Q.The colligative properties of a dilute solution depend upon the

Colligative properties depend only on the NUMBER of solute particles, not their identity. "Freezing point" as stated is not itself such a property.

A colligative property is one whose magnitude depends only on the number (mole fraction/molality) of solute particles present in a solution, and not on their chemical nature. The four classical colligative properties are: relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure.

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Osmotic pressure is a colligative property because it depends only on the number of solute particles dissolved, not their chemical identity.

Colligative properties are physical properties of a solution that depend only on the number of solute particles present, not on their nature. The four classical colligative properties are: (1) relative lowering of vapour pressure, (2) elevation in boiling point, (3) depression in freezing point, and (4) osmotic pressure.

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$\Delta T_b$, $\Delta T_f$ and $\pi$ are colligative properties (they depend on the number of solute particles); $K_b$ is a solvent-specific constant that relates them, not a property itself.

Colligative properties depend only on the number of solute particles present in a solution, not their chemical identity. The four classical colligative properties are: relative lowering of vapour pressure, elevation in boiling point ($\Delta T_b$), depression in freezing point ($\Delta T_f$), and osmotic pressure ($\pi$).

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Colligative properties are defined precisely as properties that depend on the number of solute particles in solution, not on what those particles are — so option (b) is correct by definition.

The defining feature of colligative properties

Colligative properties — relative lowering of vapour pressure, elevation in boiling point ($\Delta T_b$), depression in freezing point ($\Delta T_f$), and osmotic pressure ($\pi$) — arise purely from the dilution effect a solute has on the solvent: adding solute particles lowers the effective mole fraction/chemical potential of solvent molecules at the surface, which shifts vapour–liquid and solid–liquid equilibria. This shift depends only on how many solute particles are present per unit amount of solvent, e.g. $\pi = CRT$ or $\Delta T_b = K_b\,m$, where $C$ (or molality $m$) counts particles, with no term for the solute's identity, mass, or specific charge (beyond the van't Hoff factor $i$, which itself just corrects the particle count for dissociation/association).

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Colligative properties depend on the ratio of the number of solute particles to the number of solvent molecules in the solution.

Colligative properties (relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure) depend only on the number of solute particles present in a given amount of solvent (i.e. on molar concentration/mole fraction of solute), and are independent …

Colligative properties are a set of solution properties that depend solely on the number of dissolved solute particles relative to the total number of solvent molecules, regardless of what the solute chemically is.

When a non-volatile solute is dissolved in a solvent, several physical properties of the resulting solution change in a way that depends only on the ratio of the number of solute particles to solvent molecules — not on the size, mass, or chemical identity of the solute particles. Such properties are called colligative properties (from Latin colligatus, meaning 'bound together').

The four classical colligative properties are:

1. Relative lowering of vapour pressure, $\dfrac{p^0 - p_s}{p^0} = x_2$
2. Elevation of boiling point, $\Delta T_b = K_b\, m$
3. Depression of freezing point, $\Delta T_f = K_f\, m$ …

Colligative properties (relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure) depend solely on how many solute particles are present per unit of solvent, never on what the particles chemically are.

Colligative properties arise because dissolved solute particles physically get in the way of solvent molecules (lowering the escaping tendency of the solvent), so their magnitude depends only on the ratio of solute particles to solvent particles/moles present, not on the size, mass, or chemical nature of those particles. This is why equimolal solutions of glucose and urea — two chemically very different non-electrolytes — show identical elevation of boiling point and identical osmotic pressure: both contribute exactly one particle per formula unit.

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Colligative properties depend only on the number of solute particles, not their identity. Of the four options, only "elevation in boiling point" correctly names one.

Colligative properties are properties of a solution that depend on the number of solute particles present, not on their chemical nature. The four true colligative properties are:

1. Relative lowering of vapour pressure
2. Elevation in boiling point ($\Delta T_b$) — a non-volatile solute raises the boiling point of the solvent
3. Depression in freezing point ($\Delta T_f$) — a non-volatile solute lowers the freezing point of the solvent
4. Osmotic pressure …

Colligative properties (relative lowering of vapour pressure, boiling-point elevation, freezing-point depression, osmotic pressure) depend purely on the count of solute particles per unit amount of solvent, never on what the particles chemically are.

By definition, a colligative property changes in direct proportion to the number of solute particles (molecules or ions) present in a given amount of solvent, regardless of their size, shape, mass, or chemical nature. This is why, for example, a mole of glucose and a mole of urea (unequal molar masses, totally different chemistry) produce the same boiling-poi …