# 4.06 – Gibbs free energy

Gibbs free energy is a thermodynamic state function that combines the entropy and enthalpy of a system.  The change in free energy, ΔG, indicates the relative spontaneity of a process.  The standard free energy change of a process can be determined using ΔGf° values just like we did using Hess's Law.

Lesson Objectives

• Calculate the Gibbs free energy from the enthalpy change and entropy change at a given temperature. (19.5)
• Use free energy changes to predict whether reactions are spontaneous or not (19.5)
• Calculate standard free energy changes using standard free energies of formation (19.5)
• Predict the effect of temperature on spontaneity given ΔH and ΔS. (19.6)

You should begin this mission by reviewing the key ideas presented in the slides below.  These slides refer to sections 19.5 and 19.6 of the text.

Now that you've seen these ideas, it's time to practice the calculations.  Work through the practice problems that follow the samples in the slides below.

When you are finished working these problems out, post your notes and text practice to OneNote.

Now that you have a handle on this material, work through these mastery problems.  You can check your answers on OneNote.  Make sure to post your stamped work on OneNote after you are finished.

19.55  Using data in Appendix C, calculate ΔH°, ΔS°, and ΔG° at 298 K for each of the following reactions.  In each case, show that ΔG° = ΔH° - TΔS°.

1. H2(g) + F2(g) → 2 HF(g)
2. C(s, graphite) + 2 Cl2(g) → CCl4(g)
3. 2 PCl3(g) + O2(g) → 2 POCl3(g)
4. 2 CH3OH(g) + H2(g) → C2H6(g) + 2 H2O(g)

19.56  Using data in Appendix C, calculate ΔH°, ΔS°, and ΔG° at 298 K for each of the following reactions.  In each case, show that ΔG° = ΔH° - TΔS°.

1. 2Cr(s) + 3 Br2(g) → 2 CrBr3(s)
2. BaCO3(s) → BaO(s) + CO2(g)
3. 2 P(s) + 10 HF(g) → 2 PF5(g) + 5 H2(g)
4. K(s) + O2(g) → KO2(s)

19.68  Methanol (CH3OH) can be made by the controlled oxidation of methane:

CH4(g) +12 O2(g) → CH3OH(g)

1. Use data in Appendix C to calculate ΔH° and ΔS° for this reaction.
2. Will ΔG for the reaction increase, decrease, or stay unchanged with increasing temperature?
3. Calculate ΔG° at 298 K. Under standard conditions, is the reaction spontaneous at this temperature?
4. Is there a temperature at which the reaction would be at equilibrium under standard conditions and that is low enough so that the compounds involved are likely to be stable?

2004 FRQ #2

Wow, you did that on your own.  How spontaneous of you...