# Partial Pressure

## What is Partial Pressure?

In a mixture of gases, the pressure exerted by an individual gas is known as its partial pressure. For example, if a container contains a mixture of three gases oxygen, nitrogen and carbon dioxide then the pressure exerted by oxygen on the walls of the container is its partial pressure, in the same way the pressure exerted by nitrogen and carbon dioxide individually are partial pressures of nitrogen and carbon dioxide respectively. The total pressure exerted by the mixture of gases on the container walls is the sum of the partial pressures of the gases (oxygen, nitrogen and carbon dioxide) in the mixture.

In other words, in a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature.

Actually, the partial pressure of a gas is a measure of its thermodynamic activity. Partial pressure of a gas can tell us various properties of it. For example, reactivity of a gas in a fixed volume depends on its partial pressure. Even gases dissolve and diffuse according to their partial pressures. This property of gases helps us to understand and predict the chemical reactions of gases in biology as well. In the tests of arterial blood gases, the partial pressure of oxygen and carbon dioxide are important parameters.

The partial pressure of the gas is represented by the symbol P with the symbol of the gas in the subscript. For example,  Po2 represents partial pressure of oxygen.

## What is Dalton’s Law of Partial Pressure?

Dalton’s law of partial pressure was given by English Chemist, Physicist and meteorologist John Dalton in 1802. According to Dalton’s law of partial pressure, total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. Dalton’s law is perfectly true for ideal gas mixture. In ideal gas molecules are very far from each other so they do not react. The mixture of real gases also follows Dalton’s law with slight variation.

For example, if a mixture of ideal gases contains nitrogen, hydrogen and oxygen then the total pressure exerted by the ideal gas mixture will be –

$P_{total}$ = PN2 + PH2+PO2

Where Ptotal  = total pressure of the ideal gas mixture

PN2 = Partial pressure of the nitrogen

PH2 = Partial pressure of the hydrogen

PO2 = Partial pressure of the oxygen

Let us look at another example, a mixture of oxygen and nitrogen gas has been taken in a beaker. If the partial pressure of oxygen is 159 mm Hg and partial pressure of nitrogen is 593 mm Hg, then total pressure exerted by the gaseous mixture will be 159 mm Hg + 593 mm Hg = 752 mm Hg. Same this has been represented by the diagram below –

## Mole fraction and Partial pressure

Before understanding the relation between mole fraction and partial pressure, you need to get a basic idea about mole fraction. In chemistry mole fraction is the ratio of a particular gas component in a mixture and the total number of moles of all constituents in the mixture. It is expressed by $x_{i}$ .

Formula of Mole fraction –

$x_{i}$ = $\frac{n_{i}}{n_{total}}$

Where $x_{i}$  = mole fraction

$n_{i}$= number of moles of an individual gas constituent of the mixture

$n_{total}$ = total number of moles of all constituents of the mixture.

Mole fraction is also called amount fraction.

Relationship between Mole Fraction and Partial Pressure for Ideal Gases –

Mole fraction of an individual gas component of an ideal gas mixture can be expressed as –

$x_{i}$ = $\frac{n_{i}}{n}$ --------(1)

Where ni is the number of moles of an individual gas of the ideal gas mixture.

n = total number of moles of all constituents of the ideal gas mixture

xi = mole fraction

Mole fraction of an individual gas component of an ideal gas mixture can also be expressed as –

$x_{i}$ = $\frac{P_{i}}{P}$--------(2)

Where Pi = partial pressure of an individual gas in the ideal gas mixture

P = total pressure of the ideal gas mixture

xi = mole fraction

From equation (1) and (2), we can write –

$x_{i}$ = $\frac{n_{i}}{n}$ = $\frac{P_{i}}{P}$

So partial pressure of an individual gas of the ideal gas mixture can be expressed as –

$P_{i}$ = $x_{i}$. P

Now as we know mole fraction of a gas component in a gas mixture is equal to its volumetric fraction in the gas mixture, so we can write –

$\frac{n_{X}}{n_{total}}$ =  $\frac{P_{X}}{P_{total}}$ = $\frac{V_{X}}{V_{total}}$

Where nX = moles of the gas component X

ntotal = total number of moles of all components of the mixture

PX = partial pressure of gas X

Ptotal = total pressure of the gas mixture

VX = partial volume of any individual gas component X

Vtotal = total volume of the gas mixture

## Partial Pressure: Summary in Tabular Form

 Partial Pressure Definition of partial pressure In a mixture of gases, the pressure exerted by an individual gas is known as its partial pressure. Representation by the symbol P with the symbol of the gas in the subscript. For example, PO2 represents partial pressure of oxygen. Dalton’s Law of partial pressure Given by – John DaltonTotal pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. Representation Ptotal = P1 + P2 + P3Where Ptotal = total pressure of the gas mixtureP1, P2, P3 are the partial pressures of the individual gases 1, 2 and 3 respectively. Mole fraction $x_{i}$ = $\frac{n_{i}}{n_{total}}$Where $x_{i}$ = mole fraction $n_{i}$= number of moles of an individual gas constituent of the mixture $n_{total}$= total number of moles of all constituents of the mixture. Mole fraction is also called amount fraction. Mole fraction and partial pressure $P_{i}$ = $x_{i}$. PWhere Pi = partial pressure of an individual gas in the ideal gas mixture P = total pressure of the ideal gas mixture xi = mole fraction

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