CHM110H5 Chap.9 Entropy, Free Energy and Electrochemical Cells
Entropy, Free Energy and Electrochemical Cells
Why entropy joins enthalpy
By this point in CHM110H5 you can already calculate enthalpy changes with heat capacities and Hess's law. Heat alone cannot tell you whether a process will happen, though: ice melts on a warm day even though melting absorbs heat. The missing ingredient is entropy, a state function that measures how widely energy and matter are spread out.
The second law says spontaneous change always increases the entropy of the universe, and the course learning outcomes define free energy changes in terms of enthalpy and entropy changes on exactly that basis.
Typical entropy gains come from melting, boiling, dissolving a solid and any reaction that produces extra moles of gas; the reverse processes lower the entropy of the system.
Gibbs free energy as a single test
Combining the system and its surroundings at constant temperature and pressure gives ΔG = ΔH − TΔS.
A negative ΔG means the forward reaction is favoured, positive means the reverse is favoured, and zero means equilibrium. Because temperature multiplies the entropy term, the signs of ΔH and ΔS together decide whether a reaction is favoured at every temperature, at none, only when cold, or only when hot.
For the two temperature-dependent cases you can locate the crossover point by setting ΔG to zero, giving T = ΔH/ΔS, provided you convert kJ and J consistently.
Linking free energy, K and cell potential
The standard free energy change connects directly to the equilibrium constant you met in the equilibrium portion of the course: ΔG° = −RT ln K.
It also connects to the voltage of an electrochemical cell: ΔG° = −nFE°cell, where n is the moles of electrons transferred and F is the Faraday constant, 96485 C/mol. Putting the two together means a positive standard cell potential, a negative ΔG° and an equilibrium constant larger than one are three ways of saying the same thing.
Expect to move between all three in a single calculation.
Galvanic and electrolytic cells
A galvanic cell turns a spontaneous redox reaction into electrical work. Oxidation happens at the anode, reduction at the cathode, electrons travel through the external wire from anode to cathode, and a salt bridge lets ions migrate so each compartment stays electrically neutral.
An electrolytic cell uses an outside power supply to drive a nonspontaneous reaction, so the anode becomes the positive electrode instead of the negative one. The learning outcomes also cover the maximum work a cell can do, which equals ΔG and therefore −nFE. For example, consuming 0.0500 mol of zinc in a 1.10 V zinc and copper cell transfers 0.100 mol of electrons and can deliver at most about 10.6 kJ of electrical work.
Real cells deliver less, because some energy is lost as heat while current flows.
What this chapter covers
- 01
Entropy and the second law
- 02
Gibbs free energy: ΔG = ΔH − TΔS
- 03
Sign cases and crossover temperature
- 04
ΔG° and the equilibrium constant K
- 05
Cell potential, ΔG° and K
- 06
Labelling a galvanic cell
- 07
Electrolytic cells and maximum electrical work
Worked example · free
From standard potentials to ΔG° and K for a nickel and silver cell
- 2Silver has the higher reduction potential, so Ag⁺ is reduced at the cathode and Ni is oxidised at the anode: Ni(s) + 2Ag⁺(aq) → Ni²⁺(aq) + 2Ag(s), with n = 2 mol electrons.
- 2E°cell = E°cathode − E°anode = 0.80 − (−0.25) = +1.05 V. The silver potential is not doubled, because potential is intensive.
- 2ΔG° = −nFE° = −(2)(96485)(1.05) = −202 619 J ≈ −203 kJ per mole of reaction.
- 2ln K = −ΔG°/RT = 202619 / (8.314 × 298.15) = 202619 / 2478.8 = 81.74, so K = e^81.74 ≈ 3.2 × 10^35.
Key terms
- Entropy
- A state function, symbol S, measuring how widely energy and matter are dispersed in a system; it rises on melting, vaporising, dissolving and when reactions produce more moles of gas.
- Gibbs free energy
- The quantity G = H − TS; its change ΔG at constant temperature and pressure is negative for a spontaneous process and zero at equilibrium.
- Crossover temperature
- The temperature T = ΔH/ΔS at which ΔG equals zero, where a reaction with same-signed ΔH and ΔS switches between favoured and unfavoured.
- Standard cell potential
- The voltage E°cell of an electrochemical cell under standard conditions, found as the cathode reduction potential minus the anode reduction potential.
- Faraday constant
- The charge carried by one mole of electrons, 96485 C/mol, used to convert a cell potential into free energy through ΔG° = −nFE°.
- Salt bridge
- A tube of inert electrolyte joining the two half-cells; its ions migrate to keep each compartment electrically neutral so current can keep flowing.
- Electrolytic cell
- A cell in which an external power supply drives a nonspontaneous redox reaction; oxidation still occurs at the anode, which is now the positive electrode.
Entropy, Free Energy and Electrochemical Cells FAQ
If ΔG° is positive, does the reaction not happen at all?
Not quite. A positive ΔG° means K is less than one, so only a small amount of product forms at equilibrium. The actual ΔG = ΔG° + RT ln Q can still be negative when product concentrations are very low, so some forward reaction occurs.
Why is the anode negative in a galvanic cell but positive in an electrolytic cell?
Oxidation always defines the anode. In a galvanic cell oxidation releases electrons into the wire, giving that electrode a surplus and a negative sign. In an electrolytic cell the power supply pulls electrons away from the anode, so it is wired to the positive terminal.
Do I double E° when a half-reaction is multiplied by two?
No. Potential is energy per coulomb of charge, an intensive property, so it stays the same. The doubling shows up instead in n, the moles of electrons, when you calculate ΔG° = −nFE°.
Exam move
Draw a four-row table of ΔH and ΔS signs from memory and fill in the ΔG verdict at low and high temperature. Then practise the full chain on three cells: pick two standard reduction potentials, identify cathode and anode, compute E°cell, convert to ΔG° with n and F, and finish with K. Check each answer against the sign chain: positive E°, negative ΔG°, K above one.
Finally sketch a galvanic cell with arrows for electrons and both bridge ions, and label how an electrolytic version would differ. Then work the recommended thermodynamics textbook problems listed for the course.
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