Chapter 13, Problem 27PS

### 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

# Pure ethylene glycol, HOCH2CH2OH, is added 2.00 kg of water in the cooling system of a car. The vapor pressure of the water in the system when the temperature is 90 °C is 457 mm Hg. What mass of glycol was added? (Assume the solution is ideal. See Appendix G for the vapor pressure of water.)

Interpretation Introduction

Interpretation: The mass of glycol added to 2kg of water has to be identified.

Concept introduction:

Raoult’s law: The vapor pressure of the solvent over the solution Psolvent is proportional to the mole fraction of the solvent. The ideal solution obeys the Raoult’s law.

PsolventχsolventPsolvent,where,Psolventisthevapor pressure of the solvent over the solution,χsolventis mole fraction of solvent in solution, Psolvent is the vapor pressure of the pure solvent.

Explanation

Given data:

Massâ€‰ofâ€‰waterâ€‰=â€‰â€‰2â€‰kgPsolution=â€‰457mmHgPsolventoÂ (vaporÂ pressureÂ ofÂ waterÂ atÂ 90oCÂ )Â =â€‰525.8Â mmHg

Molesâ€‰ofâ€‰waterâ€‰=â€‰MassMolarâ€‰mass=2â€‹000â€‰g18â€‰g/mol=â€‰111.11mol

Psolution=Â Ï‡solventPsolvento,457mmHgâ€‰â€‰â€‰â€‰â€‰=â€‰(Ï‡water)(525.8Â mmHg)Ï‡waterÂ Â Â =Â 0.869

Moleâ€‰fractionâ€‰=â€‰nwaternglycol+nwater

0.869=nwaternglycol+nwater0.869(nglycol+nwater)=nwater(0

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