Notes
Entropy
Entropy ($S$) measures how dispersed matter and energy are. Entropy increases when:
- a solid melts or a liquid boils ($S_{gas} > S_{liquid} > S_{solid}$),
- a reaction makes more moles of gas,
- a solid dissolves (usually), or temperature rises.
$\displaystyle \Delta S^\circ = \sum S^\circ(\text{products}) - \sum S^\circ(\text{reactants})$.
Gibbs free energy
A process is thermodynamically favored when $\Delta G^\circ < 0$.
| $\Delta H$ | $\Delta S$ | Favored? |
|---|---|---|
| − | + | Always |
| + | − | Never |
| − | − | At low temperature |
| + | + | At high temperature |
- $\Delta G^\circ = -RT\ln K$. If $\Delta G^\circ < 0$, then $K > 1$.
- A favored reaction can still be very slow if its activation energy is high (kinetic control).
- Unfavored reactions can be driven by coupling them to favored ones (like ATP hydrolysis in cells) or by an external energy source (electrolysis).
Galvanic (voltaic) cells
A spontaneous redox reaction makes electricity.
- Oxidation at the anode, reduction at the cathode ("An Ox, Red Cat"). Electrons flow from anode to cathode through the wire.
- The salt bridge lets ions move to keep each half-cell neutral: anions toward the anode, cations toward the cathode.
- $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$ (using reduction potentials). Positive $E^\circ$ means favored.
- $\Delta G^\circ = -nFE^\circ$, with $F = 96{,}485$ C/mol $e^-$.
- Nonstandard conditions: if $Q < 1$, $E > E^\circ$; as the cell runs, $Q$ grows and $E$ falls to 0 at equilibrium.
Electrolytic cells
External power drives an unfavored reaction. Charge $q = It$ (amperes × seconds); moles of electrons $\displaystyle = \frac{q}{F}$.
Topics in this unit
Each topic has its own short notes and practice.
- 9.1Introduction to Entropy
- 9.2Absolute Entropy and Entropy Change
- 9.3Gibbs Free Energy and Thermodynamic Favorability
- 9.4Thermodynamic and Kinetic Control
- 9.5Free Energy and Equilibrium
- 9.6Free Energy of Dissolution
- 9.7Coupled Reactions
- 9.8Galvanic (Voltaic) and Electrolytic Cells
- 9.9Cell Potential and Free Energy
- 9.10Cell Potential Under Nonstandard Conditions
- 9.11Electrolysis and Faraday's Law
Practice
A gas forms from a solid.
$\Delta G < 0$ when $\displaystyle T > \frac{\Delta H}{\Delta S} = 400$ K.
Both terms make $\Delta G$ negative.
$\Delta G^\circ = -RT\ln K$, so $\ln K > 0$.
An Ox, Red Cat.
$0.34 - (-0.76) = 1.10$ V.
Thermodynamics says it can happen; kinetics says it's too slow to see.
$q = 1930$ C; $\displaystyle \frac{1930}{96485} \approx 0.0200$ mol.
Free response
Write your answer first, then open the scoring guide.
Free-response question
A galvanic cell is built from $\mathrm{Ag^+}/\mathrm{Ag}$ ($E^\circ = +0.80$ V) and $\mathrm{Cu^{2+}}/\mathrm{Cu}$ ($E^\circ = +0.34$ V) half-cells.
(a) Write the balanced overall reaction and identify the anode.
Show the answer and scoring guide
$Cu(s) + 2Ag^+(aq) \rightarrow Cu^{2+}(aq) + 2Ag(s)$. Copper is oxidized, so the copper electrode is the anode.
Check off the points you earned:
(b) Calculate $E^\circ_{cell}$ and $\Delta G^\circ$ in kJ.
Show the answer and scoring guide
$E^\circ = 0.80 - 0.34 = 0.46$ V. $\Delta G^\circ = -nFE^\circ = -(2)(96485)(0.46) = -88{,}800$ J $\approx -88.8$ kJ.
Check off the points you earned:
(c) Predict how the cell voltage changes if $[Ag^+]$ is decreased. Explain.
Show the answer and scoring guide
It decreases. Lowering $[Ag^+]$ (a reactant) makes $Q$ larger, so the reaction is less favored and $E$ drops.
Check off the points you earned: