Chapter 13, Problem 76GQ

### 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 solution is made by adding 50.0 mL of ethanol (C2H5OH, d = 0.789 g/mL) to 50.0 mL of water (d = 0.998 g/mL). What is the total vapor pressure over the solution at 20 °C? (See Study Question 75.) The vapor pressure of ethanol at 20 °C is 43.6 mm Hg.

Interpretation Introduction

Interpretation: Total vapor pressure of the solution at 200C has to be calculated if the vapor pressure of ethanol is 43.6mmHg

Concept introduction:

Raoult’s law: In a solution, vapor pressure of solvent is proportional to its mole fraction.

Psolvent=XsolventP0solvent

where,

P0solvent is the vapor pressure of pure solvent.

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Density is calculated by the equation,

Density=massvolume

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

Numberofmole=GivenmassofthesubstanceMolarmass

Explanation

Total vapour pressure of the solution at 200C is calculated.

Given,

â€‚Â Densityâ€‰ofâ€‰ethanolâ€‰=â€‰0.789â€‰g/mLDensityâ€‰ofâ€‰waterâ€‰=â€‰0.998â€‰g/mLPartialâ€‰pressureâ€‰ofâ€‰ethanol,â€‰P0ethanolâ€‰=â€‰43.6â€‰mmHgPartialâ€‰pressureâ€‰ofâ€‰water,â€‰P0waterâ€‰=17.5â€‰mmHg

Density is calculated by the equation,

â€‚Â Densityâ€‰=â€‰massvolume

Mass is calculated,

â€‚Â Massâ€‰ofâ€‰waterâ€‰=â€‰densityâ€‰Ã—â€‰volume=â€‰0.998â€‰g/mLÃ—â€‰50â€‰mL=â€‰49.9â€‰g

Mass of water is 49.9â€‰g

â€‚Â Massâ€‰ofâ€‰ethanolâ€‰=â€‰densityâ€‰Ã—â€‰volume=â€‰0.789â€‰g/mLÃ—â€‰50â€‰mL=â€‰39.45â€‰g

Mass of ethanol is 39.45â€‰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€‰

NumberÂ ofÂ molesÂ ofÂ waterâ€‰=â€‰49.9â€‰g18.02â€‰g/mol=â€‰2.77â€‰mol

Number of moles of water is 2.77â€‰mol

NumberÂ ofÂ molesÂ ofÂ ethanolâ€‰=â€‰39.45â€‰g46.07â€‰g/mol=â€‰0.856â€‰mol

Number of moles of ethanol is 0.856â€‰mol

Mole fraction of ethanol and water in liquid is calculated

â€‚Â MoleÂ fractionÂ ofÂ ethanolÂ (Ï‡ethanol)=Â â€‰nethanolÂ nethanolÂ +Â Â nwater=â€‰0

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