To one litre of 0.1 M-HCl solution, 0.025 mole of solid NH4 Cl is added. Assuming complete disso

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To one litre of 0.1 M-HCl solution, 0.025 mole of solid NH4...

To one litre of $0.1$ M-HCl solution, $0.025$ mole of solid $\mathrm{NH}_{4} \mathrm{Cl}$ is added. Assuming complete dissociation of solutes, the freezing point of solution is $\left(K_{f}\right.$ of water $\left.=1.86 \mathrm{~K}-\mathrm{kg} \mathrm{mol}^{-1}\right)$ (a) $-0.465^{\circ} \mathrm{C}$ (b) $-0.93^{\circ} \mathrm{C}$ (c) $-0.372^{\circ} \mathrm{C}$ (d) $-0.279^{\circ} \mathrm{C}$

To one litre of $0.1$ M-HCl solution, $0.025$ mole of solid $\mathrm{NH}_{4} \mathrm{Cl}$ is added. Assuming complete dissociation of solutes, the freezing point of solution is $\left(K_{f}\right.$ of water $\left.=1.86 \mathrm{~K}-\mathrm{kg} \mathrm{mol}^{-1}\right)$
(a) $-0.465^{\circ} \mathrm{C}$
(b) $-0.93^{\circ} \mathrm{C}$
(c) $-0.372^{\circ} \mathrm{C}$
(d) $-0.279^{\circ} \mathrm{C}$

Key Concepts

van’t Hoff Factor

The van’t Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For substances that fully disassociate, such as strong electrolytes, the factor quantifies the total number of ions produced, which is crucial for accurately calculating colligative effects like freezing point depression.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is used in colligative property calculations, like freezing point depression, because it is independent of temperature and directly relates the amount of solute to the mass of the solvent.

Colligative Properties

Colligative properties are solution characteristics that depend only on the number of solute particles present, not on their identity. Properties such as freezing point depression, boiling point elevation, vapor pressure lowering, and osmotic pressure are influenced by the proportion of solute particles rather than their chemical nature.

Freezing Point Depression

Freezing point depression is a colligative property where the addition of a solute to a solvent decreases the temperature at which the solvent solidifies. This effect is quantitatively described by the formula ?Tf = i·Kf·m, where ?Tf is the freezing point lowering, i is the van’t Hoff factor, Kf is the cryoscopic constant (freezing point depression constant), and m is the molality of the solution.

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