Give reasons: (a) Cooking is faster in pressure cooker than in cooking pan. (b) Red Blood Cells (RBC) shrink w

Question

Q. Give reasons:

(a) Cooking is faster in pressure cooker than in cooking pan.

(b) Red Blood Cells (RBC) shrink when placed in saline water but swell in distilled water.

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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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(a) Higher pressure raises water's boiling point, so food cooks at a hotter temperature. (b) Osmosis drives water across the semi-permeable RBC membrane toward the region of higher solute concentration—out of the cell in saline (shrinking) and into the cell in distilled water (swelling).

(a) Why cooking is faster in a pressure cooker

The heart of the matter is boiling point elevation under pressure. Water at normal atmospheric pressure boils at $100\,^\circ\text{C}$ , and no matter how much you turn up the flame, the liquid water cannot get hotter than that—any extra heat simply converts water to steam at the same temperature. But chemical reactions (including the breakdown of starches, proteins, and cellulose in food) proceed faster at higher temperatures, so cooking at $100\,^\circ\text{C}$ takes time.

A pressure cooker traps steam, which raises the pressure inside the vessel. According to the Clausius–Clapeyron relation (or simply the phase diagram of water), the boiling point of a liquid increases with pressure. At roughly $15\,\text{psi}$ above atmospheric pressure (a typical pressure-cooker setting), water boils near $121\,^\circ\text{C}$ instead of $100\,^\circ\text{C}$ .

Sealed environment: The lid locks and the steam cannot escape freely, so pressure builds.
Elevated boiling point: Water remains liquid at temperatures well above $100\,^\circ\text{C}$ .
Faster reaction kinetics: The $\sim20\,^\circ\text{C}$ increase roughly doubles or triples the rate of most cooking reactions (a rough rule of thumb from the Arrhenius equation is that reaction rates double for every $10\,^\circ\text{C}$ rise).
Result: Food cooks in a fraction of the time—what takes an hour in an open pan may take $15$ – $20$ minutes in a pressure cooker.

Tip

At high altitudes, atmospheric pressure is lower, so water boils below $100\,^\circ\text{C}$ and cooking takes longer. A pressure cooker compensates by restoring the higher pressure (and boiling point) you would have at sea level.

(b) Why RBCs shrink in saline water but swell in distilled water

Red blood cells are enclosed by a semi-permeable membrane that allows water to pass freely but blocks most dissolved solutes (salts, proteins). The movement of water across this membrane is governed by osmosis: water flows from a region of lower solute concentration (higher water potential) to a region of higher solute concentration (lower water potential) until equilibrium is reached—or until the cell bursts or shrivels.

The cytoplasm of an RBC has a certain osmolarity (roughly $0.9\%$ NaCl equivalent, or about $300\,\text{mOsm/L}$ ). What happens depends on the external solution:

In saline water (hypertonic solution)

Higher external solute concentration: If the saline is more concentrated than the cell's interior (say $>0.9\%$ NaCl), the outside has a higher osmolarity.
Water leaves the cell: Osmosis drives water out of the RBC, across the membrane, into the surrounding solution.
Cell shrinks (crenation): The cell loses volume, the membrane wrinkles, and the RBC takes on a shriveled, spiky appearance.

In distilled water (hypotonic solution)

Lower external solute concentration: Pure water has essentially zero solute, far below the cell's $\sim0.9\%$ internal salt.
Water enters the cell: Osmosis drives water into the RBC. …

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Q.Give reasons:

(a) Why cooking is faster in a pressure cooker

(b) Why RBCs shrink in saline water but swell in distilled water

In saline water (hypertonic solution)

In distilled water (hypotonic solution)

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