Cell voltage

The cell voltage is the electrical voltage of a single electrochemical cell , i.e. H. a galvanic element (including the colloquially known as batteries primary cells, accumulators and fuel cells ) or an electrolysis cell.

If no electrical current flows through the cell, the voltage on the cell is called the open circuit voltage (terminal voltage in the de-energized state), also known as the open circuit voltage . In the case of a battery, for example, the no-load voltage occurs as long as no electrical energy is drawn. The operating voltage of a galvanic cell (load voltage of the battery cell) is always lower than the open circuit voltage of the cell, since the internal resistance of the cell leads to a voltage loss during operation . The operating voltage of an electrolytic cell is always greater than its open circuit voltage, not only because of the internal resistance of the cell, but also because of overvoltages . In accordance with the first law of thermodynamics , the energy that is required when charging an accumulator or a reversible fuel cell is always greater than that which can be extracted again when discharging.

The voltage of a battery consisting of several cells, which are all connected in series , results from the sum of the cell voltages of the individual elements.

Reversible cell voltage

If the cell is in equilibrium, the rest voltage is equal to the reversible cell voltage. A historically significant, but outdated term for this equilibrium voltage is electromotive force EMF or primary voltage.

The following applies to the reversible cell voltage

${\displaystyle \mathrm {\quad } \Delta _{\text{r}}G=-z\cdot F\cdot \Delta E}$

with Gibbs energy (free enthalpy) of the cell reaction (J / mol), = number of electrons transferred during the reaction, = Faraday constant ( ≈ 96485.3 As / mol) and = reversible cell voltage (rest potential difference between the electrodes, V). ${\displaystyle \Delta _{\text{r}}G}$ ${\displaystyle z}$ ${\displaystyle F}$ ${\displaystyle F}$ ${\displaystyle \Delta E}$

Thermodynamic basics

According to the law of conservation of energy (1st law of thermodynamics) , no energy can disappear or arise again. In chemical and electrochemical reactions, however, entropy changes also always occur , in particular due to heat transport across the system boundaries. At a constant temperature of the cell, according to the second law of thermodynamics or according to the definition of entropy : ${\displaystyle T}$

${\displaystyle \Delta _{\text{r}}S-{\frac {q_{\text{rev}}}{T}}=0}$,

with change in entropy of the reaction, reversible heat of the reaction and temperature of the reaction, here: the cell. ${\displaystyle \Delta _{\text{r}}S}$ ${\displaystyle q_{\text{rev}}}$ ${\displaystyle T}$

According to the first law of thermodynamics or according to the definition of the reaction enthalpy : ${\displaystyle \Delta _{\text{r}}H}$

${\displaystyle q_{\text{rev}}+w_{\text{rev}}=\Delta _{\text{r}}H}$,

with reversible work, e.g. B. electrical work . does not include work against external pressure when the volume changes. Combining the above two equations for reversible work it follows: ${\displaystyle w_{\text{rev}}}$ ${\displaystyle w_{\text{rev}}}$

${\displaystyle w_{\text{rev}}=\Delta _{\text{r}}H-T\cdot \Delta _{\text{r}}S}$.

The reversible work depends not only on the actual reaction enthalpy but also directly on the temperature and the change in the reaction entropy.

With the definition of Gibbs energy one gets ${\displaystyle \Delta _{\text{r}}G=\Delta _{\text{r}}H-T\cdot \Delta _{\text{r}}S}$

${\displaystyle w_{\text{rev}}=\Delta _{\text{r}}G}$.

If one takes into account that the charge is per formula conversion , the electrical work per formula conversion is obtained with the equation ${\displaystyle -z\cdot F}$

${\displaystyle w_{\text{rev}}=-z\cdot F\cdot \Delta E}$.

The above equation is obtained from the last two equations . ${\displaystyle \Delta _{\text{r}}G=-z\cdot F\cdot \Delta E}$

Examples

At a temperature of 25 ° C, the reversible cell voltage of both the water electrolysis and the hydrogen-oxygen fuel cell is 1.23 V. The cell voltage of a charged lead-acid battery is about 2.0 V; a starter battery made up of six cells therefore has a voltage of around 12 V.

The cell voltage of a lithium iron phosphate battery is 3.3 V, while that of other lithium ion batteries is usually even higher. Since these values ​​are far above the decomposition voltage of water (1.23 V as stated above), such accumulators must use non-aqueous electrolytes .

Individual evidence

1. ↑ Gerd Wedler: Textbook of Physical Chemistry . 5th edition. Wiley-VCH, Weinheim 2004, ISBN 3-527-31066-5 , 1.6.1 Basic terms in electrochemistry, p. 195 .
2. ↑ Dieter Ziessow, Marco Sielaff: Electrolysis II - Electrode Properties - Decomposition Voltage. In: ChemgaPedia> Physical Chemistry> Electrochemistry. Wiley Information Services GmbH, accessed April 8, 2019 . 
3. ↑ electromotive force. In: Spektrum.de> Lexica> Lexicon of Physics. Spectrum der Wissenschaft Verlagsgesellschaft mbH, accessed on April 8, 2019 . 
4. ↑ Gerd Wedler: Textbook of Physical Chemistry . 5th edition. Wiley-VCH, Weinheim 2004, ISBN 3-527-31066-5 , 2.8.1 The thermodynamics and the reversible cell voltage, p. 449 .