Chapter 13, Problem 81GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# A 2.00% solution of H2SO4 in water freezes at −0.796 °C (a) Calculate the van’t Hoff factor, i. (b) Which of the following best represents sulfuric acid in a dilute aqueous solution: H2SO4, H2O+ + HSO4−, or 2 H3O+ + SO42−?

(a)

Interpretation Introduction

Interpretation: van’t Hoff factor of 2%ofH2SO4 has to be determined.

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

Freezing point depression: The freezing point of the solution varies with the solute concentration.

Freezing point depression = ΔTfp= Kfp. msolute.i,where,Kfp=molal freezing point depression constant,msolute= molality of solute,i=van'tHofffactor.

van’t Hoff factor, i: it is the ration between change in in freezing point measured and change in in freezing point calculated. It indicates the total number of ions that are produced.

Molality (m): Molality is the number of moles of solute present in one kilogram of solvent.

Molality (m) =Numberofmolesofsolute1kgofsolvent

The number of moles of any substance can be determined using the equation

Numberofmole=GivenmassofthesubstanceMolarmass

Explanation

Given,

â€‚Â Î”Tfpâ€‰=â€‰âˆ’0.7960Câ€‰KFpâ€‰=â€‰âˆ’1.860C/m

â€‚Â Mass of H2SO4 is 2100â€‰Ã—â€‰100â€‰gâ€‰=â€‰2â€‰g

â€‚Â Molar mass of H2SO4 is 98.08â€‰g/mol

â€‚Â Mass of water is 100â€‰gâ€‰âˆ’â€‰2â€‰gâ€‰=â€‰98â€‰g

The number of moles of any substance can be determined using the equation

â€‚Â Numberâ€‰ofâ€‰moleâ€‰=Givenâ€‰massâ€‰ofâ€‰theâ€‰substanceMolarâ€‰massâ€‰=â€‰2â€‰g98.08â€‰g/mol=â€‰0.020â€‰mol

Molality of the H2SO4 solution is,

â€‚Â MolalityÂ (m)Â =Numberâ€‰ofâ€‰molesâ€‰ofâ€‰solute1kgâ€‰ofâ€‰solvent=â€‰0

(b)

Interpretation Introduction

Interpretation: From the following, the best represents that H2SO4 is in a dilute aqueous solution has to be identified

Concept introduction:

Colligative properties: Properties of solutions which having influence on the concentration of the solute in it. Colligative properties are,

• Decrease in the vapor pressure
• Increase in the boiling point
• Decline in the freezing point
• Osmotic pressure

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