Medium Dalton’s Law Practice Questions

1. Concept Explanation

Dalton’s Law of Partial Pressures states that the total pressure exerted by a mixture of non-reactive gases is equal to the sum of the partial pressures of the individual gases in the mixture. This fundamental principle of chemistry, first formulated by John Dalton in 1801, allows us to calculate how each component in a gas mixture contributes to the overall pressure. Mathematically, it is expressed as P_total = P₁ + P₂ + P₃ + ... + P_n.

Understanding Dalton's Law is crucial when dealing with real-world scenarios, such as scuba diving, atmospheric science, and laboratory experiments where gases are collected over water. A key extension of this concept involves mole fractions. The partial pressure of a specific gas (P_i) can be determined by multiplying the total pressure by the gas’s mole fraction (X_i), which is the ratio of the number of moles of that gas to the total moles in the mixture. This relationship is represented by the formula P_i = X_i × P_total.

When solving Dalton's Law practice questions, it is often necessary to integrate other gas principles. For instance, you might use the Ideal Gas Law (PV = nRT) to find the number of moles before calculating partial pressures. Additionally, if the volume or temperature changes, applying the Combined Gas Law might be the first step in your calculation process.

2. Solved Examples

Below are worked examples that demonstrate how to apply Dalton's Law in various scenarios.

1. Example 1: Basic Summation
   A container holds oxygen at 0.45 atm, nitrogen at 0.32 atm, and argon at 0.15 atm. What is the total pressure in the container?
   
   1. Identify the partial pressures: P_O2 = 0.45 atm, P_N2 = 0.32 atm, P_Ar = 0.15 atm.
   2. Apply the formula: P_total = P_O2 + P_N2 + P_Ar.
   3. Calculate: P_total = 0.45 + 0.32 + 0.15 = 0.92 atm.
2. Example 2: Mole Fraction and Total Pressure
   A gas mixture contains 2.0 moles of Helium and 3.0 moles of Neon. If the total pressure is 10.0 atm, find the partial pressure of Helium.
   
   1. Calculate total moles: n_total = 2.0 + 3.0 = 5.0 moles.
   2. Calculate the mole fraction of Helium (X_He): X_He = 2.0 / 5.0 = 0.4.
   3. Apply the partial pressure formula: P_He = X_He × P_total.
   4. Calculate: P_He = 0.4 × 10.0 atm = 4.0 atm.
3. Example 3: Collecting Gas Over Water
   Hydrogen gas is collected over water at 25°C. The total pressure is 765 mmHg. If the vapor pressure of water at 25°C is 23.8 mmHg, what is the pressure of the dry hydrogen gas?
   
   1. Identify the components: P_total = P_H2 + P_H2O.
   2. Rearrange to solve for P_H2: P_H2 = P_total - P_H2O.
   3. Calculate: P_H2 = 765 mmHg - 23.8 mmHg = 741.2 mmHg.

3. Practice Questions

Test your knowledge with these Dalton’s Law practice questions. Ensure you pay attention to units and mole-to-pressure conversions.

1. A mixture of 0.50 mol of H₂ and 1.25 mol of He is placed in a 5.0 L container at 298 K. Calculate the partial pressure of each gas and the total pressure.
2. A 10.0 L flask contains 14.0 g of N₂ and 16.0 g of O₂ at 273 K. Determine the total pressure in the flask.
3. The total pressure of a mixture of oxygen, fluorine, and nitrogen is 1200 torr. If the partial pressure of oxygen is 300 torr and the partial pressure of fluorine is 450 torr, what is the mole fraction of nitrogen?

4. A sample of oxygen gas is collected over water at 20°C (vapor pressure = 17.5 mmHg). The total pressure is 758.0 mmHg. What volume would the dry oxygen occupy at STP if the initial volume was 250 mL?
5. A mixture of gases contains 4.46 mol of neon (Ne), 0.74 mol of argon (Ar), and 2.15 mol of xenon (Xe). Calculate the partial pressure of each gas if the total pressure is 2.00 atm.
6. A rigid tank contains 3.0 atm of Gas A and 2.0 atm of Gas B. If 1.0 mole of Gas C is added without changing the temperature, and the total pressure becomes 7.5 atm, how many moles of Gas A were originally present?
7. Calculate the mass of nitrogen gas in a 2.0 L triple-gas mixture (N₂, He, Ne) where the total pressure is 3.0 atm, the partial pressure of He is 0.5 atm, and the partial pressure of Ne is 1.2 atm at 300 K.
8. In a mixture of CO and CO₂, the mole fraction of CO is 0.35. If the total pressure is 800 mmHg, what is the partial pressure of CO₂?

4. Answers & Explanations

1. Answer: P_H2 = 2.45 atm, P_He = 6.11 atm, P_total = 8.56 atm
   First, use PV=nRT for each gas. P_H2 = (0.50 mol * 0.0821 * 298 K) / 5.0 L = 2.45 atm. P_He = (1.25 mol * 0.0821 * 298 K) / 5.0 L = 6.11 atm. Total pressure is the sum: 2.45 + 6.11 = 8.56 atm.
2. Answer: 2.24 atm
   Convert grams to moles: N₂ = 14.0/28.0 = 0.5 mol; O₂ = 16.0/32.0 = 0.5 mol. Total moles = 1.0 mol. Use PV=nRT: P = (1.0 * 0.0821 * 273) / 10.0 = 2.24 atm.
3. Answer: 0.375
   Find P_N2: 1200 - 300 - 450 = 450 torr. Mole fraction X_N2 = P_N2 / P_total = 450 / 1200 = 0.375.
4. Answer: 227 mL
   First, find P of dry oxygen: 758.0 - 17.5 = 740.5 mmHg. Use the Combined Gas Law: (740.5 * 250) / 293 = (760 * V2) / 273. Solving for V2 gives approximately 227 mL.
5. Answer: P_Ne = 1.21 atm, P_Ar = 0.20 atm, P_Xe = 0.59 atm
   Total moles = 4.46 + 0.74 + 2.15 = 7.35. X_Ne = 4.46/7.35 = 0.607; P_Ne = 0.607 * 2.0 = 1.21 atm. Repeat for others: P_Ar = (0.74/7.35)*2 = 0.20 atm; P_Xe = (2.15/7.35)*2 = 0.59 atm.
6. Answer: 1.2 moles
   Initial P_total = 3.0 + 2.0 = 5.0 atm. New P_total is 7.5 atm, so P_C = 2.5 atm. Since P is proportional to n, P_A/P_C = n_A/n_C. 3.0/2.5 = n_A/1.0. n_A = 1.2 moles.
7. Answer: 1.48 g
   P_N2 = 3.0 - 0.5 - 1.2 = 1.3 atm. Use PV=nRT to find moles of N₂: n = (1.3 * 2.0) / (0.0821 * 300) = 0.1056 mol. Mass = 0.1056 * 28.01 g/mol = 2.96 g (Note: calculation check: 1.3*2 / 24.63 = 0.105; 0.105*28 = 2.94g). Corrected Mass = 2.96 g.
8. Answer: 520 mmHg
   If X_CO = 0.35, then X_CO2 = 1 - 0.35 = 0.65. P_CO2 = 0.65 * 800 mmHg = 520 mmHg.

5. Quick Quiz

6. Frequently Asked Questions

What is the main purpose of Dalton's Law?

The main purpose is to determine the individual pressures exerted by specific gases within a mixture or to find the total pressure when individual pressures are known. This is essential for understanding gas behavior in complex environments like the lungs or industrial chemical reactors.

Does Dalton's Law apply to all gases?

Dalton's Law applies strictly to ideal gases that do not react with one another. While it provides a very close approximation for real gases at standard temperatures and pressures, significant deviations occur at extremely high pressures or low temperatures where intermolecular forces become prominent.

How do you find the mole fraction if you only have pressures?

You can find the mole fraction by dividing the partial pressure of a specific gas by the total pressure of the mixture. This relationship (X_i = P_i / P_total) works because, in an ideal gas mixture, the pressure contribution is directly proportional to the number of molecules present.

Why is water vapor pressure subtracted when collecting gas over water?

When gas is collected over water, the space above the liquid contains both the intended gas and evaporated water molecules. To find the pressure exerted solely by the collected gas, you must subtract the known vapor pressure of water at that specific temperature from the total measured pressure.

Can Dalton's Law be used to find the volume of a gas?

Dalton's Law itself only relates to pressures, but it is frequently used in conjunction with the Ideal Gas Law to determine volume. Once you have the partial pressure of a specific gas, you can plug it into V = nRT/P to find the volume that specific component would occupy alone.

What happens to partial pressure if the volume of the container is halved?

According to Boyle's Law, if the volume is halved at constant temperature, the total pressure doubles. Consequently, the partial pressure of each individual gas in the mixture will also double, as their individual concentrations relative to the total volume have increased.

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