   # In a solution with carbon tetrachloride as the solvent, the compound VCl 4 . undergoes dimerization: 2 VCl 4 ⇌ V 2 Cl 8 When 6.6834 g VCl 4 . is dissolved in 100.0 g carbon tetrachloride, the freezing point is lowered by 5.97°C. Calculate the value of the equilibrium constant for the dimerization of VCl 4 at this temperature. (The density of the equilibrium mixture is 1.696 g/cm 3 , and K f = 29.8°C kg/mol for CCl 4 .) ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 12, Problem 117IP
Textbook Problem
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## In a solution with carbon tetrachloride as the solvent, the compound VCl4. undergoes dimerization: 2 VCl 4 ⇌ V 2 Cl 8 When 6.6834 g VCl4. is dissolved in 100.0 g carbon tetrachloride, the freezing point is lowered by 5.97°C. Calculate the value of the equilibrium constant for the dimerization of VCl4 at this temperature. (The density of the equilibrium mixture is 1.696 g/cm3, and Kf = 29.8°C kg/mol for CCl4.)

Interpretation Introduction

Interpretation: The equilibrium constant for the dimerization reaction is to be calculated.

Concept introduction: The equilibrium constant K describes the ratio of the reactant to the product on the equilibrium conditions in terms of molar concentration.

The equilibrium constant depends upon temperature.

At equilibrium sum of all the partial pressure is equal to the total pressure.

Law of mass action is applicable on the equilibrium reactions.

The Le Chatelier’s principle states that the addition of the reactants shifts the equilibrium to the right while the addition of product shifts the equilibrium to the left at constant temperature.

Dimerization is a process in which two species combines together and forms a one species.

To determine: The value of equilibrium constant for the dimerization of VCl4 for the given reaction at 5.97°C .

### Explanation of Solution

Explanation

Total moles of solute is 0.0200mol_ .

Given

The reaction is given as,

2VCl4V2Cl8

Density of the equilibrium mixture is 1.696g/cm3 .

Freezing point constant Kf is 29.8°Ckg/mol .

The amount of solvent is 0.100kg .

The initial moles of VCl4 is calculated by the formula,

n=m'M

Where,

• n is the number of moles.
• m' is the given mass.
• M is the molar mass.

Substitute the values of m and M in the above equation.

n=m'M=6.6834g192.74g=0.34675moles

The molality of the solute is calculated by the formula,

m=ΔTKf

Where,

• m is the molality of the solution.
• ΔT is the lowering in freezing point.
• Kf is the molal depression constant.

Substitute the values of ΔT and Kf in the above equation.

m=ΔTKf=0.57°C29.8°Ckgmol1=0.200mol/kg

The total moles of solute particles present in the solvent is calculated by the formula,

nt=m×Mt

Where,

• nt is the total moles.
• m is the total molality of the solute.
• Mt is the total mass of the solvent.

Substitute the values of m and Mt in the above equation.

nt=m×Mt=0.200mol/kg×0.100kg=0.0200mol_

The value of equilibrium constant is 55.84_ .

The ICE-table for the dimerization of VCl4 reaction is given as,

2VCl4V2Cl8Initial(mol)0.034670Change(mol)2x+xEquilibrium(mol)0

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