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The atmospheric concentration of \(\mathrm{CO}_{2}\) gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every \(10^{6} \mathrm{~L}\) of the atmosphere are \(\mathrm{CO}_{2}\) ). What is the mole fraction of \(\mathrm{CO}_{2}\) in the atmosphere?

Short Answer

Expert verified
The mole fraction of \(\mathrm{CO}_2\) in the atmosphere is \(4.07 \times 10^{-4}\).

Step by step solution

01

Understand Parts per Million

Parts per million (ppm) is a unit of measurement that denotes the concentration of one part per one million parts of the whole. Here, 407 ppm of \(\mathrm{CO}_{2}\) indicates that in every \(10^6\) liters of the atmosphere, 407 liters are \(\mathrm{CO}_{2}\).
02

Calculate Total Moles of Gas

Assume a sample size of \(10^6\) liters of atmospheric gases. According to the Ideal Gas Law, 22.4 liters of any gas at standard temperature and pressure (STP) is equivalent to 1 mole. Calculate the total moles of atmospheric gases as follows: \[\text{Total moles of gas} = \frac{10^6 \text{ L}}{22.4 \text{ L/mol}}.\]
03

Calculate Moles of \(\mathrm{CO}_2\)

Find the moles of \(\mathrm{CO}_2\) in 407 liters: \[\text{Moles of } \mathrm{CO}_2 = \frac{407 \text{ L}}{22.4 \text{ L/mol}}.\]
04

Determine the Mole Fraction of \(\mathrm{CO}_2\)

The mole fraction is the ratio of moles of \(\mathrm{CO}_2\) to the total moles of atmospheric gases. Calculate it using the formula: \[x_{\mathrm{CO}_2} = \frac{\text{Moles of } \mathrm{CO}_2}{\text{Total moles of gas}}.\]
05

Simplify and Compute

Substitute the values from Steps 2 and 3 into the equation from Step 4 to find the mole fraction: \[x_{\mathrm{CO}_2} = \frac{407/22.4}{10^6/22.4} = \frac{407}{10^6} = 4.07 \times 10^{-4}.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Carbon Dioxide: A Key Component of Our Atmosphere
Carbon dioxide, often abbreviated as COâ‚‚, is a colorless and odorless gas that is vital to life on Earth. It's a natural part of the atmosphere and plays a crucial role in the process of photosynthesis, where plants absorb COâ‚‚ and convert it to oxygen, benefiting all breathing organisms.
Despite its natural presence, human activities such as the burning of fossil fuels, deforestation, and industrial processes have significantly increased its concentration in the atmosphere. This change contributes to global warming and climate change by enhancing the greenhouse effect, which traps heat in the Earth's atmosphere.
Observing and understanding the concentration of COâ‚‚ in the atmosphere is important to evaluate environmental impacts. Its concentration is often measured in parts per million (ppm), reflecting even minute variations accurately.
By keeping track of COâ‚‚ levels, scientists can monitor the progress and impact of climate change, providing valuable data for policy-making and environmental protection strategies.
Understanding Parts Per Million (ppm)
Parts per million, abbreviated as ppm, is a measure of concentration that shows how many parts of a particular substance are in one million parts of a total solution or mixture. It's used across various scientific disciplines to describe very dilute concentrations of chemicals in the atmosphere, water or other media.
For example, when scientists say that the atmospheric concentration of carbon dioxide is 407 ppm, they mean that in every one million parts of the atmosphere, 407 parts are carbon dioxide.
This measurement is particularly useful in atmospheric science, as atmospheric gases are generally present in low concentrations. Using ppm allows scientists and researchers to easily communicate and compare gas concentrations without dealing with very small numbers that can be cumbersome to work with.
If you think about it, ppm is like a magnifying glass for understanding concentrations of substances that aren't apparent just by looking. It isn't about specifying weight or volume, but rather about ratio and proportion, offering a clearer picture of the component make-up of our air.
Atmospheric Concentration and Its Importance
The term atmospheric concentration refers to the amount of a particular substance present in the atmosphere. Concentration can be described in various units, but the mole fraction or parts per million (ppm) are commonly used for gases.
Atmospheric concentration is crucial as it helps to understand the chemical makeup of the atmosphere and the influence of different gases. It affects weather patterns, climate systems, and even human health. Understanding these concentrations is key to addressing issues such as pollution and climate change.
Mole fraction is a way to express atmospheric concentration that is particularly useful in chemical calculations. It represents the ratio of the number of moles of one component to the total number of moles of all components in the atmosphere.
For students and professionals working with atmospheric science, knowing the concentration levels provides insight into how different gases behave and interact under various environmental conditions. It further equips us better to address environmental challenges and promotes sustainability.

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Most popular questions from this chapter

A sample of \(3.00 \mathrm{~g}\) of \(\mathrm{SO}_{2}(g)\) originally in a \(5.00-\mathrm{L}\) vessel at \(21^{\circ} \mathrm{C}\) is transferred to a \(10.0-\mathrm{L}\) vessel at \(26^{\circ} \mathrm{C}\). A sample of \(2.35 \mathrm{~g}\) of \(\mathrm{N}_{2}(g)\) originally in a \(2.50-\mathrm{L}\) vessel at \(20^{\circ} \mathrm{C}\) is transferred to this same \(10.0-\mathrm{L}\) vessel. (a) What is the partial pressure of \(\mathrm{SO}_{2}(g)\) in the larger container? (b) What is the partial pressure of \(\mathrm{N}_{2}(g)\) in this vessel? (c) What is the total pressure in the vessel?

A sample of \(5.00 \mathrm{~mL}\) of diethylether \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5},\right.\) density \(=0.7134 \mathrm{~g} / \mathrm{mL}\) ) is introduced into a 6.00 -L vessel that already contains a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), whose partial pressures are \(P_{\mathrm{N}_{2}}=21.08 \mathrm{kPa}\) and \(P_{\mathrm{O}_{2}}=76.1 \mathrm{kPa}\). The temperature is held at \(35.0^{\circ} \mathrm{C}\), and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container.

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. (a) Convert this pressure to torr. (b) Convert this pressure to atm.

Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, \((\mathbf{b})\) increasing the temperature, (c) increasing the molar mass of the gas.

Propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\), liquefies under modest pressure, allowing a large amount to be stored in a container. (a) Calculate the number of moles of propane gas in a 20 -L container at \(709.3 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C} .\) (b) Calculate the number of moles of liquid propane that can be stored in the same volume if the density of the liquid is \(0.590 \mathrm{~g} / \mathrm{mL}\). (c) Calculate the ratio of the number of moles of liquid to moles of gas. Discuss this ratio in light of the kinetic-molecular theory of gases.

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