In
electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between Electric potential, electrical potential difference and identifiable chemical change. These reactions involve Electron, electrons moving via an electronic ...
, 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 () is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant extern ...
and ''F'' is the
Faraday constant
In physical chemistry, the Faraday constant (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...
.
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 chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction ( half-cell or full cell reaction) from the standard electrode potential, absolute tempera ...
:
:
where
is the
Gibbs energy
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a ther ...
and ''F'' is the
Faraday constant
In physical chemistry, the Faraday constant (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...
. 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 chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction ( half-cell or full cell reaction) from the standard electrode potential, absolute tempera ...
can be used to calculate the standard potential at other conditions.
The cell reaction is generally
endothermic
An endothermic process is a chemical or physical process that absorbs heat from its surroundings. In terms of thermodynamics, it is a thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, ...
: 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 significant amount of heat is added or extracted. As ...
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 during heat process to evaluate the efficiency of the process.
Short history
Entropy is produced in irreversible processes. The importance of avoiding irreversible p ...
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 () is the sum of a thermodynamic system's internal energy and the product of its pressure and volume. It is a state function in thermodynamics used in many measurements in chemical, biological, and physical systems at a constant extern ...
.
[
]
:
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