   # A 2.00% solution of H 2 SO 4 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: H 2 SO 4 , H 2 O + + HSO 4 − , or 2 H 3 O + + SO 4 2− ? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 13, Problem 81GQ
Textbook Problem
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## 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 of Solution

Given,

ΔTfp=0.7960CKFp=1.860C/m

Mass of H2SO4 is 2100×100g=2g

Molar mass of H2SO4 is 98.08g/mol

Mass of water is 100g2g=98g

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

Numberofmole=GivenmassofthesubstanceMolarmass=2g98.08g/mol=0.020mol

Molality of the H2SO4 solution is,

Molality (m) =Numberofmolesofsolute1kgofsolvent=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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