Partial Pressure

Each gas in a mixture adds to the total pressure of the mixture. The partial pressure is responsible for this contribution. The partial pressure is the pressure that a gas would have if it were in its own volume and temperature. While pressure is usually denoted by the letters P or p, partial pressure is denoted by a subscript (e.g., P1 or p1).In the domains of chemistry, physics, and biology, partial pressure is crucial. The partial pressure of oxygen and carbon dioxide in the blood is used to determine their levels. 

Dalton’s law of partial pressure

The overall pressure of a mixture of ideal gasses is equal to the sum of the partial pressures of the individual gasses in the mixture, according to Dalton’s law. This equivalence emerges from the fact that the molecules in an ideal gas are so far apart that they do not interact. The majority of real-world gasses come near to this ideal. 

Ptotal  = P1 + P2 +…….+Pn

The partial pressures of each chemical are represented by P1, P2, and Pn. The gasses are believed not to react with one another.

Vapor pressure

The phrase is most commonly used to describe the tendency of a liquid to evaporate. It is a measurement of a liquid or solid tendency for molecules and atoms to escape. The normal boiling point of a liquid is the temperature at which its vapor pressure equals the ambient atmospheric pressure, therefore it is often referred to as the atmospheric pressure boiling point.

For example, methyl chloride has the highest vapor pressure of any of the liquids in the figure at any given temperature. It also has the lowest normal boiling point (24.2 °C), which is the point at which the methyl chloride vapor pressure curve (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure. Because the atmospheric pressure at higher elevations is lower than at sea level, the boiling points of liquids are lower.Because the atmospheric pressure at the summit of Mount Everest is around 0.333 atm, the boiling point of diethyl ether would be approximately 7.5 °C against 34.6 °C at sea level if the graph were used (1 atm).

How to find partial pressure and total pressure

Partial pressure

The partial pressure of a single gas within a mixture, pi, can be stated as follows:

Pi=PtotalXi

The mole fraction is denoted by xi.

Example

The total pressure of a mixture of 2 mol Hydrogen and 3 mol He is 3 atm. How much partial pressure does He have?

PHe = Ptotal xHe =  (3)(3/5) = 9/5atm

Total partial pressure

We know from Boyle’s Law that the total pressure of a mixture is solely determined by the number of moles of gas present, regardless of the types and amounts of gases present; the Ideal Gas Law reveals that the pressure exerted by a mole of molecules is independent of the identity of those molecules; and Dalton’s Law now allows us to calculate the total pressure in a system when we know each gas’s individual contribution.

Example

Consider a 25.0 L container with a fixed volume. At 298 K, we pump 0.78 moles of N2 gas into the container. We can simply calculate the measured pressure of nitrogen gas to be 0.763 atm using the Ideal Gas Law.

We now take a similar container with a constant volume of 25.0 L and inject 0.22 moles of O2 gas at 298K into it. The oxygen gas has a measured pressure of 0.215 atm.

We inject 0.22 moles of O2 gas at 298K into the first container, which already contains 0.78 moles of N2, as a third measurement. (It’s worth noting that the gas mixture we’ve created is quite similar to air.)The pressure in this container has now been determined to be 0.975 atm.

The overall pressure of the N2 and O2 mixture in the container is equal to the sum of the pressures of the N2 and O2 samples obtained individually, according to our findings. The partial pressure of each gas in the mixture is now defined as its pressure if it were the only gas present. According to our findings, the partial pressure of N2 in the gas PN2 is 0.763 atm, while the partial pressure of O2 in the gas PO2 is 0.215 atm.

Conclusion

The partial pressure of a gas is a measure of the thermodynamic activity of the gas’s molecules. In gas mixtures and liquids, gases dissolve, distribute, and react according to their partial pressures, not their concentrations.This common feature of gases is also true in biological chemical reactions involving gases. The partial pressure of oxygen, for example, determines the amount of oxygen required for human respiration as well as the amount that is harmful. As a result, mixture ratios, such as those of breathable 20% oxygen and 80% helium, are determined by volume rather than weight or mass across a wide range of variable oxygen concentrations present in various inhaled breathing gases or dissolved in blood.Furthermore, oxygen and carbon dioxide partial pressures are significant quantities in arterial blood gas testing. However, similar pressures can also be measured in other fluids, such as cerebral fluid.