Physical Chemistry
Physical Chemistry
2nd Edition
ISBN: 9781133958437
Author: Ball, David W. (david Warren), BAER, Tomas
Publisher: Wadsworth Cengage Learning,
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Chapter 22, Problem 22.47E
Interpretation Introduction

Interpretation:

The validation corresponding to the fact that data of carbon monoxide coverage and pressure follows a Langmuir isotherm is to be stated. The equilibrium constant for the adsorption process is to be stated.

Concept introduction:

The isotherm model that describes the adsorption process, if an adsorbate acts as an ideal gas at the isothermal situation is known as Langmuir adsorption isotherm model. In the given isothermal situation, the partial pressure of the adsorbate is related to the volume of the adsorbate which is adsorbed on the solid adsorbent.

Expert Solution & Answer
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Answer to Problem 22.47E

The occurrence of the linear straight line between 1/Coverage and 1/Concentration in the graph proves that the given data of carbon monoxide coverage and pressure follows a Langmuir isotherm.

The equilibrium constant for the adsorption process is 6.94×1011.

Explanation of Solution

The given temperature is 450K.

The given data of carbon monoxide coverage and pressure in torr is mentioned in the table below.

Coverage Pressure (torr)
0.25
0.45
0.65
0.72
0.78
0.82
1.5×108
7.0×108
3.5×107
8.7×107
1.9×106
6.8×106

The concentration of carbon monoxide is calculated by the formula given below.

PV=nRTnV=PRT

Where,

P is the pressure of the gas.

V is the volume of the gas.

n is the number of moles.

R is the universal gas constant.

T is the temperature of the gas.

nV equals to the concentration of carbon monoxide.

The value of universal gas constant is 62.364litertorrK1mol.

Pressure Coverage 1/Coverage nV=PRT 1/Concentration
1.5×108 0.25 4 1.5×108450×62.364=5.34496×1013 15.34496×1013=1.87092×1012
7.0×108 0.45 2.222222 7.0×108450×62.364=2.49432×1012 12.49432×1012=4.00911×1011
3.5×107 0.65 1.538462 3.5×107450×62.364=1.24716×1011 11.24716×1011=8.0182286×1010
8.7×107 0.72 1.388889 8.7×107450×62.364=3.1008×1011 13.1008×1011=3.225724×1010
1.9×106 0.78 1.282051 1.9×106450×62.364=6.77029×1011 16.77029×1011=1.477042×1010
6.8×106 0.82 1.2195122 6.8×106450×62.364=2.42305×1010 12.42305×1010=4.127029×109

The graph between 1/Coverage and 1/Concentration is plotted as follows.

Physical Chemistry, Chapter 22, Problem 22.47E

Figure 1

As, the plot between 1/Coverage and 1/Concentration is showing linear straight line, thus, it proves that the given data of carbon monoxide coverage and pressure follows a Langmuir isotherm.

The value of slope is predicted as 1.44116×1012.

The value of equilibrium constant is calculated by the expression given below.

K=1Slope

Substitute the value of slope in the above expression.

K=11.44116×1012=6.94×1011

Therefore, the value of equilibrium constant is 6.94×1011.

Conclusion

The given data of carbon monoxide coverage and pressure follows a Langmuir isotherm.

The equilibrium constant for the adsorption process is 6.94×1011.

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