\(25 \,mL\) of an aqueous solution of \(KCl\) was found to require \(20\, mL\) of \(1\, M\) \(AgNO _3\) solution when titrated using \(K _2 CrO _4\) as an indicator What is the depression in freezing point of \(KCl\) solution of the given concentration? _________ (Nearest integer) (Given: \(K _f=20 \,K \,kg \,mol ^{-1}\))
Assume 1) \(100 \%\) ionization and
2) density of the aqueous solution as \(1 \,g \,mL ^{-1}\)
Assume 1) \(100 \%\) ionization and
2) density of the aqueous solution as \(1 \,g \,mL ^{-1}\)
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The van ’t Hoff factor (i) accounts for the number of particles into which a so lute dissociates in solution. For ionic compounds like KCl, i is the number of ions formed
Correct Answer: 3
Approach Solution - 1
Calculation of Depression in Freezing Point:
- Calculate the moles of AgNO3:
Moles of AgNO3 = Molarity × Volume (L) = 1 × 0.020 = 0.020 mol. - Determine the moles of KCl:
From the reaction:
AgNO3 + KCl → AgCl + KNO3,
1 mole of AgNO3 reacts with 1 mole of KCl. Therefore, the moles of KCl are:
Moles of KCl = 0.020 mol. - Calculate the molality of the KCl solution:
The volume of the solution is 25 mL, and the density is 1 g/mL, so the mass of the solution is:
Mass of solution = 25 g.
Since the KCl solution is dilute, the mass of the solvent is approximately:
Mass of solvent = 25 g = 0.025 kg.
The molality is:
Molality = Moles of solute / Mass of solvent (kg) = 0.020 / 0.025 = 0.8 mol/kg. - Calculate the depression in freezing point:
KCl dissociates completely into K+ and Cl−, so the van ’t Hoff factor (i) is 2.
The depression in freezing point is given by:
∆Tf = i × Kf × Molality
Substituting the values:
∆Tf = 2 × 2.0 × 0.8 = 3.2 K.
The nearest integer is:
∆Tf = 3 K.
Conclusion: The depression in freezing point is 3 K.
Approach Solution -2
The correct answer is 3
mmole of mmole of
mole
Volume of solution
Mass of solution
Mass of solvent
mass of solute
Molality of
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.