# 7.03 – Free Energy & Nonstandard Cells

It's time to connect the concepts of free energy and equilibrium to redox reactions.  We will determine cell spontaneity as well as how cells might operate if we change the concentration of our solutions.

Learning Objectives

• Relate E°cell to ΔG° and equilibrium constants. (20.5)
• Calculate emf under nonstandard conditions. (20.6)

To become familiar with the topics presented in this mission, view the slides below and take note of the key ideas.  These are from sections 20.5-20.6 of your text.

Now work through practice problems 20.9-20.13, and post your work to OneNote.

Work through these mastery problems and post your work to OneNote.  The key is available on OneNote also.

20.50  For each of the following reactions, write a balanced equation, calculate the standard emf, calculate ΔG° at 298 K, and calculate the equilibrium constant K at 298 K.

(a) Aqueous iodide ion is oxidized to I2(s) by Hg22+(aq).

(b) In acidic solution, copper(I) ion is oxidized to copper(II) ion by nitrate ion.

(c) In basic solution, Cr(OH)3(s) is oxidized to CrO42–(aq) by ClO(aq).

20.54  Using the standard reduction potentials listed in Appendix E, calculate the equilibrium constant for each of the following reactions at 298 K:

(a) Cu(s) + 2 Ag+(aq) → Cu2+ (aq) + 2 Ag(s)

(b) 3 Ce4+(aq) + Bi(s) + H2O(l) → 3 Ce3+(aq) + BiO+(aq) + 2 H+(aq)

(c) N2H5+(aq) + 4 Fe(CN)63–(aq) → N2(g) + 5 H+(aq) + 4 Fe(CN)64–(aq)

20.99  A voltaic cell is constructed from an Ni2+(aq)/Ni(s) half-cell and an Ag+(aq)/Ag(s) half-cell. The initial concentration of Ni2+(aq) in the Ni2+/Ni half-cell is [Ni2+] = 0.0100 M. The initial cell voltage is +1.12 V.

(a) By using data in Table 20.1, calculate the standard emf of this voltaic cell.

(b) Will the concentration of Ni2+(aq) increase or decrease as the cell operates?

(c) What is the initial concentration of Ag+(aq) in the Ag+/Ag half-cell?

20.100            A voltaic cell is constructed that uses the following half-cell reactions:

Cu+(aq) + e → Cu(s)

I2(s) + 2 e → 2 I(aq)

The cell is operated at 298 K with [Cu+] = 0.25 M and [I] = 3.5 M.

(a) Determine E for the cell at these concentrations.

(b) Which electrode is the anode of the cell?

(c) Is the answer to part (b) the same as it would be if the cell were operated under standard conditions?

(d) If [Cu+] were equal to 0.15 M, at what concentration of I would the cell have zero potential?

20.112            In a galvanic cell the cathode is an Ag+ (1.00 M)/Ag(s) half-cell. The anode is a standard hydrogen electrode immersed in a buffer solution containing 0.10 M benzoic acid (C6H5COOH) and 0.050 M sodium benzoate (C6H5COONa+). The measured cell voltage is 1.030 V. What is the pKa of benzoic acid?

20.116            Hydrogen gas has the potential for use as a clean fuel in reaction with oxygen. The relevant reaction is

2 H2(g) + O2(g) → 2 H2O(l)

Consider two possible ways of utilizing this reaction as an electrical energy source: (i) Hydrogen and oxygen gases are combusted and used to drive a generator, much as coal is currently used in the electric power industry; (ii) hydrogen and oxygen gases are used to generate electricity directly by using fuel cells that operate at 85 °C.

(a) Use data in Appendix C to calculate ΔH° and ΔS° for the reaction. We will assume that these values do not change appreciably with temperature.

(b) Based on the values from part (a), what trend would you expect for the magnitude of ΔG for the reaction as the temperature increases?

(c) What is the significance of the change in the magnitude of ΔG with temperature with respect to the utility of hydrogen as a fuel?

(d) Based on the analysis here, would it be more efficient to use the combustion method or the fuel-cell method to generate electrical energy from hydrogen?

2004 FRQ#6

We're almost done Visitor!  Now we can see how nonspontaneous reactions can happen if we apply a current to some half-cells :)