# Partial Pressure Formula

In 1802 the English chemist John Dalton proposed Dalton’s law of Partial Pressure. The scientist researched non-reactive gas mixtures confined in a vessel extensively and concluded that the overall pressure exerted by the mixture is equal to the sum of partial pressures exerted by separate gases when kept at a specific temperature and volume. Let’s take a closer look at the partial pressure formula.

### Partial Pressure

The partial pressure of an individual gas in a mixture of gases is the pressure exerted by that gas. For example, if a container contains a combination of three gases, oxygen, nitrogen, and carbon dioxide, the pressure imposed by oxygen on the container’s walls is its partial pressure, just as the pressure exerted by nitrogen and carbon dioxide separately is their partial pressures. The sum of the partial pressures of the gases (oxygen, nitrogen, and carbon dioxide) in the mixture exerts a total pressure on the container walls.

To put it another way, each constituent gas in a mixture of gases has a partial pressure that is equal to the pressure of that constituent gas if it alone occupied the complete volume of the original mixture at the same temperature. In fact, a gas’s partial pressure is a metric of its thermodynamic activity. A gas’s partial pressure can reveal a variety of characteristics. The partial pressure of a gas in a certain volume, for example, influences its reactivity. The partial pressures of gases cause them to dissolve and disseminate. This feature of gases aids in the comprehension and prediction of gas chemical reactions in biology. The partial pressures of oxygen and carbon dioxide in arterial blood gases are critical parameters in these assays. The symbol P denotes the partial pressure of the gas, with the gas symbol in the subscript. The partial pressure of oxygen, for example, is PO_{2}.

### Law of Partial Pressure by Dalton

The overall pressure of a gas mixture is equal to the sum of the partial pressures of the constituent gases in the mixture, according to Dalton’s partial pressure equation. For optimal gas mixtures, Dalton’s law holds perfectly. Molecules in an ideal gas are extremely far apart and do not react. With minor variations, genuine gas mixtures obey Dalton’s law.

**Partial Pressure Formula**

Partial Pressure is calculated using the following formula,

Consider a vessel filled with non-reactive gases such as helium (He), oxygen (O2), and hydrogen (H) that is held at a fixed temperature and volume to better comprehend Dalton’s Law. All three gases will put pressure on the vessel’s walls in such a circumstance. As a result, the total pressure equals the sum of the partial pressures exerted by the He, O2, and H molecules.

P_{total}= P_{He}+ P_{O2}+ P_{H}Dalton’s Law of Partial Pressure is expressed in this manner. When two or more non-reacting gases are held at the same temperature and volume in a closed vessel, the total pressure exerted by the mixture equals the sum of their partial pressures.

The total pressure is typically expressed as,

P_{total}= P_{1}+ P_{2}+ P_{3}+ … + P_{n}Where,

- P
_{total}= Total Pressure of Mixture gas,- P
_{1}+ P_{2}+ P_{3}+ … + P_{n}= Individual gas partial pressures up to n.

### Sample Questions

**Question 1: State Dalton’s Law of Partial pressure.**

**Answer:**

Dalton’s Law of Partial pressure is states that, the sum of the partial pressures of the various individual gases in a mixture equals the total pressure.

**Question 2: When the Partial pressure of He is 0.1 atm, Ne is 2.1 atm, O _{2} is 2 atm and UF_{6} is 0.7 atm then calculate the total partial pressure.**

**Solution:**

Given: P

_{He}= 0.1 atm, P_{Ne}= 2.1 atm, P_{O2}= 2 atm, P_{UF6}= 0.7 atm.Since,

P

_{total}= P_{He}+ P_{Ne}+ P_{O2}+P_{UF6}∴ P

_{total}= 0.1 + 2.1 + 2 + 0.7

∴ P_{total}= 4.9 atm

**Question 3: We add an anonymous quantity of CO _{2 }to a tank containing O_{2} at 2 atm and N_{2} at 2.4 atm until the total pressure inside the tank reaches 5.7 atm. What is the partial pressure of CO_{2}?**

**Solution:**

Given: PO

_{2}= 2 atm, PN_{2}= 2.4 atm, Ptotal = 5.7 atmSince,

P

_{total}= P_{O2}+ P_{N2}+ P_{CO2}∴ P

_{CO2}= P_{total}– P_{O2}– P_{N2}∴ P

_{CO2}= 5.7 – 2 – 2.4

∴ P_{CO2}= 1.3 atm

**Question 4: Calculate the total partial pressure when P _{1} partial pressure is 0.3 atm, P_{2} partial pressure is 2 atm, and P_{3} partial pressure is 3 atm.**

**Solution:**

Given: P

_{1}= 0.3 atm, P_{2}= 2 atm, P_{3}= 3 atmSince,

P

_{total}= P_{1}+ P_{2 }+ P_{3}∴ P

_{total}= 0.3 + 2 + 3

∴ P_{total}= 5.3 atm

**Question 5: If the partial pressure of N _{2} is 3.1 atm and O_{2 }is 2 atm then calculate the total partial pressure of the gas.**

**Solution:**

Given: P

_{N2}= 3.1 atm, P_{O2}= 2 atmSince,

P

_{total}= P_{N2}+ P_{O2}∴ P

_{total}= 3.1 + 2

∴ P_{total}= 5.1 atm

**Question 6: If the Partial pressure of P _{1} is 2 atm, P_{2} is 1.8 atm, P_{3} is 3 atm and P_{4} is 1.2 atm then what is the Total partial pressure?**

**Solution:**

Given: P

_{1}= 2 atm, P_{2}= 1.8 atm, P_{3}= 3 atm, P_{4}= 1.2 atmSince,

P

_{total}= P1 + P_{2}+ P_{3 }+ P_{4}∴ P

_{total}= 2 + 1.8 + 3 + 1.2

∴ P_{total}= 8 atm

**Question 7: Partial pressure of P _{1} is 2.1 atm and P_{2} is 3.2 atm then what is the total partial pressure of the gas?**

**Solution:**

Given: P

_{1}= 2.1 atm, P_{2 }= 3.2 atmSince,

P

_{total}= P_{1}+ P_{2}∴ P

_{total }= 2.1 + 3.2∴

P_{total}= 5.3 atm