Ch.10 - Gases

Problem 62

Previous problem

Next problem

Chapter 10, Problem 62

Consider a mixture of two gases, A and B, confined in a closed vessel. A quantity of a third gas, C, is added to the same vessel at the same temperature. How does the addition of gas C affect the following: (a) the partial pressure of gas A?

Verified step by step guidance

Understand the concept of partial pressure: The partial pressure of a gas in a mixture is the pressure that the gas would exert if it occupied the entire volume of the mixture alone.

Recall Dalton's Law of Partial Pressures: The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.

Consider the initial state: Initially, gases A and B are in the vessel, each contributing to the total pressure with their respective partial pressures.

Analyze the effect of adding gas C: When gas C is added to the vessel, it increases the total pressure of the system because it contributes its own partial pressure.

Determine the effect on the partial pressure of gas A: The partial pressure of gas A remains unchanged because it depends only on the amount of gas A and the volume and temperature of the vessel, which are constant.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

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

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. Each gas in the mixture behaves independently, and its partial pressure is determined by its mole fraction and the total pressure. This principle is crucial for understanding how the addition of gas C influences the partial pressures of gases A and B.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas. This law helps predict how changes in the amount of gas, such as adding gas C, will affect the overall pressure and the partial pressures of the other gases in the system. It assumes ideal behavior, which is a good approximation under many conditions.

Mole Fraction

Mole fraction is the ratio of the number of moles of a particular gas to the total number of moles of all gases in the mixture. It is a key factor in calculating partial pressures, as the partial pressure of a gas is directly proportional to its mole fraction in the mixture. Understanding mole fractions is essential for determining how the addition of gas C alters the distribution of pressures among gases A and B.

Recommended video:

Guided course

00:36

Mole Fraction Formula

Previous problem

Next problem

Related Practice

Textbook Question

Calcium hydride, CaH2, reacts with water to form hydrogen gas:

CaH2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+2 H2(𝑔)

This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating H2 is desired. How many grams of CaH2 are needed to generate 145 L of H2 gas if the pressure of H2 is 825 torr at 21°C?

Textbook Question

Both Jacques Charles and Joseph Louis Guy-Lussac were avid balloonists. In his original flight in 1783, Jacques Charles used a balloon that contained approximately 31,150 L of H2. He generated the H2 using the reaction between iron and hydrochloric acid: Fe1s2 + 2 HCl1aq2 ¡ FeCl21aq2 + H21g2 How many kilograms of iron were needed to produce this volume of H2 if the temperature was 22 °C?

844

views

Textbook Question

Acetylene gas, C2H2(𝑔), can be prepared by the reaction of calcium carbide with water:

CaC2(𝑠)+2 H2O(𝑙)⟶Ca(OH)2(𝑎𝑞)+C2H2(𝑔)

Calculate the volume of C2H2 that is collected over water at 23°C by reaction of 1.524 g of CaC2 if the total pressure of the gas is 753 torr. (The vapor pressure of water is tabulated in Appendix B.)

Textbook Question

The atmospheric concentration of CO2 gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every 106 L of the atmosphere are CO2). What is the mole fraction of CO2 in the atmosphere?.

1949

views

Textbook Question

A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, 0.900 mm×0.300 mm×10.0 mm, contains Xe, Ne, and He atoms in a ratio of 1:12:12, respectively, at a total pressure of 500 torr at 298 K. Calculate the number of Xe, Ne, and He atoms in the cell.

Textbook Question

A piece of dry ice (solid carbon dioxide) with a mass of 5.50 g is placed in a 10.0-L vessel that already contains air at 705 torr and 24°C. After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant CO2 gas, and the total pressure in the container, at 24°C?