have equal$
(a) osmotic pressure
(b) vapour pressure
(c) relative lowering of vapour pressure
(d) elevation of boiling point
›Reveal solutionSolution

Isotonic solutions have equal osmotic pressure.

By definition, two solutions are isotonic if they exert the same osmotic pressure at the same temperature. Because osmotic pressure pi = C R T, isotonic solutions must have the same molar concentration of particles.

…

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CBSE 2025Set ANNUAL1 markMCQ
$Q. The porous membrane used in reverse osmosis plant is made up by:$
(a) Cellulose acetone
(b) Potassium nitrate
(c) Mercuric iodide
(d) Starch
›Reveal solutionSolution

The semi-permeable membrane used in reverse osmosis water purification plants is made of cellulose acetate.

In reverse osmosis, a pressure greater than the osmotic pressure of the solution (e.g. seawater) is applied on the solution side, forcing pure solvent (water) to flow through a semi-permeable membrane from the concentrated to the dilute side — the reverse of normal osmosis. The membrane commonly used for this purpose in desalination/purification plants is made of cellulose acetate — a synthetic semi-permeable …

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CBSE 2025Set ANNUAL1 markMCQ
$Q. Which of the following colligative properties is used to determine molar masses of proteins, polymers or other macromolecules?$
(a) Depression in freezing point
(b) Relative lowering of vapour pressure
(c) Osmotic pressure
(d) Elevation in boiling point
›Reveal solutionSolution
Colligative properties are inversely proportional to molar mass, so for very large molecules (proteins, polymers) most of them become too small to measure precisely — except osmotic pressure, which stays measurable even in very dilute solutions.

Why the other options fail

(a) Depression in freezing point $\Delta T_f = K_f m$ and (d) Elevation in boiling point $\Delta T_b = K_b m$ : for a macromolecule of large $M$ , the molality $m = \dfrac{w_2 \times 1000}{M \times w_1}$ is tiny, so $\Delta T_f$ / $\Delta T_b$ become too small (often a few thousandths of a kelvin) to measure accurately with an ordinary thermometer.

(b) Relative lowering of vapour pressure $\dfrac{p_1^\circ - p_1}{p_1^\circ} = x_2$ also becomes vanishingly small and is experimentally hard to measure with the needed precision for dilute macromolecular solutions. …
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CBSE 2025Set ANNUAL1 mark
$Q. What are hypertonic solutions?$
›Reveal solutionSolution

A hypertonic solution has a greater osmotic pressure (higher effective solute concentration) than a reference solution, so it draws water out of a cell placed in it.

Definition

When two solutions are compared, the one with the higher osmotic pressure (i.e. higher concentration of osmotically active solute particles) is called the hypertonic solution relative to the other (which is then called hypotonic).

…

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CBSE 2024Set D1 markMCQ
$Q. Isotonic solutions have the same$
(a) Density
(b) Normality
(c) Strength
(d) Molar concentration
›Reveal solutionSolution

Isotonic solutions have the same osmotic pressure. Since osmotic pressure pi = CRT, equal pi at the same temperature means equal molar concentration C.

Osmotic pressure of a dilute solution: pi = CRT, where C is molar concentration, R the gas constant and T the temperature.

…

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CBSE 2024Set D1 markMCQ
$Q. The osmotic pressure of a solution is represented by which of the following equations?$
(a) pi = CR/T
(b) pi/C = RT
(c) pi = CT/R
(d) pi = RT/C
›Reveal solutionSolution

Osmotic pressure: pi = CRT, i.e. pi/C = RT.

For a dilute solution the osmotic pressure (pi) is given by the van't Hoff equation:

pi = CRT

…

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CBSE 2024Set ANNUAL1 mark
$Q. The two solutions with equal osmotic pressure are called ______.$
›Reveal solutionSolution

Two solutions having equal osmotic pressure at a given temperature are called isotonic solutions.

Osmotic pressure (pi) is the colligative property that measures the pressure needed to stop the net flow of solvent across a semipermeable membrane. If two solutions have exactly the same osmotic pressure at the same temperature, no net osmosis occurs when they are separated by a semipermeable membrane and placed in contact - such solutions are called isotonic solutions.

…

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Part (a)

CaCl2_22​ needed for π=0.70\pi = 0.70π=0.70 atm

Raisins swelling …

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CaCl $_2$ needed for $\pi = 0.70$ atm

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