Ch.6 - Gases

Problem 90a

Chapter 6, Problem 90a

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. a. Which of the two gases exerts the greater partial pressure?

Verified step by step guidance

insert step 1> Understand that partial pressure is the pressure exerted by a single type of gas in a mixture of gases.

insert step 2> Recall Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.

insert step 3> Note that the partial pressure of a gas in a mixture is proportional to its mole fraction in the mixture.

insert step 4> Since the problem states that there are exactly equal amounts (in moles) of nitrogen and xenon, their mole fractions are equal.

insert step 5> Conclude that both gases exert the same partial pressure because they have the same mole fraction in the mixture.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Partial Pressure

Partial pressure is the pressure that a single gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. Understanding this concept is crucial for determining how each gas contributes to the overall pressure in a container.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T) of a gas. This law helps predict the behavior of gases under various conditions. In this scenario, it can be used to compare the behavior of nitrogen and xenon, particularly their pressures at the same temperature and volume.

Molar Mass and Density

Molar mass is the mass of one mole of a substance, and it influences the density of gases. In this case, nitrogen (N2) has a lower molar mass compared to xenon (Xe), which means that at the same temperature and volume, nitrogen will have a higher number of moles per unit volume, leading to a greater partial pressure. Understanding the relationship between molar mass, density, and gas behavior is essential for this question.

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Textbook Question

Chlorine gas reacts with fluorine gas to form chlorine trifluoride. Cl₂(g) + 3 F₂(g) → 2 ClF₃(g) A 2.00-L reaction vessel, initially at 298 K, contains chlorine gas at a partial pressure of 337 mmHg and fluorine gas at a partial pressure of 729 mmHg. Identify the limiting reactant. Determine the theoretical yield of ClF₃ in grams.

Carbon monoxide gas reacts with hydrogen gas to form methanol. CO(g) + 2 H₂(g) → CH₃OH(g) A 1.50-L reaction vessel, initially at 305 K, contains carbon monoxide gas at a partial pressure of 232 mmHg and hydrogen gas at a partial pressure of 397 mmHg. Identify the limiting reactant. Determine the theoretical yield of methanol in grams.

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Textbook Question

Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure. a. Do the atoms in the helium sample have the same average kinetic energy as the atoms in the argon sample?

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Textbook Question

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. c. The molecules of which gas have the greater average kinetic energy?

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Textbook Question

Calculate the root mean square velocity of F₂, Cl₂, and Br₂ at 298 K.

Calculate the kinetic energy of F₂, Cl₂, and Br₂ at 298 K.

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