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Chapter 5: Q. 5.49 (page 185)
Use the result of the previous problem and the approximate values of a and b to find the value of Tc, Pc, Vc/N for N2, H2O and He.
| () | role="math" localid="1647074922910" | ||
| (Pa) | |||
| (K) | 143 | 572 | 21.5 |
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Everything in this section assumes that the total pressure of the system is fixed. How would you expect the nitrogen-oxygen phase diagram to change if you increase or decrease the pressure? Justify your answer.
Seawater has a salinity of , meaning that if you boil away a kilogram of seawater, when you're finished you'll have of solids (mostly localid="1647507373105" ) left in the pot. When dissolved, sodium chloride dissociates into separate and ions.
(a) Calculate the osmotic pressure difference between seawater and fresh water. Assume for simplicity that all the dissolved salts in seawater are .
(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.
In constructing the phase diagram from the free energy graphs in Figure 5.30, I assumed that both the liquid and the gas are ideal mixtures. Suppose instead that the liquid has a substantial positive mixing energy, so that its free energy curve, while still concave-up, is much flatter. In this case a portion of the curve may still lie above the gas's free energy curve at TA. Draw a qualitatively accurate phase diagram for such a system, showing how you obtained the phase diagram from the free energy graphs. Show that there is a particular composition at which this gas mixture will condense with no change in composition. This special composition is called an azeotrope.
Consider a fuel cell that uses methane ("natural gas") as fuel. The reaction is
(a) Use the data at the back of this book to determine the values of and for this reaction, for one mole of methane. Assume that the reaction takes place at room temperature and atmospheric pressure.
(b) Assuming ideal performance, how much electrical work can you get out of the cell, for each mole of methane fuel?
(c) How much waste heat is produced, for each mole of methane fuel?
(d) The steps of this reaction are
What is the voltage of the cell?
Consider a completely miscible two-component system whose overall composition is x, at a temperature where liquid and gas phases coexist. The composition of the gas phase at this temperature is and the composition of the liquid phase is . Prove the lever rule, which says that the proportion of liquid to gas is . Interpret this rule graphically on a phase diagram.
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