Dalton's Law Of Partial Pressure Worksheet With Answers

Dalton's Law of Partial Pressure Worksheet: A Comprehensive Guide with Answers

Dalton's Law of Partial Pressure is a fundamental concept in chemistry, particularly crucial in understanding gas behavior in mixtures. This worksheet will guide you through various problems, providing detailed solutions and explanations to solidify your understanding. We'll cover a range of scenarios, from simple calculations to more complex applications involving mole fractions and real-world examples. By the end, you'll be confident in applying Dalton's Law to solve diverse problems.

Understanding Dalton's Law: A Quick Recap

Before diving into the worksheet, let's briefly revisit Dalton's Law itself. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases. In simpler terms, each gas in a mixture contributes to the overall pressure independently, as if it were the only gas present in the container.

This is mathematically expressed as:

P_total = P₁ + P₂ + P₃ + ... + P_n

Where:

• P_total is the total pressure of the gas mixture.
• P₁, P₂, P₃, ... P_n are the partial pressures of individual gases (1, 2, 3... n) in the mixture.

Key Concepts and Formulas

To effectively solve problems related to Dalton's Law, we need to understand a few key concepts and formulas:

1. Partial Pressure:

The partial pressure of a gas is the pressure that the gas would exert if it occupied the entire volume alone at the same temperature. It's a measure of the gas's contribution to the total pressure.

2. Mole Fraction:

The mole fraction (χ) of a gas in a mixture is the ratio of the number of moles of that gas to the total number of moles of all gases in the mixture.

χ_i = n_i / n_total

Where:

• χ_i is the mole fraction of gas i.
• n_i is the number of moles of gas i.
• n_total is the total number of moles of all gases in the mixture.

3. Relationship between Partial Pressure and Mole Fraction:

The partial pressure of a gas is directly proportional to its mole fraction in the mixture. This is expressed as:

P_i = χ_i * P_total

This formula is incredibly useful for calculating partial pressures when the total pressure and mole fractions are known.

Dalton's Law of Partial Pressure Worksheet: Problems and Solutions

Now, let's tackle some problems. Remember to show your work clearly, including units throughout your calculations.

Problem 1: A container holds a mixture of oxygen (O2) and nitrogen (N2) gases. The partial pressure of oxygen is 150 mmHg, and the partial pressure of nitrogen is 350 mmHg. Calculate the total pressure of the gas mixture.

Solution:

According to Dalton's Law:

P_total = P_O2 + P_N2 = 150 mmHg + 350 mmHg = 500 mmHg

Therefore, the total pressure of the gas mixture is 500 mmHg.

Problem 2: A gas mixture contains 0.5 moles of helium (He) and 1.5 moles of argon (Ar) in a 10-liter container at 25°C. Calculate the partial pressure of each gas and the total pressure of the mixture. (Assume ideal gas behavior; R = 0.0821 L·atm/mol·K).

Solution:

First, calculate the total number of moles:

n_total = n_He + n_Ar = 0.5 mol + 1.5 mol = 2.0 mol

Now, use the ideal gas law (PV = nRT) to find the total pressure:

P_total = (n_total * R * T) / V = (2.0 mol * 0.0821 L·atm/mol·K * 298 K) / 10 L ≈ 4.89 atm

Next, calculate the mole fractions:

χ_He = n_He / n_total = 0.5 mol / 2.0 mol = 0.25

χ_Ar = n_Ar / n_total = 1.5 mol / 2.0 mol = 0.75

Finally, calculate the partial pressures:

P_He = χ_He * P_total = 0.25 * 4.89 atm ≈ 1.22 atm

P_Ar = χ_Ar * P_total = 0.75 * 4.89 atm ≈ 3.67 atm

Therefore, the partial pressure of helium is approximately 1.22 atm, the partial pressure of argon is approximately 3.67 atm, and the total pressure is approximately 4.89 atm.

Problem 3: A mixture of gases contains 20% oxygen, 70% nitrogen, and 10% carbon dioxide by volume. If the total pressure is 760 mmHg, calculate the partial pressure of each gas.

Solution:

Since the percentages are given by volume, they are also the mole fractions (Avogadro's Law).

χ_O2 = 0.20

χ_N2 = 0.70

χ_CO2 = 0.10

Now, calculate the partial pressures:

P_O2 = χ_O2 * P_total = 0.20 * 760 mmHg = 152 mmHg

P_N2 = χ_N2 * P_total = 0.70 * 760 mmHg = 532 mmHg

P_CO2 = χ_CO2 * P_total = 0.10 * 760 mmHg = 76 mmHg

Therefore, the partial pressure of oxygen is 152 mmHg, the partial pressure of nitrogen is 532 mmHg, and the partial pressure of carbon dioxide is 76 mmHg.

Problem 4: A scuba tank contains a mixture of air (approximately 21% oxygen and 79% nitrogen by volume) at a total pressure of 200 atm. What are the partial pressures of oxygen and nitrogen in the tank?

Solution:

Similar to Problem 3, we can use the volume percentages as mole fractions:

χ_O2 = 0.21

χ_N2 = 0.79

Now calculate the partial pressures:

P_O2 = χ_O2 * P_total = 0.21 * 200 atm = 42 atm

P_N2 = χ_N2 * P_total = 0.79 * 200 atm = 158 atm

Therefore, the partial pressure of oxygen is 42 atm, and the partial pressure of nitrogen is 158 atm.

Problem 5 (More Challenging): A 5.00-liter container at 25°C contains 2.00 g of hydrogen gas (H2) and 16.0 g of methane (CH4). Calculate the partial pressure of each gas and the total pressure of the gas mixture.

Solution:

First, calculate the number of moles of each gas using their molar masses (H2 = 2 g/mol, CH4 = 16 g/mol):

n_H2 = (2.00 g) / (2 g/mol) = 1.00 mol

n_CH4 = (16.0 g) / (16 g/mol) = 1.00 mol

n_total = n_H2 + n_CH4 = 1.00 mol + 1.00 mol = 2.00 mol

Now, use the ideal gas law to find the total pressure:

P_total = (n_total * R * T) / V = (2.00 mol * 0.0821 L·atm/mol·K * 298 K) / 5.00 L ≈ 9.78 atm

Next, calculate the mole fractions:

χ_H2 = n_H2 / n_total = 1.00 mol / 2.00 mol = 0.50

χ_CH4 = n_CH4 / n_total = 1.00 mol / 2.00 mol = 0.50

Finally, calculate the partial pressures:

P_H2 = χ_H2 * P_total = 0.50 * 9.78 atm ≈ 4.89 atm

P_CH4 = χ_CH4 * P_total = 0.50 * 9.78 atm ≈ 4.89 atm

Therefore, the partial pressure of hydrogen is approximately 4.89 atm, the partial pressure of methane is approximately 4.89 atm, and the total pressure is approximately 9.78 atm.

Applying Dalton's Law in Real-World Scenarios

Dalton's Law isn't just a theoretical concept; it has numerous real-world applications:

• Scuba Diving: Understanding partial pressures is critical for scuba divers. At increased depths, the partial pressures of gases increase, leading to potential risks like oxygen toxicity or nitrogen narcosis.

• Aviation: The composition and pressure of the air in aircraft cabins are carefully controlled using Dalton's Law to ensure passenger safety and comfort at high altitudes.

• Respiratory Physiology: Dalton's Law plays a crucial role in understanding gas exchange in the lungs. The partial pressures of oxygen and carbon dioxide drive the diffusion of these gases across the alveolar membranes.

• Industrial Processes: Many industrial processes involving gases rely on principles from Dalton's Law for efficient operation and safety.

Conclusion

This comprehensive worksheet has provided a detailed exploration of Dalton's Law of Partial Pressure, equipping you with the knowledge and skills to solve various problems. Remember that understanding the underlying concepts of partial pressure, mole fraction, and their relationship is key to successfully applying Dalton's Law. By practicing these problems and understanding the real-world applications, you can build a strong foundation in this essential area of chemistry. Continue to practice and explore further to master this important concept!