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Ch.10 - Gases
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.
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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.
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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

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?

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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 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?

Textbook Question

A sample of 5.00 mL of diethyl ether (C2H5OC2H5,density=0.7134 g/mL) is introduced into a 6.00-L vessel that already contains a mixture of N2 and O2, whose partial pressures are 𝑃N2=0.751atm and 𝑃O2=0.208atm. The temperature is held at 35.0°C, and the diethyl ether totally evaporates. b. Calculate the total pressure in the container.