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Chapter 5: Q. 5.52 (page 185)

Plot the Van der Waals isotherm for T/Tc = 0.95, working in terms of reduced variables. Perform the Maxwell construction (either graphically or numerically) to obtain the vapor pressure. Then plot the Gibbs free energy (in units of NkTc) as a function of pressure for this same temperature and check that this graph predicts the same value for the vapor pressure.

Short Answer

Expert verified

The pressure of the phase transition is 0.812

Step by step solution

01

Step 1  Given information

From problem 5.51 we know that

p=8t3v-1-3v2

02

Substituting the value of t=0.95 and iterating the values

The new equation becomes

p=8(0.95)3v-1-3v2p=7.63v-1-3v2

03

Gibbs free energy

We know Gibbs energy is described as follows

G=NkTlnV-Nb+(NKT)(NB)(V-Nb)-2aN2V+c(T)

Converting the equation into reduced variables

t=TTCv=VVCVC=3NbTC=827ab

WE GET,


Substituting t=0.95 we get


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Most popular questions from this chapter

Seawater has a salinity of 3.5%, meaning that if you boil away a kilogram of seawater, when you're finished you'll have 35gof solids (mostly localid="1647507373105" NaCl) left in the pot. When dissolved, sodium chloride dissociates into separate Na+and Cl-ions.

(a) Calculate the osmotic pressure difference between seawater and fresh water. Assume for simplicity that all the dissolved salts in seawater are NaCl.

(b) If you apply a pressure difference greater than the osmotic pressure to a solution separated from pure solvent by a semipermeable membrane, you get reverse osmosis: a flow of solvent out of the solution. This process can be used to desalinate seawater. Calculate the minimum work required to desalinate one liter of seawater. Discuss some reasons why the actual work required would be greater than the minimum.

When carbon dioxide "dissolves" in water, essentially all of it reacts to form carbonic acid, H2CO3:

CO2(g)+H2O(l)⟷H2CO3(aq)

The carbonic acid can then dissociate into H* and bicarbonate ions,

H2CO3(aq)⟷H+(aq)+HCO3-(aq)

(The table at the back of this book gives thermodynamic data for both of these reactions.) Consider a body of otherwise pure water (or perhaps a raindrop) that is in equilibrium with the atmosphere near sea level, where the partial pressure of carbon dioxide is 3.4 x 10-4 bar (or 340 parts per million). Calculate the molality of carbonic acid and of bicarbonate ions in the water, and determine the pH of the solution. Note that even "natural" precipitation is somewhat acidic.

Prove that the entropy of mixing of an ideal mixture has an infinite slope, when plotted vs. x, at x = 0 and x= 1.

Suppose you need a tank of oxygen that is 95% pure. Describe a process by which you could obtain such a gas, starting with air.

Problem 5.64. Figure 5.32 shows the phase diagram of plagioclase feldspar, which can be considered a mixture of albite NaAlSi3O8and anorthiteCaAl2Si2O8

a) Suppose you discover a rock in which each plagioclase crystal varies in composition from center to edge, with the centers of the largest crystals composed of 70% anorthite and the outermost parts of all crystals made of essentially pure albite. Explain in some detail how this variation might arise. What was the composition of the liquid magma from which the rock formed?

(b) Suppose you discover another rock body in which the crystals near the top are albite-rich while the crystals near the bottom are anorthite-rich. Explain how this variation might arise.
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