# Nernst Equation

## The Nernst Equation

## Calculation of oxygen concentration from SIRO_{2} sensor signal

Please enter the operating temperature (500 - 1700 deg C) and the measured mV (0 - 1200 mV) signal.
The corresponding oxygen concentration is calculated. If it is very low, it is displayed in
scientific notation.

The Nernst equation is **E = (RT/nF)ln(pO**_{2}/pO_{2}')

Where:

E = sensor electromotive force, (mV)

R = gas constant

T = temperature, (Kelvin)

n = number of charges per reactant species

F = Faraday constant

p = partial pressure (mole fraction)

This equation describes the electromotive force (emf) developed when there are different concentrations
of a reactant on each side of an electrolyte.

If oxygen is to be measured, using a zirconia ceramic electrolyte and atmospheric air,
with pO_{2} = 0.209, as a reference, this equation simplifies to:

**pO**_{2} = 0.209 exp(-46.421 E/T)

The equation may be re-arranged, to allow calculation of the emf from a known reference
concentration and a measured oxygen concentration:

**E = 0.0496 T log(pO**_{2}/0.209 )

## Calculation of Nernst voltage from oxygen concentration.

Note that the oxygen concentration can be entered either as a decimal fraction
(so that 1% would be entered as 0.01) or in power of 10 notation ( so that 0.001% would be 1.00*10^-5).

**Australian Oxytrol Systems supplies a range of industrial, scientific and
pottery probes for the measurement of oxygen at high temperature.**

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