Amount of substance

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

The amount of substance (German: Stoffmenge) describes the number of particles (atoms, molecules, ions) in a substance. It is one of the seven SI base quantities and, in electrical engineering, is mainly relevant to electrochemical processes.

1 Quantity symbol and unit

The quantity symbol for the amount of substance is $n$.
Its unit (SI base unit) is the mole, with the unit symbol $\mathrm{mol}$.

$$[n]=\mathrm{mol}$$

Definition via the Avogadro constant:

$$N_A=6.022\cdot 10^{23}\mathrm{mo}{\mathrm{l}}^{-1}$$

One mole contains $N_A$ particles.

2 Practical and worked examples

No calculations are carried out with the luminous intensity in the fundamentals of electrical engineering. It appears here primarily because I wanted to cover the base quantities completely. Nevertheless, a few worked examples follow for those who are interested.

2.1 Electrolysis (Faraday’s laws)

In electrolysis, $F=96.485\mathrm{kC}$ (Faraday constant) is required per mole of monovalent ions:

$$Q=n\cdot z\cdot F$$

Example: deposition of $n=0.1\mathrm{mol}$ of copper (doubly ionized, $z=2$):

$$Q=0.1\mathrm{mol}\cdot 2\cdot 96.485kC/mol=\underline{19.3\mathrm{kC}}$$

2.2 Battery capacity

Theoretical capacity of a zinc-carbon battery:

$$Q=n_{Zn}\cdot z\cdot F=n_{Zn}\cdot 2\cdot 96.485kC/mol$$

With $n_{Zn}=0.05\mathrm{mol}$ of zinc: $Q=\underline{9.6\mathrm{kC}}=2.7\mathrm{Ah}$

3 Typical orders of magnitude

• Electrolysis in the laboratory: $n\approx 10^{-3}$ to $10^{-1}\mathrm{mol}$
• Batteries (active material): $n\approx 0.1$ to $10\mathrm{mol}$
• Industrial electrolysis: $n\approx 10$ to $10^4\mathrm{mol}$
• Fuel cells: $n\approx 10^{-6}$ to $1mol/s$ (flow rate)

4 Example phrasings

• ‘The electrolysis releases $0.2\mathrm{mol}$ of hydrogen.’
• ‘An electric charge of $96.5\mathrm{kC}$ flows per mole of electrons.’
• ‘The battery contains $2.5\mathrm{mol}$ of active material.’

5 Related quantities

• Electric charge via the Faraday constant:

$$Q=n\cdot z\cdot F$$

• Number of particles:

$$N=n\cdot N_A$$

• Mass via the molar mass:

$$m=n\cdot M$$

6 Related components

• Battery: the amount of substance of the active material determines the capacity
• Rechargeable battery: electrochemical reactions are based on amounts of substance