General Chemistry
General Chemistry
4th Edition
ISBN: 9781891389603
Author: Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly
Publisher: University Science Books
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Chapter 16, Problem 16.54P
Interpretation Introduction

Interpretation:

The partial pressure of each component in equilibrium at 25C with a solution of compositions χprop=0.25,0.50,and0.75 has to be calculated.  The composition of the vapor phase has to be determined.

Concept Introduction:

According to Raoult’s law, in an ideal solution of two volatile liquids, the total vapor pressure of the solution is the sum of individual vapor pressure.

  Ptotal=PA+PB....(1)

Where, PA=χAPAandPB=χBPB.

The equation (1) can be further modified.

  Ptotal=PA+PBPtotal=χAPA+χBPBPtotal=χAPA+(1χA)PB[χA+χB=1]Ptotal=PB+χA(PAPB)

Expert Solution & Answer
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Answer to Problem 16.54P

The partial pressures of 1 propanol are 5.2Torr,10.45Torrand16Torr.  The partial pressures of isopropanol are 34Torr,23Torrand11Torr.

The composition of vapor phase is χprop=0.13,0.31,0.59andχiso=0.85,0.70,and0.41.

Explanation of Solution

Given that, the mole fraction of 1 propanol is 0.25,0.50,and0.75.  Then the mole fraction of isopropanol is given below.

  χiso=1χprop=10.25=0.75χiso=1χprop=10.50=0.50χiso=1χprop=10.75=0.25

The partial pressure of each component can be calculated as given below.

  Pprop=χpropPprop=0.25×20.9Torr=5.2TorrPprop=χpropPprop=0.50×20.9Torr=10.45TorrPprop=χpropPprop=0.75×20.9Torr=16TorrPiso=χisoPiso=0.75×45.2Torr=34TorrPiso=χisoPiso=0.50×45.2Torr=23TorrPiso=χisoPiso=0.25×45.2Torr=11Torr

The total vapor pressure can be calculated as given below.

  When,χiso=0.75Ptotal=Pprop+χiso(PisoPprop)Ptotal=20.9Torr+(0.75)(45.220.9)TorrPtotal=40Torr.When,χiso=0.50Ptotal=20.9Torr+(0.50)(45.220.9)TorrPtotal=33Torr.When,χiso=0.25Ptotal=20.9Torr+(0.25)(45.220.9)TorrPtotal=27Torr.

The pressure of a gas is directly proportional to the number of moles of the gas.  Hence, the mole fraction of each component in the vapor can be calculated as given below.

For 1-propanol:

  When,Ptotal=40Torryprop=npropnprop+niso=PpropPprop+Piso=PpropPtotal=5.2Torr40Torryprop=0.13.When,Ptotal=33Torryprop=PpropPtotal=10.45Torr33Torryprop=0.31.When,Ptotal=27Torryprop=PpropPtotal=16Torr27Torryprop=0.59.

For isopropanol:

  When,Ptotal=40Torryiso=nisoniso+nprop=PisoPprop+Piso=PisoPtotal=34Torr40Torryiso=0.85.When,Ptotal=33Torryiso=nisoniso+nprop=PisoPtotal=23Torr33Torryiso=0.70.When,Ptotal=27Torryiso=nisoniso+nprop=PisoPtotal=11Torr27Torryiso=0.41.

Therefore, the partial pressures of 1 propanol are 5.2Torr,10.45Torrand16Torr.  The partial pressures of isopropanol are 34Torr,23Torrand11Torr. The composition of vapor phase is χprop=0.13,0.31,0.59andχiso=0.85,0.70,and0.41.

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Chapter 16 Solutions

General Chemistry

Ch. 16 - Prob. 16.11PCh. 16 - Prob. 16.12PCh. 16 - Prob. 16.13PCh. 16 - Prob. 16.14PCh. 16 - Prob. 16.15PCh. 16 - Prob. 16.16PCh. 16 - Prob. 16.17PCh. 16 - Prob. 16.18PCh. 16 - Prob. 16.19PCh. 16 - Prob. 16.20PCh. 16 - Prob. 16.21PCh. 16 - Prob. 16.22PCh. 16 - Prob. 16.23PCh. 16 - Prob. 16.24PCh. 16 - Prob. 16.25PCh. 16 - Prob. 16.26PCh. 16 - Prob. 16.27PCh. 16 - Prob. 16.28PCh. 16 - Prob. 16.29PCh. 16 - Prob. 16.30PCh. 16 - Prob. 16.31PCh. 16 - Prob. 16.32PCh. 16 - Prob. 16.33PCh. 16 - Prob. 16.34PCh. 16 - Prob. 16.35PCh. 16 - Prob. 16.36PCh. 16 - Prob. 16.37PCh. 16 - Prob. 16.38PCh. 16 - Prob. 16.39PCh. 16 - Prob. 16.40PCh. 16 - Prob. 16.41PCh. 16 - Prob. 16.42PCh. 16 - Prob. 16.43PCh. 16 - Prob. 16.44PCh. 16 - Prob. 16.45PCh. 16 - Prob. 16.46PCh. 16 - Prob. 16.47PCh. 16 - Prob. 16.48PCh. 16 - Prob. 16.49PCh. 16 - Prob. 16.50PCh. 16 - Prob. 16.51PCh. 16 - Prob. 16.52PCh. 16 - Prob. 16.53PCh. 16 - Prob. 16.54PCh. 16 - Prob. 16.55PCh. 16 - Prob. 16.56PCh. 16 - Prob. 16.57PCh. 16 - Prob. 16.58PCh. 16 - Prob. 16.59PCh. 16 - Prob. 16.60PCh. 16 - Prob. 16.61PCh. 16 - Prob. 16.62PCh. 16 - Prob. 16.63PCh. 16 - Prob. 16.64PCh. 16 - Prob. 16.65PCh. 16 - Prob. 16.66PCh. 16 - Prob. 16.67PCh. 16 - Prob. 16.68PCh. 16 - Prob. 16.69PCh. 16 - Prob. 16.70PCh. 16 - Prob. 16.71PCh. 16 - Prob. 16.72PCh. 16 - Prob. 16.73PCh. 16 - Prob. 16.74PCh. 16 - Prob. 16.75PCh. 16 - Prob. 16.76PCh. 16 - Prob. 16.77PCh. 16 - Prob. 16.78PCh. 16 - Prob. 16.79PCh. 16 - Prob. 16.80PCh. 16 - Prob. 16.81PCh. 16 - Prob. 16.82PCh. 16 - Prob. 16.83PCh. 16 - Prob. 16.84PCh. 16 - Prob. 16.85PCh. 16 - Prob. 16.86PCh. 16 - Prob. 16.87PCh. 16 - Prob. 16.88PCh. 16 - Prob. 16.89PCh. 16 - Prob. 16.90PCh. 16 - Prob. 16.91PCh. 16 - Prob. 16.93P
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