# Dalton’s law formula

Dalton’s law formula, expressed as PTotal = P1 + P2 + P3 + … + Pn, states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. In this formula, PTotal represents the total pressure of the gas mixture, while P1, P2, P3, and so on, represent the partial pressures of each individual gas in the mixture.

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## Practice problems

### Problem #1

A cylinder is filled with a mixture of nitrogen, oxygen, and helium gases. The mixture exerts a total pressure of 12 atm on the cylinder wall. The partial pressures of nitrogen and oxygen are 2 atm and 3 atm, respectively. Calculate the partial pressure of helium.

Solution

Given data:

• Total pressure of the gas, PTotal = 12 atm
• Partial pressure of the nitrogen gas, P1 = 2 atm
• Partial pressure of the oxygen gas, P2 = 3 atm
• Partial pressure of the helium gas, P3 = ?

Applying the formula:

• PTotal = P1 + P2 + P3 + … Pn
• PTotal = P1 +P2 + P3 (Because, a mixture is made up of three gases)
• 12 = 2 + 3 + P3
• P3 = 12 – 5
• P3 = 7 atm

Therefore, the partial pressure of the helium gas is 7 atm.

### Problem #2

In a solid container, there is a mixture of four gases with partial pressures of 4 atm, 3 atm, 5 atm, and 8 atm, respectively. Calculate the total pressure of the gas mixture.

Solution

Given data:

• Partial pressure of the gas 1, P1 = 4 atm
• Partial pressure of the gas 2, P2 = 3 atm
• Partial pressure of the gas 3, P3 = 5 atm
• Partial pressure of the gas 4, P4 = 8 atm
• Total pressure of the gas, PTotal = ?

Applying the formula:

• PTotal = P1 + P2 + P3 + … Pn
• PTotal = P1 +P2 + P3 + P4 (Because, a mixture is made up of four gases)
• PTotal = 4 + 3 + 5 + 8
• PTotal = 20 atm

Therefore, the total pressure of the gas is 20 atm.

### Problem #3

A container is filled with a mixture of hydrogen and argon gases. If the total pressure of the mixture is 9 atm and the partial pressure of hydrogen gas is 6 atm, calculate the partial pressure of argon gas.

Solution

Given data:

• Total pressure of the gas, PTotal = 9 atm
• Partial pressure of the hydrogen gas, P1 = 6 atm
• Partial pressure of the argon gas, P2 = ?

Applying the formula:

• PTotal = P1 + P2 + P3 + … Pn
• PTotal = P1 +P2 (Because, a mixture is made up of two gases)
• 9 = 6 + P2
• P2 = 9 – 6
• P2 = 3 atm

Therefore, the partial pressure of the argon gas is 3 atm.

### Problem #4

A container is filled with five gases that exert a total pressure of 24 atm on the container’s walls. The partial pressures of four of the gases are 2 atm, 5 atm, 6 atm, and 8 atm, respectively. What is the partial pressure of the fifth gas?

Solution

Given data:

• Total pressure of the gas, PTotal = 24 atm
• Partial pressure of the gas 1, P1 = 2 atm
• Partial pressure of the gas 2, P2 = 5 atm
• Partial pressure of the gas 3, P3 = 6 atm
• Partial pressure of the gas 4, P4 = 8 atm
• Partial pressure of the gas 5, P5 = ?

Applying the formula:

• PTotal = P1 + P2 + P3 + … Pn
• 24 = 2 +5 + 6 + 8 + P5 (Because, a mixture is made up of five gases)
• 24 = 21 + P5
• P5 = 24 – 21
• P5 = 3 atm

Therefore, the partial pressure of the fifth gas is 3 atm.