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Chapter 5: Q. 5.4 (page 155)
In a hydrogen fuel cell, the steps of the chemical reaction are
Calculate the voltage of the cell. What is the minimum voltage required for electrolysis of water? Explain briefly.
The minimum voltage required is We=1.23 eV
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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.
Express in terms of the volumes of solutions of reactants and products, for a chemical reaction of dilute solutes. Plug in some reasonable numbers, to show that a pressure increase of 1 atm has only a negligible effect on the equilibrium constant.
Use the data at the back of this book to verify the values of and quoted above for the lead-acid reaction 5.13.
A formula analogous to that for relates the isothermal and isentropic compressibilities of a material:
(Here is the reciprocal of the adiabatic bulk modulus considered in Problem 1.39.) Derive this formula. Also check that it is true for an ideal gas.
Suppose that an unsaturated air mass is rising and cooling at the dry adiabatic lapse rate found in problem 1.40. If the temperature at ground level is 25 C and the relative humidity there is 50%, at what altitude will this air mass become saturated so that condensation begins and a cloud forms (see Figure 5.18)? (Refer to the vapor pressure graph drawn in Problem 5.42)
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