ideal gas law practice worksheet

Neter

3 min read

·

23-11-2024

1

0

Share

The Ideal Gas Law is a cornerstone of chemistry, providing a powerful tool to understand and predict the behavior of gases under various conditions. This article serves as a comprehensive guide, offering a practice worksheet with solutions to help you master this important concept. We'll cover the core equation, its applications, and provide examples to solidify your understanding of the Ideal Gas Law.

Understanding the Ideal Gas Law Equation

The Ideal Gas Law is expressed mathematically as:

PV = nRT

Where:

• P represents pressure (typically in atmospheres, atm)
• V represents volume (typically in liters, L)
• n represents the number of moles of gas (mol)
• R is the ideal gas constant (0.0821 L·atm/mol·K)
• T represents temperature (always in Kelvin, K)

Remember to always convert units to match the units of the ideal gas constant (R). Failing to do so will result in incorrect calculations.

Practice Problems: Ideal Gas Law Worksheet

Let's put your knowledge to the test with these practice problems. Remember to show your work and clearly state your units.

Problem 1: A sample of nitrogen gas (N₂) occupies a volume of 5.00 L at a pressure of 1.20 atm and a temperature of 25°C. How many moles of nitrogen gas are present?

Problem 2: A balloon filled with helium gas has a volume of 2.50 L at a temperature of 20°C and a pressure of 1.00 atm. If the temperature is increased to 35°C and the pressure remains constant, what is the new volume of the balloon?

Problem 3: 2.00 moles of oxygen gas (O₂) are contained in a 10.0 L tank at 27°C. What is the pressure of the oxygen gas in the tank?

Problem 4: A sample of carbon dioxide gas (CO₂) at a pressure of 1.50 atm and a temperature of 20°C occupies a volume of 7.50 L. What would be the volume of this gas sample if the pressure were decreased to 1.00 atm at a constant temperature?

Problem 5 (Challenge): A mixture of gases contains 1.00 mol of nitrogen, 0.50 mol of oxygen, and 0.25 mol of argon. The total pressure of the mixture is 2.00 atm at 25°C. What is the partial pressure of each gas in the mixture? (Remember Dalton's Law of Partial Pressures: The total pressure of a mixture of gases is the sum of the partial pressures of the individual gases.)

Solutions to Ideal Gas Law Worksheet

Problem 1 Solution:

1. Convert temperature to Kelvin: 25°C + 273.15 = 298.15 K
2. Rearrange the Ideal Gas Law to solve for n: n = PV/RT
3. Substitute values and solve: n = (1.20 atm)(5.00 L) / (0.0821 L·atm/mol·K)(298.15 K) = 0.245 mol N₂

Problem 2 Solution:

1. Convert temperatures to Kelvin: 20°C + 273.15 = 293.15 K; 35°C + 273.15 = 308.15 K
2. Use the combined gas law (a variation of the Ideal Gas Law): V₁/T₁ = V₂/T₂
3. Substitute values and solve for V₂: (2.50 L)/(293.15 K) = V₂/(308.15 K) => V₂ = 2.64 L

Problem 3 Solution:

1. Convert temperature to Kelvin: 27°C + 273.15 = 300.15 K
2. Rearrange the Ideal Gas Law to solve for P: P = nRT/V
3. Substitute values and solve: P = (2.00 mol)(0.0821 L·atm/mol·K)(300.15 K) / (10.0 L) = 4.93 atm

Problem 4 Solution:

1. Use Boyle's Law (a variation of the Ideal Gas Law at constant temperature): P₁V₁ = P₂V₂
2. Substitute values and solve for V₂: (1.50 atm)(7.50 L) = (1.00 atm)V₂ => V₂ = 11.25 L

Problem 5 Solution:

1. Calculate the total number of moles: 1.00 mol + 0.50 mol + 0.25 mol = 1.75 mol
2. Calculate the mole fraction of each gas: N₂: 1.00 mol / 1.75 mol = 0.57; O₂: 0.50 mol / 1.75 mol = 0.29; Ar: 0.25 mol / 1.75 mol = 0.14
3. Calculate the partial pressure of each gas using the mole fraction: P(N₂) = 0.57 * 2.00 atm = 1.14 atm; P(O₂) = 0.29 * 2.00 atm = 0.58 atm; P(Ar) = 0.14 * 2.00 atm = 0.28 atm

Further Practice and Resources

This worksheet provides a foundational understanding of the Ideal Gas Law. For more advanced practice, consider problems involving gas stoichiometry, gas mixtures, and real gases (which deviate from ideal behavior under certain conditions). You can find numerous additional practice problems and resources online, including interactive simulations and tutorials. Remember consistent practice is key to mastering the Ideal Gas Law!