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Chapter 5: 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
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Calculate the Helmholtz free energy of a van der Waals fluid, up to an undetermined function of temperature as in . Using reduced variables, carefully plot the Helmholtz free energy (in units of ) as a function of volume for Identify the two points on the graph corresponding to the liquid and gas at the vapor pressure. (If you haven't worked the preceding problem, just read the appropriate values off .) Then prove that the Helmholtz free energy of a combination of these two states (part liquid, part gas) can be represented by a straight line connecting these two points on the graph. Explain why the combination is more stable, at a given volume, than the homogeneous state represented by the original curve, and describe how you could have determined the two transition volumes directly from the graph of .
Suppose that a hydrogen fuel cell, as described in the text, is to be operated at and atmospheric pressure. We wish to estimate the maximum electrical work done by the cell, using only the room temperature data at the back of this book. It is convenient to first establish a zero-point for each of the three substances, . Let us take for both to be zero at , so that G for a mole of is at .
(a) Using these conventions, estimate the Gibbs free energy of a mole of at . Repeat for .
(b) Using the results of part (a), calculate the maximum electrical work done by the cell at , for one mole of hydrogen fuel. Compare to the ideal performance of the cell at.
Let the system be one mole of argon gas at room temperature and atmospheric pressure. Compute the total energy (kinetic only, neglecting atomic rest energies), entropy, enthalpy, Helmholtz free energy, and Gibbs free energy. Express all answers in SI units.
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)
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.
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