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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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A mixture of one part nitrogen and three parts hydrogen is heated, in the presence of a suitable catalyst, to a temperature of 500° C. What fraction of the nitrogen (atom for atom) is converted to ammonia, if the final total pressure is 400 atm? Pretend for simplicity that the gases behave ideally despite the very high pressure. The equilibrium constant at 500° C is 6.9 x 10-5. (Hint: You'l have to solve a quadratic equation.)
Repeat the previous problem for the diagram in Figure 5.35 (right), which has an important qualitative difference. In this phase diagram, you should find that and liquid are in equilibrium only at temperatures below the point where the liquid is in equilibrium with infinitesimal amounts of and . This point is called a peritectic point. Examples of systems with this behaviour include water + NaCl and leucite + quartz.
Suppose you have a box of atomic hydrogen, initially at room temperature and atmospheric pressure. You then raise the temperature, keeping the volume fixed.
(a) Find an expression for the fraction of the hydrogen that is ionised as a function of temperature. (You'll have to solve a quadratic equation.) Check that your expression has the expected behaviour at very low and very high temperatures.
(b) At what temperature is exactly half of the hydrogen ionised?
(c) Would raising the initial pressure cause the temperature you found in part (b) to increase or decrease? Explain.
(d) Plot the expression you found in part (a) as a function of the dimension- less variable t = kT/I. Choose the range of t values to clearly show the interesting part of the graph.
Repeat the preceding problem with T/TC=0.8
When carbon dioxide "dissolves" in water, essentially all of it reacts to form carbonic acid, H2CO3:
The carbonic acid can then dissociate into H* and bicarbonate ions,
(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.
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