[Note: two or more options may be correct] Isotonic solutions must have the same _______. (i) solute (ii) dens

NCERT Exemplar · Q31

Q. [Note: two or more options may be correct] Isotonic solutions must have the same _____________.

(i) solute

(ii) density

(iii) elevation in boiling point

(iv) depression in freezing point

Karnataka PUCMCQ· 1mImportance★★★★★

74% · 97/131 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

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 | …

Start your 14-day free trial to unlock the full solution →

Isotonic solutions have the same osmotic pressure. Since osmotic pressure, elevation in boiling point, and depression in freezing point are all colligative properties that depend on the effective concentration of solute particles, isotonic solutions (with the same solvent and temperature) must have the same elevation in boiling point and depression in freezing point. The correct options are (iii) and (iv).

When we talk about isotonic solutions, we are fundamentally discussing a concept rooted in colligative properties. Understanding this connection is key to solving the problem.

What are Colligative Properties?

Colligative properties are properties of solutions that depend solely on the number of solute particles in a given amount of solvent, and not on the identity of the solute particles. There are four main colligative properties:

Relative lowering of vapor pressure
Elevation in boiling point
Depression in freezing point
Osmotic pressure

What are Isotonic Solutions?

Two solutions are said to be isotonic if they have the same osmotic pressure at a given temperature. This definition is crucial.

\Pi

If two solutions are isotonic, it means their osmotic pressures are equal:

$\Pi_1 = \Pi_2$

$i_1 C_1 R T = i_2 C_2 R T$

Assuming the temperature $T$ is the same for both solutions, and $R$ is a constant, this simplifies to:

$i_1 C_1 = i_2 C_2$

This tells us that isotonic solutions have the same effective molar concentration of solute particles.

Now, let's analyze each option based on this understanding. We will assume that the solutions being compared are in the same solvent (e.g., water), which is the standard context for discussing isotonicity.

Option (i) solute
- Reasoning: Isotonic solutions do not need to have the same solute. For example, a $0.9\% \text{ (w/v)}$ NaCl solution is isotonic with blood plasma. A $5\% \text{ (w/v)}$ glucose solution is also isotonic with blood plasma. These two solutions (NaCl and glucose) are isotonic with each other, but they contain different solutes. The key is that they produce the same effective concentration of particles.
- Conclusion: This option is incorrect.
Option (ii) density
- Reasoning: Density is a mass-to-volume ratio. While the effective concentration of particles might be the same, the actual mass of solute and solvent, and thus the overall density, can differ significantly between solutions with different solutes. For instance, a glucose solution and an NaCl solution that are isotonic will have different densities because glucose molecules are much larger than NaCl formula units, and their concentrations (in g/L) will differ to achieve the same particle count.
- Conclusion: This option is incorrect.
Option (iii) elevation in boiling point
- Reasoning: Elevation in boiling point ( $\Delta T_b$ ) is a colligative property, given by the formula: $\Delta T_b = iK_b m$

Start your 14-day free trial to unlock the full solution →

First, the correct answer

Isotonic solutions are solutions with the same osmotic pressure.

For dilute solutions, osmotic pressure ( $\pi$ ) is given by:

\pi = iCRT

where $i$ is the van't Hoff factor, $C$ is molar concentration, $R$ is the gas constant, and $T$ is temperature.

Since $\pi$ depends on the total particle concentration ( $iC$ ), isotonic solutions must have the same effective particle concentration at the same temperature.

Now, which options follow from this?

(i) solute — ✗ Not necessary. Two different solutes can give the same particle concentration.
(ii) density — ✗ Not necessary. Density depends on solute mass and volume, not just particle count.
(iii) elevation in boiling point — ✓ Yes. $\Delta T_b = i K_b m$ . If $iC$ is same, molality ( $m$ ) is approximately same for dilute solutions, so $\Delta T_b$ is same.
(iv) depression in freezing point — ✓ Yes. $\Delta T_f = i K_f m$ . Same logic — same particle concentration gives same $\Delta T_f$ .

Correct options: (iii) and (iv).

Common mistakes students make

✗ Mistake 1: Picking (i) — "same solute"

Why it happens: Students think "isotonic" means "same composition" because of the prefix iso-.

How to avoid: Remember — isotonic means same osmotic pressure, not same chemical identity. Two different solutes (e.g., glucose and urea) can produce the same particle concentration.

✗ Mistake 2: Picking (ii) — "same density"

Why it happens: Density feels related to concentration, so students assume equal concentration means equal density.

How to avoid: Density depends on the mass of solute per volume, not just the number of particles. A solution of a heavy solute (e.g., sucrose) will have higher density than an equimolar solution of a light solute (e.g., urea), even if both are isotonic.

✗ Mistake 3: Not connecting colligative properties

Why it happens: Students treat boiling point elevation, freezing point depression, and osmotic pressure as separate topics. …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ30 — [Note: two or more options may be correct] Van't Hoff factor i is give…→Next questionQ32 — [Note: two or more options may be correct] Which of the following bina…

Q.[Note: two or more options may be correct] Isotonic solutions must have the same _____________.

Concept understanding — Osmotic Pressure

Osmotic Pressure: The Push of Pure Solvent

The Precise Definition

The van't Hoff Equation

Why It Matters for Macromolecules

Method: Conceptual Elimination using Henry’s Law & Colligative Properties

Step 1 — Recall the definition of isotonic solutions

Step 2 — Relate to the given options

First, the correct answer

Common mistakes students make

✗ Mistake 1: Picking (i) — "same solute"

✗ Mistake 2: Picking (ii) — "same density"

✗ Mistake 3: Not connecting colligative properties

Q.[Note: two or more options may be correct] Isotonic solutions must have the same _____________.

🎓Unlock everything free for 14 days

Unlock everything free for 14 days