Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.10 - Gases

Problem 65

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?.

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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}.

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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.

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.

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.

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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?

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Textbook Question

A plasma-screen TV contains thousands of tiny cells filledwith a mixture of Xe, Ne, and He gases that emits light ofspecific wavelengths when a voltage is applied. A particularplasma cell, 0.900 mm * 0.300 mm * 10.0 mm, contains4% 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 andstate the assumptions you need to make in your calculation.

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Textbook Question

A piece of dry ice (solid carbon dioxide) with a mass of 20.0 g isplaced in a 25.0-L vessel that already contains air at 50.66 kPaand 25 °C. After the carbon dioxide has totally sublimed, whatis the partial pressure of the resultant CO2 gas, and the totalpressure in the container at 25 °C?

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Textbook Question

A sample of 5.00 mL of diethylether 1C2H5OC2H5,density = 0.7134 g>mL2 is introduced into a 6.00-L vesselthat already contains a mixture of N2 and O2, whose partialpressures are PN2 = 21.08 kPa and PO2 = 76.1 kPa. The temperatureis held at 35.0 °C, and the diethylether totally evaporates.(b) Calculate the total pressure in the container.

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