Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
Question
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Chapter 5, Problem 5A.4P
Interpretation Introduction

Interpretation:

The partial pressures of methylbenzene (A) and butanone have to be calculated.  The calculated partial pressures have to be plotted against the mole fraction of the liquid mixture.  Henry’s law constant for both the components has to be calculated.

Concept introduction:

Henry’s law states that the partial vapour pressure is directly proportional to the amount of substance dissolved.  It involves an empirical constant KH called Henry’s law constant.

Expert Solution & Answer
Check Mark

Answer to Problem 5A.4P

The partial pressures of methylbenzene (A) are calculated in the table given below.

yAxAp/kPapA/kPa
0036.0660
0.0410.089834.1211.398961
0.11540.247630.93.56586
0.17620.357728.6265.043901
0.27720.519425.2396.996251
0.33930.603623.4027.940299
0.4450.718820.69849.210788
0.54350.801918.59210.10475
0.72840.910515.49611.28729
1112.29512.295

The partial pressures of butanone are calculated in the table given below.

yBxBp/kPapB/kPa
1136.06636.066
0.9590.910234.12132.72204
0.88460.752430.927.33414
0.82380.642328.62623.5821
0.72280.480625.23918.24275
0.66070.396423.40215.4617
0.5550.281220.698411.48761
0.45650.198118.5928.487248
0.27160.089515.4964.208714
0012.2950

The partial pressure of methylbenzene (A) is plotted against the mole fraction of the liquid mixture in the graph shown below.

Atkins' Physical Chemistry, Chapter 5, Problem 5A.4P , additional homework tip  1

Figure 1

The partial pressure of butanone is plotted against the mole fraction of the liquid mixture in the graph shown below.

Atkins' Physical Chemistry, Chapter 5, Problem 5A.4P , additional homework tip  2

Figure 2

The value of Henry’s law constant for methylbenzene (A) is 15.578kPa_.  The value of Henry’s law constant for butanone is 47.025kPa_.

Explanation of Solution

The data for the mole fraction of methylbenzene (A) in the liquid phase, xA, vapour phase, yA and the total pressure, p is given below.

xAyAp/kPa
0036.066
0.08980.04134.121
0.24760.115430.9
0.35770.176228.626
0.51940.277225.239
0.60360.339323.402
0.71880.44520.6984
0.80190.543518.592
0.91050.728415.496
1112.295

According to Dalton’s law of partial pressures, the partial pressure of methylbenzene (A) (pA) is calculated by the formula given below.

    pA=yAp                                                                                                       (1)

Where,

  • yA is the mole fraction of methylbenzene (A) in the vapour phase.
  • p is the total vapour pressure.

The total pressure (p) at yA=0.0410 is 34.121kPa.

Substitute the value of p and yA in equation (1).

    pA=0.0410×34.121kPa=1.398961kPa_

Therefore, the partial pressure of methylbenzene (A) (pA) is calculated for all vapour phase composition (yA) in the table below.

yAxAp/kPapA/kPa
0036.0660
0.0410.089834.1211.398961
0.11540.247630.93.56586
0.17620.357728.6265.043901
0.27720.519425.2396.996251
0.33930.603623.4027.940299
0.4450.718820.69849.210788
0.54350.801918.59210.10475
0.72840.910515.49611.28729
1112.29512.295

The graph between the mole fraction in the liquid phase, xA and the partial pressure, pA is given below.

Atkins' Physical Chemistry, Chapter 5, Problem 5A.4P , additional homework tip  3

Figure 1

In the above graph, when xA is 0.0898, pA is 1.398961kPa.

According to Henry’s law, the partial pressure of methylbenzene (A)  is given as,

  pA=xAKH                                                                                             (2)

Where,

  • pA is the partial pressure of methylbenzene (A).
  • KH is Henry’s law constant.
  • xA is the mole fraction of methylbenzene (A) in the liquid phase.

Substitute the value of xA and pA in equation (2).

    1.398961kPa=0.0898×KHKH=1.398961kPa0.0898=15.578kPa_

Therefore, the value of Henry’s law constant for methylbenzene (A) is 15.578kPa_.

The total mole fraction in the vapour phase equal to 1.

    yA+yB=1yB=1yA                                                                                              (3)

Where,

  • yB is the mole fraction of butanone in the vapour phase.

The mole fraction of methylbenzene (A) in the vapour phase (yA) is 0.0410.

Substitute the value of yA in equation (3).

    yB=10.0410=0.959

According to Dalton’s law of partial pressures, the partial pressure of butanone (B) (pB) is calculated by the formula given below.

    pB=yBp                                                                                                        (4)

Where,

  • yB is the mole fraction of butanone (B) in the vapour phase.
  • p is the total vapour pressure.

The total pressure (p) at yB=0.959 is 34.121kPa.

Substitute the value of p and yB in equation (4).

    pB=0.959×34.121kPa=32.722kPa_

Therefore, the partial pressure of butanone (B) (pB) is calculated for all vapour phase composition (yB) in the table below.

yBxBp/kPapB/kPa
1136.06636.066
0.9590.910234.12132.72204
0.88460.752430.927.33414
0.82380.642328.62623.5821
0.72280.480625.23918.24275
0.66070.396423.40215.4617
0.5550.281220.698411.48761
0.45650.198118.5928.487248
0.27160.089515.4964.208714
0012.2950

The graph between the mole fraction in the liquid phase, xB and the partial pressure, pB is given below.

Atkins' Physical Chemistry, Chapter 5, Problem 5A.4P , additional homework tip  4

Figure 2

In the above graph, when xB is 0.0895, pB is 4.208714kPa.

According to Henry’s law, the partial pressure of butanone (B) is given as,

  pB=xBKH                                                                                              (5)

Where,

  • pB is the partial pressure of butanone (B).
  • KH is Henry’s law constant.
  • xB is the mole fraction of butanone (B) in the liquid phase.

Substitute the value of xB and pB in equation (5).

    4.208714kPakPa=0.0895×KHKH=4.208714kPa0.0895=47.025kPa_

Therefore, the value of Henry’s law constant for butanone is 47.025kPa_.

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Chapter 5 Solutions

Atkins' Physical Chemistry

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