講義教程說明14-chapter8

1、2. Derivation of phase rule There are many phases in the system, ,. There are S substances in each phase, the composition of which is expressed by mole fraction of every species. _ _ _ _X1, X2, , Xs_ Then we have: a.Independent concentration variables for S species in one phase (S-1)Since Xs=1- X1-

2、X2- b.Independent concentration variables for p similar phases p(S-1)c. Intensive variables for T and Pd. Total independent variables p(S-1)+2a. Concentration restrictions for one species i=i i=i i=i Since there is a relation of chemical potential between two phases, p phases have relations: (p-1)b.

3、 Concentration restrictions for S species S(p-1)c. Independent chemical equilibrium among S species Rd. Concentration restrictions produced by equilibriums R So F=total variables-relations among them =p(S-1)+2-S(p-1)+R+R =S-R-R-p+2 F=C-p+2This is Gibbs phase rule. 3. Examples for applicationThere ar

4、e five substances in the system which reach the chemical equilibriums: C(s), H2O(g), H2 (g), CO(g), CO2(g)What is the number of degree of freedom for the system? S=5 R=2 R=0 C=3 F=3-2+2=3 (three independent variables: T, P and X) 6-2 Phase diagram for pure substance For ponent system,F=C-p+2=1-p+2=3

5、-pIf p=1, the biggest degree of freedom is 2 (T and P);If F=0, p=3, the biggest phase number in which the system coexists is 3. 1. Phase diagram of water There are three phase areas in the phase diagram of water. F=C-p+2=1-1+2=2So there are two independent variables in a single-phase area.2. Phase p

6、oint There is only one triple point in the phase diagram of water. F=C-p+2=1-3+2=0There is no independent variable thus temperature and pressure are both determined. Temperature is 273.16 K, and saturated vapor pressure is 0.61 kPa at the triple point of water according to the experiment. 3. Clapeyr

7、on equation For OA, OB and OD lines, So the slope of the curve is positive. But the slope of OC is negative because from ice to liquid: This is the application of Clapeyron equation to the phase equilibrium.Discussion Question:In the phase diagram of carbon, where are the gaseous carbon and fulleren

8、es according to your opinion? Why do you think so?Chapter 8 Phase diagrams8-1 Ideal binary liquid mixture Binary means two components. Ideal means two kinds of liquid can completely dissolve with each other to form ideal solution.For binary system, F=C-p+2=2-p+2=4-pIf p=1, the biggest degree of free

9、dom is 3 (T, P and X); F*=C-p+1=2-p+1=3-pIf p=1, the biggest degree of condition freedom F* is 2 (T-X or P-X);1. Vapor position diagram (P-X) a. P-XA diagram Each component in ideal solution obeys Raoults law. For the binary ideal system,PA=PAXAPB=PBXBPtotal= PA+ PB= PAXA+ PBXB= PAXA+ PB(1-XA)=( PA-

10、 PB) XA+ PBAsolvent; Bsolute; Pivapor pressure of i ; Pi vapor pressure of pure i ; Ximole fraction of i in solution.Obviously, PAXA (blue line) PBXB (reddish line) PtotalXA (yellow line) Plotting three straight lines in the same diagram as follows: In the diagram, PA PB (B: easily volatile componen

11、t) b. P-YA diagram According to Daltons law of partial pressure, If A is an easily volatile component, then we have: YA=1, P=PA; YB=1, P=PB. 0YA1, P is in inverse proportion to YA. 2. position diagram (T-X) There are two kinds of methods to obtain a T-X diagram. One is directly from the experiment j

12、ust as you do in the experiment of determination of the phase diagram for the binary liquid system, and the other is gotten from a P-X diagram.A P-X diagram depends on PAand PB, whereas PAand PB change with temperature. So the P-X diagram changes with temperature. A P-X diagram for benzene and tolue

13、ne at different temperature is as follows: The horizontal line at pressure of P crosses with the four P-X lines to get four crossing points, the compositions of which are x1, x2, x3, x4. The boiling points of the four solutions are 84, 92, 100 and 108, then plotting T-X diagram can obtain the liquid

14、 phase line (the bubble-point line). The gas phase line (the dew point line) can be gotten by Daltons law of partial pressure. If XA is known, YA can be calculated. Motivation Question:What is a lever? What is it used for?3. Lever rule For a T-X diagram, the horizontal line at T1 temperature has thr

15、ee crossing points with the liquid phase line, the line of the system and the gas phase line. The three points D, C, and E correspond the composition of x1, xA, x2. C is the point of the system, D and E are points of phases. As an example of A mole fraction, total mole number of A equals to the mole number of A in liquid phase plus the mole number of A in gaseous phase as follows: This is lever rule in which C is the bearing point. This rule is suitable for the two-phase equilibrium area in T-X and P-X diagra