Mixed Gas Laws Worksheet Answer Key

Understanding the Mixed Gas Laws

The mixed gas laws, comprising of Boyle’s Law, Charles’ Law, Avogadro’s Law, and Gay-Lussac’s Law, are fundamental principles in chemistry that describe the behavior of gases. Mastering these laws is essential for solving problems involving gases. This worksheet will guide you through the mixed gas laws, providing examples and exercises to reinforce your understanding.

Boyle’s Law

Boyle’s Law states that, at constant temperature, the volume of a gas is inversely proportional to the pressure.

Mathematical Expression: P1V1 = P2V2

Example: A cylinder contains 2.5 liters of oxygen at a pressure of 1.5 atm. If the pressure is increased to 3.0 atm, what is the new volume of the oxygen?

Solution:

P1 = 1.5 atm V1 = 2.5 L P2 = 3.0 atm V2 =?

P1V1 = P2V2 (1.5 atm)(2.5 L) = (3.0 atm)V2 V2 = (1.5 atm)(2.5 L) / (3.0 atm) V2 = 1.25 L

Charles’ Law

Charles’ Law states that, at constant pressure, the volume of a gas is directly proportional to the temperature in Kelvin.

Mathematical Expression: V1/T1 = V2/T2

Example: A balloon contains 3.0 liters of helium at a temperature of 25°C. If the temperature is increased to 50°C, what is the new volume of the helium?

Solution:

V1 = 3.0 L T1 = 25°C + 273 = 298 K V2 =? T2 = 50°C + 273 = 323 K

V1/T1 = V2/T2 (3.0 L)/(298 K) = V2/(323 K) V2 = (3.0 L)(323 K) / (298 K) V2 = 3.25 L

Avogadro’s Law

Avogadro’s Law states that, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas.

Mathematical Expression: V1/n1 = V2/n2

Example: A tank contains 2.0 moles of nitrogen at a volume of 10.0 liters. If 3.0 moles of nitrogen are added, what is the new volume of the nitrogen?

Solution:

n1 = 2.0 mol V1 = 10.0 L n2 = 3.0 mol V2 =?

V1/n1 = V2/n2 (10.0 L)/(2.0 mol) = V2/(3.0 mol) V2 = (10.0 L)(3.0 mol) / (2.0 mol) V2 = 15.0 L

Gay-Lussac’s Law

Gay-Lussac’s Law states that, at constant volume, the pressure of a gas is directly proportional to the temperature in Kelvin.

Mathematical Expression: P1/T1 = P2/T2

Example: A container holds 1.5 liters of carbon dioxide at a pressure of 2.5 atm and a temperature of 30°C. If the temperature is increased to 40°C, what is the new pressure of the carbon dioxide?

Solution:

P1 = 2.5 atm T1 = 30°C + 273 = 303 K P2 =? T2 = 40°C + 273 = 313 K

P1/T1 = P2/T2 (2.5 atm)/(303 K) = P2/(313 K) P2 = (2.5 atm)(313 K) / (303 K) P2 = 2.58 atm

Mixed Gas Laws Worksheet

Complete the following exercises using the mixed gas laws:

1. A cylinder contains 3.5 liters of oxygen at a pressure of 2.2 atm and a temperature of 25°C. If the temperature is increased to 35°C and the pressure is decreased to 1.8 atm, what is the new volume of the oxygen?

2. A tank holds 2.0 moles of nitrogen at a volume of 15.0 liters and a temperature of 30°C. If 1.5 moles of nitrogen are added and the temperature is increased to 40°C, what is the new volume of the nitrogen?

3. A balloon contains 2.5 liters of helium at a pressure of 1.2 atm and a temperature of 20°C. If the temperature is increased to 30°C and the pressure is increased to 1.5 atm, what is the new volume of the helium?

Answer Key:

1. V2 = 4.13 L
2. V2 = 23.1 L
3. V2 = 3.08 L

Notes:

• Always convert temperatures to Kelvin when using the mixed gas laws.
• Use the correct mathematical expression for each gas law.
• Pay attention to the units and ensure they are consistent throughout the problem.

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