Ideal Gas Law Practice Worksheet Answers

Ideal Gas Law Practice Worksheet: Answers and Detailed Explanations

Understanding the Ideal Gas Law is crucial for anyone studying chemistry or physics. This worksheet provides a comprehensive set of problems to test your knowledge and understanding of the Ideal Gas Law (PV = nRT), including calculations involving pressure, volume, temperature, and the number of moles of a gas. This article provides not just the answers, but also detailed explanations for each problem, ensuring you grasp the underlying principles and can confidently tackle similar problems in the future. We'll cover various scenarios, from simple calculations to more complex problems involving gas mixtures and stoichiometry.

Understanding the Ideal Gas Law: PV = nRT

Before diving into the answers, let's briefly review the Ideal Gas Law: PV = nRT. This equation relates the pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas. R is the ideal gas constant, a proportionality constant that depends on the units used for other variables. Common values for R include:

• 0.0821 L·atm/mol·K
• 8.314 J/mol·K
• 62.36 L·torr/mol·K

It's crucial to use consistent units throughout your calculations. If you use the R value in L·atm/mol·K, your pressure should be in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K).

Practice Problems and Detailed Answers

Here are several practice problems with detailed step-by-step solutions. Remember to always identify the known variables and the unknown variable you need to solve for before starting your calculation.

Problem 1: A sample of gas occupies 5.00 L at 25°C and 1.00 atm. What volume will it occupy at 100°C and 2.00 atm?

Answer:

1. Identify knowns and unknowns:

   • V₁ = 5.00 L
   • T₁ = 25°C + 273.15 = 298.15 K (Remember to convert Celsius to Kelvin!)
   • P₁ = 1.00 atm
   • T₂ = 100°C + 273.15 = 373.15 K
   • P₂ = 2.00 atm
   • V₂ = ?

2. Use the combined gas law: Since we're dealing with changes in pressure, volume, and temperature, the combined gas law is most appropriate: (P₁V₁)/T₁ = (P₂V₂)/T₂

3. Solve for V₂: Rearrange the equation to solve for V₂: V₂ = (P₁V₁T₂)/(P₂T₁)

4. Substitute and calculate: V₂ = (1.00 atm * 5.00 L * 373.15 K) / (2.00 atm * 298.15 K) = 3.13 L

Therefore, the gas will occupy 3.13 L at 100°C and 2.00 atm.

Problem 2: How many moles of gas are in a 10.0 L container at 273 K and 1.50 atm?

Answer:

1. Identify knowns and unknowns:

   • V = 10.0 L
   • T = 273 K
   • P = 1.50 atm
   • n = ?
   • R = 0.0821 L·atm/mol·K (We're using this R value because our other units match it)

2. Use the Ideal Gas Law: PV = nRT

3. Solve for n: Rearrange the equation to solve for n: n = PV/RT

4. Substitute and calculate: n = (1.50 atm * 10.0 L) / (0.0821 L·atm/mol·K * 273 K) = 0.668 mol

Therefore, there are 0.668 moles of gas in the container.

Problem 3: A 2.00 L flask contains 0.500 moles of nitrogen gas (N₂) at 25°C. What is the pressure of the gas in atmospheres?

Answer:

1. Identify knowns and unknowns:

   • V = 2.00 L
   • n = 0.500 mol
   • T = 25°C + 273.15 = 298.15 K
   • P = ?
   • R = 0.0821 L·atm/mol·K

2. Use the Ideal Gas Law: PV = nRT

3. Solve for P: Rearrange the equation to solve for P: P = nRT/V

4. Substitute and calculate: P = (0.500 mol * 0.0821 L·atm/mol·K * 298.15 K) / 2.00 L = 6.12 atm

Therefore, the pressure of the nitrogen gas is 6.12 atm.

Problem 4: A mixture of gases contains 0.200 moles of oxygen (O₂) and 0.300 moles of nitrogen (N₂). The total pressure of the mixture is 1.50 atm. What is the partial pressure of oxygen? (Assume ideal gas behavior)

Answer:

1. Understand Partial Pressures: Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of the individual gases.

2. Calculate mole fractions:

   • Mole fraction of O₂ = moles of O₂ / total moles = 0.200 mol / (0.200 mol + 0.300 mol) = 0.400
   • Mole fraction of N₂ = moles of N₂ / total moles = 0.300 mol / (0.200 mol + 0.300 mol) = 0.600

3. Calculate partial pressure of O₂: The partial pressure of a gas is equal to its mole fraction multiplied by the total pressure.

   • Partial pressure of O₂ = mole fraction of O₂ * total pressure = 0.400 * 1.50 atm = 0.600 atm

Therefore, the partial pressure of oxygen is 0.600 atm.

Problem 5: Stoichiometry and the Ideal Gas Law

2.00 grams of magnesium metal reacts completely with excess hydrochloric acid according to the following balanced equation:

Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

The hydrogen gas produced is collected at 25°C and 760 torr. What volume of hydrogen gas is collected?

Answer:

1. Convert grams of Mg to moles: The molar mass of Mg is 24.31 g/mol. Moles of Mg = 2.00 g / 24.31 g/mol = 0.0823 mol

2. Use stoichiometry to find moles of H₂: From the balanced equation, 1 mole of Mg produces 1 mole of H₂. Therefore, 0.0823 moles of Mg will produce 0.0823 moles of H₂.

3. Identify knowns and unknowns:

   • n = 0.0823 mol
   • T = 25°C + 273.15 = 298.15 K
   • P = 760 torr / 760 torr/atm = 1.00 atm (Convert torr to atm)
   • V = ?
   • R = 0.0821 L·atm/mol·K

4. Use the Ideal Gas Law: PV = nRT

5. Solve for V: Rearrange the equation to solve for V: V = nRT/P

6. Substitute and calculate: V = (0.0823 mol * 0.0821 L·atm/mol·K * 298.15 K) / 1.00 atm = 2.01 L

Therefore, 2.01 L of hydrogen gas is collected.

Frequently Asked Questions (FAQ)

Q1: What is an ideal gas?

A1: An ideal gas is a theoretical gas composed of many randomly moving point particles that do not interact except when they collide elastically. Real gases behave ideally only under certain conditions (low pressure and high temperature).

Q2: Why is it important to convert Celsius to Kelvin in gas law calculations?

A2: The Kelvin scale is an absolute temperature scale, meaning it starts at absolute zero (0 K), where all molecular motion ceases. Gas law calculations require absolute temperature because the volume of a gas is directly proportional to its absolute temperature (Charles's Law).

Q3: What happens if I use the wrong value of R?

A3: Using the incorrect value of R will lead to an incorrect answer. Always ensure you use the R value that corresponds to the units of pressure, volume, and temperature you're using in your calculations.

Q4: How do I handle gas mixtures?

A4: For gas mixtures, use Dalton's Law of Partial Pressures. The total pressure is the sum of the partial pressures of each gas. The partial pressure of a gas is proportional to its mole fraction in the mixture.

Q5: What if the gas doesn't behave ideally?

A5: The Ideal Gas Law is an approximation. At high pressures or low temperatures, real gases deviate significantly from ideal behavior due to intermolecular forces and the finite volume of gas molecules. More complex equations, like the van der Waals equation, are necessary to accurately model real gases under these conditions.

Conclusion

The Ideal Gas Law is a fundamental concept in chemistry and physics. By mastering the principles and practicing various problem types, you'll build a solid foundation for understanding gas behavior. Remember to always pay close attention to units and choose the appropriate equation for the problem at hand. Consistent practice and a thorough understanding of the underlying concepts will allow you to confidently solve a wide range of gas law problems. Don't hesitate to review these examples and try additional problems to solidify your understanding. Good luck!