In
electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outco ...
, a thermoneutral voltage is a voltage drop across an electrochemical cell which is sufficient not only to drive the cell reaction, but to also provide the heat necessary to maintain a constant temperature. For a reaction of the form
:
The thermoneutral voltage is given by
:
where
is the change in
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
and ''F'' is the
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
.
Explanation
For a cell reaction characterized by the chemical equation:
:
at constant temperature and pressure, the thermodynamic voltage (minimum voltage required to drive the reaction) is given by the
Nernst equation
In electrochemistry, the Nernst equation is a Thermodynamics#Chemical thermodynamics, chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or electrochemical cell, full cell reacti ...
:
:
where
is the
Gibbs energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work (physics), work that may be performed by a closed system, thermodynamically closed system a ...
and ''F'' is the
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of S ...
. The standard thermodynamic voltage (i.e. at standard temperature and pressure) is given by:
:
and the
Nernst equation
In electrochemistry, the Nernst equation is a Thermodynamics#Chemical thermodynamics, chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or electrochemical cell, full cell reacti ...
can be used to calculate the standard potential at other conditions.
The cell reaction is generally
endothermic
In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. p. ...
: i.e. it will extract heat from its environment. The Gibbs energy calculation generally assumes an infinite
thermal reservoir
A thermal reservoir, also thermal energy reservoir or thermal bath, is a thermodynamic system with a heat capacity so large that the temperature of the reservoir changes relatively little when a much more significant amount of heat is added or ex ...
to maintain a constant temperature, but in a practical case, the reaction will cool the electrode interface and slow the reaction occurring there.
If the cell voltage is increased above the thermodynamic voltage, the product of that voltage and the current will generate heat, and if the voltage is such that the heat generated matches the heat required by the reaction to maintain a constant temperature, that voltage is called the "thermoneutral voltage". The rate of delivery of heat is equal to
where ''T'' is the temperature (the standard temperature, in this case) and ''dS/dt'' is the rate of
entropy production
Entropy production (or generation) is the amount of entropy which is produced in any irreversible processes such as heat and mass transfer processes including motion of bodies, heat exchange, fluid flow, substances expanding or mixing, anelastic d ...
in the cell. At the thermoneutral voltage, this rate will be zero, which indicates that the thermoneutral voltage may be calculated from the
enthalpy
Enthalpy , a property of a thermodynamic system, is the sum of the system's internal energy and the product of its pressure and volume. It is a state function used in many measurements in chemical, biological, and physical systems at a constant ...
.
[
]
:
An example
For water at standard temperature (25 C) the net cell reaction may be written:
:
Using Gibbs potentials (
kJ/mol),
the thermodynamic voltage at standard conditions is
:
1.229 Volt (2 electrons needed to form H
2(g))
Just as the combustion of hydrogen and oxygen generates heat, the reverse reaction generating hydrogen and oxygen will absorb heat. The thermoneutral voltage is (using
kJ/mol):
:
1.481 Volts.
References
{{reflist
Physical chemistry
Electrochemistry
Electrochemical equations