Skip to main content
Pearson+ LogoPearson+ Logo
Ch.10 - Gases
All textbooksBrown 14th EditionCh.10 - GasesProblem 65
Previous problem
Next problem
Chapter 10, Problem 65

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?.

Verified step by step guidance
1
Understand that ppm (parts per million) is a way of expressing very dilute concentrations of substances. In this case, 407 ppm means 407 liters of CO2 per 1,000,000 liters of air.
To find the mole fraction, we need to convert the volume ratio to a mole ratio. Assume ideal gas behavior, where the volume ratio is equivalent to the mole ratio.
The mole fraction (X) is defined as the ratio of the number of moles of the component (CO2) to the total number of moles in the mixture (air).
Since the volume ratio is equivalent to the mole ratio under ideal conditions, the mole fraction of CO2 is simply the volume of CO2 divided by the total volume of the atmosphere.
Calculate the mole fraction using the formula: X_{CO2} = \frac{407}{10^6}.

Verified Solution

Video duration:
1m
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.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. In this case, to find the mole fraction of CO2, you would divide the number of moles of CO2 by the total number of moles of all gases in the atmosphere.
Recommended video:
Guided course
00:36
Mole Fraction Formula

Parts Per Million (ppm)

Parts per million (ppm) is a unit of measurement used to describe the concentration of one substance in a million parts of another. In the context of gases in the atmosphere, 407 ppm of CO2 means that for every million air molecules, 407 are CO2. This measurement helps in understanding trace gas concentrations in the atmosphere.
Recommended video:
Guided course
01:38
Parts per Million (ppm)

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature. This law can be useful for converting between different units of gas concentration and understanding the behavior of gases under various conditions.
Recommended video:
Guided course
01:15
Ideal Gas Law Formula
Previous problem
Next problem
Related Practice
Textbook Question

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?

834
views
Open Question
A mixture containing 0.50 mol H2(g), 1.00 mol O2(g), and 3.50 mol N2(g) is confined in a 25.0-L vessel at 25 °C. Calculate the partial pressure of H2, O2, and N2.
Open Question
A deep-sea diver uses a gas cylinder with a volume of 10.0 L and a content of 51.2 g of O2 and 32.6 g of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is 19 °C.
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 4% Xe in a 1:1 Ne:He mixture at a total pressure of 66.66 kPa. Calculate the number of Ne atoms in the cell and state the assumptions you need to make in your calculation.
864
views
Textbook Question
A piece of dry ice (solid carbon dioxide) with a mass of 20.0 g is placed in a 25.0-L vessel that already contains air at 50.66 kPa and 25 °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 25 °C?
1245
views
Textbook Question
A sample of 5.00 mL of diethylether 1C2H5OC2H5, density = 0.7134 g>mL2 is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are PN2 = 21.08 kPa and PO2 = 76.1 kPa. The temperature is held at 35.0 °C, and the diethylether totally evaporates. (b) Calculate the total pressure in the container.
988
views