1 Chemical Engineering Thermodynamics Lecturer: Zhenxi Jiang (Ph.D. U.K.) School of Chemical...

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Chemical Engineering Chemical Engineering ThermodynamicsThermodynamics

Lecturer: Zhenxi Jiang (Ph.D. U.K.)Lecturer: Zhenxi Jiang (Ph.D. U.K.)

School of Chemical EngineeringSchool of Chemical Engineering

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13.4 Effect of Temperature on the 13.4 Effect of Temperature on the Equilibrium Constant Equilibrium Constant

Because the standard-state temperature is Because the standard-state temperature is that of the equilibrium mixture, the that of the equilibrium mixture, the standard property changes of reaction, standard property changes of reaction, such as such as ΔΔG°G° and and ΔΔH H °, vary with the °, vary with the equilibrium temperature. The dependence equilibrium temperature. The dependence of of ΔΔGG ° on ° on TT is given by Eq. (13.13), which is given by Eq. (13.13), which may be rewritten:may be rewritten:

2

( )o od G RT H

dT RT

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Inview of Eq. (13.11b), this becomes:Inview of Eq. (13.11b), this becomes:

(13.14)(13.14)

Equation (13.14) gives the effect of Equation (13.14) gives the effect of temperature on the equilibrium constant, temperature on the equilibrium constant, and hence on the equilibrium conversion. and hence on the equilibrium conversion. If If ΔΔH H ° is negative, i.e., if the reaction is ° is negative, i.e., if the reaction is exothermic, the equilib rium constant exothermic, the equilib rium constant decreases as the temperature increases. decreases as the temperature increases.

2

ln od K H

dT RT

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Conversely, Conversely, K K increases with increases with T T for an for an endothermic reaction.endothermic reaction.

If If ΔΔH° , H° , the standard enthalpy change the standard enthalpy change (heat) of reaction, is assumed (heat) of reaction, is assumed independent of independent of T, T, integration of Eq. integration of Eq. (13.14) from a particular temperature T’ to (13.14) from a particular temperature T’ to an arbitrary temperature an arbitrary temperature T T leads to the leads to the simple result: simple result:

(13.15)(13.15)

1 1ln

oK H

K R T T

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This approximate equation implies that a This approximate equation implies that a plot of In plot of In K K vs. the reciprocal of absolute vs. the reciprocal of absolute temperature is a straight line. Figure 13.2, temperature is a straight line. Figure 13.2, a plot of ln a plot of ln K K vs. vs. 1/T 1/T for a number of for a number of common reactions, illustrates this near common reactions, illustrates this near linearity. Thus, Eq. (13.15) provides a linearity. Thus, Eq. (13.15) provides a reasonably accurate relation for the reasonably accurate relation for the interpolation and extrapolation of interpolation and extrapolation of equilibrium-constant data.equilibrium-constant data.

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QuestionsQuestions::

1.1. WWhat is the key points in this Section?hat is the key points in this Section?

2.2. Please explain Figure 13.2Please explain Figure 13.2

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AnswersAnswers::

WWhat is the key points in this Section?hat is the key points in this Section?

Relationship between equilibrium Relationship between equilibrium constant and temperature.constant and temperature.

Please explain Figure 13.2Please explain Figure 13.2

横坐标代表温度的倒数横坐标代表温度的倒数 1/T1/T 的的 1000010000 倍，倍，纵坐标代表平衡常数的对数；纵坐标代表平衡常数的对数； lnlnK K 对（对（ 1/1/TT ）） **101044

是直线关系。每一条直线对应一个反应方程是直线关系。每一条直线对应一个反应方程式。式。

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13.5 Evaluation of Equilibrium Constants13.5 Evaluation of Equilibrium Constants

Aim of this section:Aim of this section:

TTo find the equilibrium constantso find the equilibrium constants

the approachesthe approaches

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13.5 Evaluation of Equilibrium Constants13.5 Evaluation of Equilibrium Constants Values of Values of ΔΔG°G° for for many formation many formation

reactions reactions are tabulated in standard are tabulated in standard references.references.44 The reported values of The reported values of ΔΔGG°°f f

are not measured experimentally, but are are not measured experimentally, but are calculated by Eq. (13.16). The calculated by Eq. (13.16). The determination of determination of ΔΔGG°°ff may be based on may be based on the third law of thermodynamics, the third law of thermodynamics, discussed in Sec. 5.10. Combination of discussed in Sec. 5.10. Combination of values from Eq. (5.40) for the absolute values from Eq. (5.40) for the absolute entropies of the species taking part in the entropies of the species taking part in the reaction gives the value of reaction gives the value of ΔΔGG°°f f . . Entropies (and heat capacities) are also Entropies (and heat capacities) are also commonly determined from statistical commonly determined from statistical calculations based on spectroscopic data.calculations based on spectroscopic data.

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Values of Values of ΔΔG°G°f f for a limited number of for a limited number of chemical compounds are listed in Table chemical compounds are listed in Table C.4 of App. C. These are for a temperature C.4 of App. C. These are for a temperature of 298.15 K, as are the values of of 298.15 K, as are the values of ΔΔH° H° listed listed in the same table. Values of in the same table. Values of ΔΔG° G° for other for other reactions are calculated from formation-reactions are calculated from formation-reaction values in exactly the same way reaction values in exactly the same way that that ΔΔH°H°f 298 f 298 values for other reactions are values for other reactions are determined from formation-reaction determined from formation-reaction values (Sec. 4.4). In more extensive values (Sec. 4.4). In more extensive compilations of data, values of compilations of data, values of ΔΔG°G°f f and and ΔΔH°H°f f are given for a wide range of are given for a wide range of temperatures, rather than just at 298.15 temperatures, rather than just at 298.15 K. Where data are lacking, methods of K. Where data are lacking, methods of estimation are available. estimation are available.

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That is all for todayThat is all for today

HomeworkHomework

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1 Chemical Engineering Thermodynamics Lecturer: Zhenxi Jiang (Ph.D. U.K.) School of Chemical...

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