Thermodynamics and Electrochemistry

This is Unit Eleven of Chemistry, Part Three: redox chemistry and the galvanic cell. Parts One and Two built thermodynamics, and this part spends it. Two things carry forward: Gibbs free energy, whose sign decides whether a reaction runs, and Part Two's closing result that free energy and the equilibrium constant are one fact written two ways. This part adds a third notation for that fact — a voltage. A spontaneous redox reaction with its halves separated into two compartments drives electrons through a wire, and the resulting potential difference is the same spontaneity verdict measured in volts. By the end you will be able to identify anode and cathode without relying on which one is negative; say why a half-cell potential is always a difference; compute a standard cell potential from tabulated values; say how cell potential, free energy and the equilibrium constant are one fact rather than three; and say what the Nernst equation adjusts and when it changes nothing.

Three entries recovering ground from Unit Three, because every cell here is a redox reaction with its halves pulled apart. What oxidation and reduction are, how to tell a reaction is one, and the balancing method that treats the two halves separately on purpose.

Lost and gained.

Chem 2140 Oxidation and Reduction Defined by Electron Transfer

Oxidation is the loss of electrons, reduction is the gain, and the two always occur together in one reaction. Zinc metal reacting with copper ions loses electrons from the zinc while the copper ions gain them. Oxidation without a reduction happening somewhere in the same reaction describes an impossible half of a process.

Before, and after.

Chem 2143 Using Oxidation Numbers to Identify Oxidized and Reduced Species

Compare an atom's oxidation number before and after the reaction: where it rises, that species was oxidised; where it falls, reduced. Iron going from zero to plus two while copper falls from plus two to zero is a redox reaction. A changed formula on its own does not prove one — the number has to have moved.

Split, balance, then combine.

Chem 2146 Balancing a Redox Equation by the Half-Reaction Method

Split the reaction into oxidation and reduction half-reactions, balance each for atoms and then for charge by adding electrons, and scale the two so the electrons lost cancel those gained before combining. For iron two plus with dichromate in acid, the oxidation half is scaled by six. Combining before scaling leaves electrons uncancelled — an unbalanced result that looks balanced.

Five entries build the device. Separating a spontaneous reaction's halves and joining them by a wire forces the electrons to travel, and that is a current. Then the electrodes get their names — and the unit's one delicate point sits here, because the names are fixed by which reaction occurs while the charge signs attached to them are not fixed at all.

Make the electrons travel.

Chem 2150 Galvanic Cell: Spontaneous Redox Generates Current

A galvanic cell separates a spontaneous redox reaction's oxidation and reduction halves into two compartments joined by a wire, forcing the electrons through it as current. A zinc-copper cell drives electrons from zinc through the wire to copper and lights a bulb. Run unseparated, the same reaction still transfers electrons — but with no circuit there is no current.

Named by what happens.

Chem 2153 Anode and Cathode by Reaction, Not by Charge

The anode is always where oxidation occurs and the cathode always where reduction occurs, in every electrochemical cell, whatever charge each electrode carries. In a galvanic cell the anode is the negative terminal, but identify it from where electrons are released, not from its sign. Memorising anode is negative as a fixed fact breaks at the next kind of cell.

The signs swap.

Chem 2156 Twin: The Anode/Cathode Charge-Sign Reversal

A galvanic cell's anode is negative and its cathode positive; an electrolytic cell's are the reverse, because there an external source forces the electron flow rather than the reaction driving it. Neither convention is the correct one — the sign follows from which process drives the cell, while oxidation at the anode holds throughout.

Ions, not electrons.

Chem 2159 Salt Bridge Maintains Circuit and Neutrality

A salt bridge completes the circuit by letting ions move between the half-cells, keeping each compartment electrically neutral as electrons travel the wire. Without one, charge builds up in each half-cell and the current stops almost immediately. The bridge carries ions — electron flow stays confined to the wire.

A shorthand for a cell.

Chem 2162 Cell Notation Convention

Cell notation puts the anode half-cell on the left and the cathode half-cell on the right, marking phase boundaries with a single vertical line and the salt bridge with a double one. Zinc, zinc ion, double line, copper ion, copper names the familiar cell. The single line is a phase boundary, not the bridge.

Four entries on measuring what a cell can do. The awkward fact underneath them is that a single electrode has no potential of its own. The way out is to choose one half-cell, declare it zero, and report everything else against it.

Between two, never one.

Chem 2165 Cell Potential Defined

Cell potential is the potential difference measured between a galvanic cell's two half-cells, because an individual half-cell's potential can only be assessed relative to another. A voltmeter across the two electrodes reads it directly in volts. A single electrode has no potential in isolation — every measured value is already a difference.

Somebody has to be zero.

Chem 2168 The Standard Hydrogen Electrode

The standard hydrogen electrode is assigned a potential of exactly zero volts by convention, and serves as the universal reference for every other half-cell's standard potential. A half-cell paired against it and reading plus zero point three four volts reports that value relative to the chosen zero. Zero here is a reference point, not a claim that the electrode does nothing.

Everything, written as a reduction.

Chem 2171 Standard Reduction Potentials Tabulated

A standard reduction potential is a half-reaction's potential written as a reduction and measured against the hydrogen electrode, tabulated so half-cells can be looked up and combined. Copper two plus gaining two electrons carries plus zero point three four volts. The value describes the reduction as written — reversing the half-reaction flips the sign, not the magnitude.

Cathode minus anode.

Chem 2174 Calculating Standard Cell Potential

The more positive reduction potential is the cathode; subtract the anode's tabulated value from the cathode's. Copper at plus zero point three four against zinc at minus zero point seven six gives one point one zero volts, positive and so spontaneous as written. Subtract the two reduction values directly — reversing a half-reaction and flipping its sign first applies the change twice.

Two entries on what the number is worth once you have it. The sign settles direction, as ΔG's sign did in Part Two. And the table read down its length, rather than in pairs, ranks how strongly species pull electrons either way.

Positive runs forward.

Chem 2178 Sign of E°cell Predicts Spontaneity

A positive standard cell potential indicates a spontaneous redox reaction under standard conditions; a negative one indicates the reaction as written is nonspontaneous. The zinc-copper cell's plus one point one zero volts confirms it proceeds as written. Negative does not mean nothing happens — the reverse direction is spontaneous instead.

Read the whole column.

Chem 2181 Standard Reduction Potential Ranks Strength

A more positive standard reduction potential marks a stronger oxidising agent, one eager to be reduced; a more negative value marks a stronger reducing agent, eager to be oxidised. Fluorine sits near one end, lithium near the other. Ranking by magnitude while ignoring sign confuses the strongest oxidiser with the strongest reducer.

Four entries close the loop back to Part Two. A cell potential and a standard free energy change are joined by a fixed conversion, and Part Two already joined that free energy change to the equilibrium constant — so all three are one fact in three notations, and any one determines the other two.

Volts into joules.

Chem 2184 ΔG° Relates to E°cell

Standard free energy change relates to standard cell potential by ΔG° equals minus n F E°cell, where n is the moles of electrons transferred and F is Faraday's constant. A large positive cell potential yields a large negative free energy change — the same verdict from two quantities. The electron count must match the balanced overall reaction, not either half-reaction's own count.

Charge per mole.

Chem 2187 Faraday's Constant

Faraday's constant is the electric charge carried by one mole of electrons, the conversion factor between moles of electrons and coulombs. Two moles of electrons carry twice that charge, whatever reaction produced them. It is a conversion factor and nothing more — on its own it says nothing about any particular reaction's spontaneity.

Three notations, one claim.

Chem 2190 E°cell, ΔG°, and K as One Fact

Cell potential, standard free energy change and the equilibrium constant describe one reaction's spontaneity from three connected angles, and any one determines the other two through ΔG° equals minus n F E°cell and ΔG° equals minus R T log K. A large positive potential implies a large negative free energy change, which implies a large K. These are one relationship viewed three ways, not three facts to memorise.

Straight from the voltage.

Chem 2193 Calculating K from E°cell

Combining the two relationships gives the log of K as n F E°cell over R T; solve and exponentiate. A two-electron reaction at plus zero point four six three volts gives a log near thirty-six, so K is around four times ten to the fifteenth. The same K is reachable through free energy first, and the routes agree. A wrong electron count scales the exponent and can miss by orders of magnitude.

Everything so far assumed standard conditions. Four entries relax that. The Nernst equation adjusts a cell's potential for the concentrations actually present — which matters, because a real cell is almost never at standard conditions and drifts as it discharges. Then a cell running on a concentration difference alone, and the capstone.

Adjust for what is present.

Chem 2196 The Nernst Equation

The Nernst equation gives a cell's potential under nonstandard conditions: Ecell equals E°cell minus R T over n F, times the log of Q. A cell with unusually high reactant concentrations reads higher than its standard value alone would suggest. E°cell is a fixed reference and Ecell is what the cell reads now — the two agree only where Q equals one.

Q from the real concentrations.

Chem 2199 Applying the Nernst Equation

Write the reaction quotient from the actual concentrations present, substitute it with the electron count and temperature, and solve. A cell at minus zero point one four six volts with Q of twenty-five hundred comes out near minus zero point two four seven — more negative than the standard value, not less. Which way it moves depends entirely on whether Q is above or below one. Building Q from standard values defeats the point of the equation.

Same reaction, both sides.

Chem 2203 Concentration Cells

A concentration cell generates a potential from a concentration difference alone: the same half-reaction runs at both electrodes, so the standard cell potential is zero and the whole reading comes from Q. Two silver electrodes in silver nitrate solutions of different concentration generate a small potential. Looking up the electrode's tabulated value and reporting that misses where the potential comes from.

One cell, four numbers.

Chem 2206 Capstone: Full Electrochemical Profile of a Galvanic Cell

Silver at plus zero point eight zero as cathode against copper at plus zero point three four as anode gives a standard cell potential of zero point four six volts, so spontaneous as written. With two electrons transferred the free energy change is about minus eighty-nine kilojoules, and the equilibrium constant near three point six times ten to the fifteenth — both agreeing. Under nonstandard conditions, with silver ion at a hundredth molar and copper at one and a half, Q is fifteen thousand and the Nernst reading falls to about zero point three four volts, lower but still positive. One standard potential, and every other number follows from it.

Five things to carry out of this part. Anode and cathode are named by the reaction occurring there — oxidation at the anode, reduction at the cathode, in every cell without exception — while the charge signs are a separate question that reverses between a galvanic cell and an electrolytic one. Neither sign convention is the correct one; the reaction-based rule survives both. A half-cell potential is always a difference, because a single electrode has no potential in isolation, which is why the hydrogen electrode is assigned exactly zero volts and every tabulated value is reported against that chosen reference. A standard cell potential is the cathode's tabulated reduction potential minus the anode's, both taken as tabulated. Cell potential, free energy change and the equilibrium constant are one fact in three notations, joined by ΔG° equals minus n F E°cell and ΔG° equals minus R T log K, so any one determines the other two. And the Nernst equation adjusts a cell's potential for the concentrations actually present, moving it up or down according to whether Q sits below or above one — and changing nothing when Q equals one, which is what standard conditions means. Part Four puts the cell to work: batteries, corrosion, and running it backwards on purpose.