 # O2 Sensor Working Principle : What is Partial Pressure of Oxygen and How Do You Calculate It?

The zirconium dioxide O2 sensor working principle measures partial pressure of oxygen in a mixture of gases. This typically causes confusion amongst SST’s customers as most oxygen sensors on the market measure oxygen concentration.

But, what is partial pressure? It is a question we are asked frequently when it comes to the O2 sensor working principle. In this article, we will address the definition of partial pressure, the physics behind it, how you calculate partial pressure and how to convert the oxygen partial pressure into volumetric content for those interested in oxygen concentration.

#### Partial Pressure: The Definition

The partial pressure is defined as the pressure of a single gas component in a mixture of gases. It corresponds to the total pressure which the single gas component would exert if it alone occupied the whole volume.

#### Daltons Law: The Physics

The theory of the o2 sensor working principle is detailed here. The total pressure (Ptotal) of a mixture of ideal gases is equal to the sum of the partial pressures (Pi) of the individual gases in that mixture.

From Equation 1 it can be derived that the ratio of the number of particles (ni) of an individual gas component to the total number of particles (ntotal) of the gas mixture equals the ratio of the partial pressure (Pi) of the individual gas component to the total pressure (Ptotal) of the gas mixture.

ni                            Number of particles in gas i

ntotal                       Total number of particles

pi                            Partial pressure of gas i

Ptotal                       Total pressure Figure 1 Ptotal = P1 + P2 + P3 (Constant Volume & Temperature)

##### Example 1:

The atmospheric pressure at sea level (under standard atmospheric conditions) is 1013.25mbar. Here, the main components of dry air are nitrogen (78.08% Vol.), oxygen (20.95% Vol.), argon (0.93% Vol.) and carbon dioxide (0.040% Vol.). The volumetric content (%) can be equated to the number of particles (n) since the above gases can be approximated as ideal gases.

Equation 2 can be solved for the partial pressure of an individual gas (i) to get:

The oxygen partial pressure then equates to: Figure 2 Partial Pressure at 0% Humidity

Of course, this value is only relevant when the atmosphere is dry (0% humidity). If moisture is present a proportion of the total pressure is taken up by water vapour pressure. Therefore, the partial oxygen pressure (ppO₂) can be calculated more accurately when relative humidity and ambient temperature are measured along with the total barometric pressure. Figure 3 Liquid Vapour Pressure

Firstly, water vapour pressure is calculated:

WVP      Water Vapour Pressure (mbar)

HRel         Relative Humidity (%)

WVPmax Maximum Water Vapour Pressure (mbar) The maximum water vapour pressure is also referred to as the dewpoint. Warmer air can hold more water vapour and so has a higher WVPmax.

Partial oxygen pressure then equates to:

ppO2      Partial Pressure O2 (mbar)

BP           Barometric Pressure (mbar)

WVP      Water Vapour Pressure (mbar)

##### Example 2:

Example 2 below describes the effect of humidity reducing the partial oxygen pressure and therefore the volumetric content of oxygen.

On a typical day, the following information is recorded from a calibrated weather station:

Temperature:                    22°C

Humidity:                            32%

Barometric Pressure:      986mbar

Using the Water Vapour Pressure look up table above, WVPMAX = 26.43mbar.

Partial oxygen pressure then equates to:

As we now know the oxygen partial pressure and the total barometric pressure we can work out the volumetric content of oxygen.