Faculty of Chemical Engineering CPE553 Chemical Engineering Thermodynamics

Semester March-July 2013 29 March 2013

TUTORIAL 4 1. The general form of summability relation of molar properties for a binary solution is given by

iii

M x M

By using above equation, prove that partial molar properties 1M and 2M for a binary systems at

constant T and P are

1 2

1

dMM M x

dx and 2 1

1

dMM M x

dx

2. The molar volume (cm3 mol-1) of a binary liquid mixture at T and P is given by

1 2 1 2 1 2120 70 15 8V x x x x x x

(a) Find expressions for the partial molar volumes of species 1 and 2 at T and P.

(b) Show that when these expressions are combined in accord with eq. (11.11) the given equation for V is recovered.

(c) Show that these expressions satisfy eq. (11.14), the Gibbs/Duhem equation.

(d) Show that

1 1

1 1 2 11 0

0x x

dV dx dV dx .

(e) Plot values of

1 2, , and V V V calculated by the given equation for V and by the equations

developed in (a) vs. x1. Label points

1 2 1 2, , , and V V V V , and show their values.

3. Figure 1 shows a plot of 1 2, and H H H vs. x1 (J/mol) at constant T and P for a binary liquid

mixture. Label the below points and show their values on the plot. (a) Enthalpy of pure species 1. (b) Enthalpy of pure species 2. (c) Partial enthalpy of pure species 1. (d) Partial enthalpy for pure species 2. (e) Partial enthalpy at infinite dilution of species 1. (f) Partial enthalpy at infinite dilution of species 2. (g) Enthalpy of the mixture that contains 22 mole % species 2. (h) Partial enthalpy of species 2 if the mixture contains 64 mole % species 1. (i) Partial enthalpy of species 1 if the mixture contains 52 mole % species 2.

4. Figure 2 shows a plot of entropy (kJ/kg.K) vs. x1 at constant T and P for a binary liquid mixture.

Explain how to obtain the below points from the plot and show the values. Then, label and show their values on the plot. (a) Partial entropy of pure species 1 at 60 mole % species 1. (b) Partial entropy of pure species 2 at 60 mole % species 1. (c) Partial entropy at infinite dilution of species 1. (d) Partial entropy at infinite dilution of species 2.

Faculty of Chemical Engineering CPE553 Chemical Engineering Thermodynamics

Semester March-July 2013 29 March 2013

Figure 1

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H

Faculty of Chemical Engineering CPE553 Chemical Engineering Thermodynamics

Semester March-July 2013 29 March 2013

Figure 2

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S(kJ

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