An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because _______. (i) it gai

NCERT Exemplar · Q12

Q. An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because _____________.

(i) it gains water due to osmosis.

(ii) it loses water due to reverse osmosis.

(iii) it gains water due to reverse osmosis.

(iv) it loses water due to osmosis.

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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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Water moves from the mango (dilute solution) into the concentrated salt solution through osmosis, causing the mango to shrivel. The answer is (iv).

When you place an unripe mango in concentrated salt brine, you're creating a classic osmotic scenario. Understanding what happens requires clarity on what osmosis actually is and why water moves the way it does.

Osmosis is the spontaneous movement of solvent molecules (water, in biological contexts) across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration. The membrane allows water through but blocks most dissolved solutes. The driving force? Water naturally moves to dilute the more concentrated solution, trying to equalize concentrations on both sides.

The mango cells contain water with dissolved sugars, acids, and salts—a relatively dilute solution compared to the concentrated salt brine outside. The cell membranes act as semipermeable barriers.

Here's what happens step by step:

Identify the concentration gradient. The salt solution outside is hypertonic (higher solute concentration) relative to the mango's cell sap, which is hypotonic (lower solute concentration).
Determine the direction of water movement. Water always flows from hypotonic to hypertonic—from inside the mango cells outward into the salt solution. This is osmosis in its textbook form.
Observe the physical consequence. As water leaves the cells, they lose turgor pressure and shrink. The mango tissue shrivels, becoming wrinkled and firm—exactly what you want in a pickle. …

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

The Correct Answer

The correct answer is (iv) it loses water due to osmosis.

The mango shrivels because the concentrated salt solution has a higher solute concentration than the mango cells. Water moves out of the mango (from low solute concentration inside to high solute concentration outside) via osmosis.

Common Mistake #1: Confusing the direction of water movement

What students do wrong:

They think water moves from the salt solution into the mango, so they pick (i) or (iii).

Why this happens:

Students remember that “osmosis is movement of water from high to low concentration” but forget to compare the solute concentration. They see “salt solution” and assume it’s the “watery” side.

How to avoid:

Always compare solute concentration (not water concentration).
In a concentrated salt solution, solute is high → water is low relative to the mango cells.
Water moves from high water concentration (inside mango) to low water concentration (outside).
Mnemonic: “Water follows the salt” — water moves toward the higher solute concentration.

Common Mistake #2: Misunderstanding “reverse osmosis”

What students do wrong:

They pick (ii) or (iii) because they think “reverse osmosis” means water moves against its natural direction, and they assume that’s what happens here.

Why this happens:

The term “reverse osmosis” sounds like it could apply to any situation where water moves out, but it has a specific meaning.

How to avoid:

Reverse osmosis requires external pressure to force water from a high-solute region to a low-solute region (e.g., in water purifiers).
In a pickle jar, no external pressure is applied — it’s just natural osmosis.
Key rule: If no pump or pressure is mentioned, it’s not reverse osmosis.

Common Mistake #3: Forgetting that the mango is the “cell”

What students do wrong:

They treat the mango as an inert object and think it “gains” or “loses” water without considering its cellular structure.

Why this happens: …

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Q.An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because _____________.

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:

Concept: Osmosis and Tonicity

Steps:

The Correct Answer

Common Mistake #1: Confusing the direction of water movement

Common Mistake #2: Misunderstanding “reverse osmosis”

Common Mistake #3: Forgetting that the mango is the “cell”

Q.An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because _____________.

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