Basics

Activity and Concentration – both terms are used in electrochemistry. But what is the difference?

The concentration of substance c indicates the amount of substance n of a dissolved species in a defined volume and thus the unit is mol/L. Furthermore, the designation molarity M is commonly used in chemistry for the concentration of substance in mol/L.
The concentration of substance is dependent on the temperature because the volume is temperature-dependent. You can also relate the concentration of substance of a dissolved species to the weight of the solvents in kg. Then, you get the molality b in mol/kg. The molality is temperature-independent. The molality is especially found in older tables.
Moreover, we can find the term of the activity of a species. The activity of a substance is a thermodynamic value, a kind of a corrective concentration.
In a solution the charged ions are surrounded by solvation shells (hydrate shells in water as solvent) and thus sealed off each other. The ions are less effective. The activity therefore corresponds to the remaining effective concentration, which is usually lower than the concentration because of the interactions between the ions in the solution. Only in very diluted solutions are the activity and the concentration almost equal.
In highly concentrated solutions, however, the activities can reach values higher than the concentration because there are not enough solvate molecules to completely solvate all ions.

The deviation between activity and concentration is reflected in a correction factor, the so-called activity coefficient y, γ or f (depending on the kind in which the concentration of substance is stated).

a = y ∗ c      c = concentration of substance in mol/L (molarity)

a = γ ∗ c      c = concentration of substance in mol/kg (molality)

a = f ∗ c       c = content of the dissolved substance as mole fraction

Universal definition of the activity (does not correspond to the physicochemical definition) according to Jander, Jahr; Maßanalyse; 15. Auflage, 1989, de Gruyter

Potential – Voltage – Electromotive Force

All three terms refer to a voltage difference between two systems. If the reference point for the measurement is known, it is called potential; otherwise, it is called voltage.
Electromotive force refers to the potential difference of a cell, which is measured if the cell works reversibly and no current flows.

According to the convention of the IUPAC¹, a standard potential (or standard voltage) E is calculated by the equation
E = E(right) – E(left) (standard electrode potential of the right cell minus standard electrode potential of the left cell).

The IUPAC² also determines: “The standard potential of an electrochemical reaction, abbreviated as standard potential, is defined as the standard potential of a hypothetical cell, in which the electrode (half-cell) at the left of the cell diagram is the standard hydrogen electrode (SHE) and the electrode at the right is the electrode in question.“

If you always consider the standard hydrogen electrode as the “left” cell, the standard potentials of the electrochemical series automatically arise, indicated as standard reduction potential. In old tables one often finds standard oxidation potentials, in which case the algebraic signs must be reversed. Whether oxidation or reduction potentials are indicated in a table can be seen from the algebraic signs for the reaction Cu/Cu²⁺, because then the standard potential is +0.34 V.

In doing so, the question arises as to which electrode has to be connected to which input of the measurement instrument, because the algebraic sign of the measured potential changes  depending on the connection of the electrodes. The values of the electrochemical series are the result of the measurements if you connect the standard hydrogen electrode to the minus input (COM). If you measure against another reference electrode, you connect it to the minus input (COM). Thus, the measurement electrode is always connected to the positive pole:

E = E_{(measurement electrode)} – E_{(reference electrode)}.

The algebraic sign of the measured potentials shows which of the electrode is more positive, in which direction the current flows and which of the reaction runs spontaneously, since the potential is directly related to the equilibrium constant of the reactants. E > 0 for E(right) > E(left) means that the right electrode is positively charged towards the left electrode. There is therefore a shortage of electrons at the right electrode caused by the reduction of particles. This electrode is also called the cathode, where the reduction takes place. Therefore, the electrones flow from left to right. Thus, the electric current, unfortunately defined as a flow of positive particles, flows in the opposite direction.
There is an excess of electrons at the left electrode, because particles are being oxidised there. This electrode is called the anode, where the oxidation takes places. The reaction therefore tends to runs spontaneously from left (oxidation) to right (reduction). E < 0 for E(right) < E(left) by implication means that the reaction runs spontaneously from right to left.

Conversion of the potentials of common reference electrodes (png)

1: Cohen et al: Quantities, units and symbols in physical chemistry, IUPAC Green Book, 3rd edn., 2nd printing, IUPAC & RSC Publishing, Cambridge, 2008, p. 71
2: Cohen et al: Quantities, units and symbols in physical chemistry, IUPAC Green Book, 3rd edn., 2nd printing, IUPAC & RSC Publishing, Cambridge, 2008, p. 74