Practicing Using Dalton's Law of Partial Pressures
Four gases were combined in a gas cylinder with these partial pressures: 3.5 atm N2, [tex]2.8 atm O 2,0.25[/tex] atm Ar , and 0.15 atm He .
What is the total pressure inside the cylinder?
Answer (2)
To find the total pressure inside the gas cylinder, we apply Dalton's Law of Partial Pressures, which states that the total pressure is the sum of the partial pressures of the individual gases. By adding the given partial pressures (3.5 atm, 2.8 atm, 0.25 atm, and 0.15 atm), we calculate that the total pressure is 6.7 atm.
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Apply Dalton's Law of Partial Pressures: P T = P 1 + P 2 + P 3 + ... + P n .
Substitute the given partial pressures: P T = 3.5 + 2.8 + 0.25 + 0.15 .
Calculate the sum: P T = 6.7 atm.
The total pressure inside the cylinder is 6.7 atm.
Explanation
Understanding the Problem We are given the partial pressures of four gases in a cylinder: Nitrogen ( N 2 ), Oxygen ( O 2 ), Argon ( A r ), and Helium ( He ). We are asked to find the total pressure inside the cylinder. Dalton's Law of Partial Pressures states that the total pressure of a mixture of gases is the sum of the partial pressures of each individual gas.
Applying Dalton's Law Dalton's Law of Partial Pressures is expressed as: P T = P N 2 + P O 2 + P A r + P He where P T is the total pressure, P N 2 is the partial pressure of Nitrogen, P O 2 is the partial pressure of Oxygen, P A r is the partial pressure of Argon, and P He is the partial pressure of Helium.
Listing Given Pressures We are given the following partial pressures: P N 2 = 3.5 atm P O 2 = 2.8 atm P A r = 0.25 atm P He = 0.15 atm
Calculating Total Pressure Now, we substitute these values into Dalton's Law: P T = 3.5 + 2.8 + 0.25 + 0.15 P T = 6.7
Final Answer Therefore, the total pressure inside the cylinder is 6.7 atm.
Examples
Dalton's Law of Partial Pressures is useful in many real-world scenarios, such as scuba diving. When divers breathe compressed air, the air is a mixture of gases, primarily nitrogen and oxygen. Understanding the partial pressures of these gases at different depths is crucial for avoiding nitrogen narcosis and oxygen toxicity. By knowing the percentage of each gas in the mixture and the total pressure at a certain depth, divers can calculate the partial pressure of each gas and adjust their dive plan accordingly to ensure their safety.
