Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 65

The atmospheric concentration of \(\mathrm{CO}_{2}\) gas is presently 407 ppm (parts per million, by volume; that is, \(407 \mathrm{~L}\) 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 CO₂ in the atmosphere can be found directly from the given ppm value. Simply convert the ppm value to a fraction and use the same fraction for the mole fraction. Therefore, the mole fraction of CO₂, \(X_{CO₂} = \frac{407}{10^6}\), which simplifies to approximately \(4.07 \times 10^{-4}\).

Step by step solution

01

Convert ppm value to a fraction

In the problem, we are given that 407 L of CO₂ is present in every 10⁶ L of the atmosphere. We can write this concentration as a fraction by placing the volume of CO₂ over the total volume of the atmosphere, which is: \( \frac{407}{10^6} \)
02

Find the number of moles of CO₂ and air

Knowing that the volume of an ideal gas is proportional to the amount of moles, we can convert the volume fraction to moles fraction. Since the ratio of both moles will be the same as the ratio of volumes, then the mole fraction of CO₂ can be found directly from the volume fraction: \( \frac{n_{CO₂}}{n_{Total}} = \frac{407}{10^6} \)
03

Find the mole fraction of CO₂

To find the mole fraction of CO₂, we simply use the same fraction as calculated in step 2: Mole fraction of CO₂, \(X_{CO₂} = \frac{n_{CO₂}}{n_{Total}} = \frac{407}{10^6}\)
04

Simplify the mole fraction

We have found the mole fraction of CO₂. Now let's simplify the fraction: \(X_{CO₂} = \frac{407}{10^6}\) The mole fraction of CO₂ in the atmosphere is approximately \(4.07 \times 10^{-4}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Carbon dioxide, which is recognized as the major contributor to global warming as a "greenhouse gas," is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of \(\mathrm{CO}_{2}\) added to the atmosphere is to store it as a compressed gas in underground formations. Consider a 1000-megawatt coal-fired power plant that produces about \(6 \times 10^{6}\) tons of \(\mathrm{CO}_{2}\) per year. (a) Assuming ideal-gas behavior, $101.3 \mathrm{kPa}\(, and \)27^{\circ} \mathrm{C}$, calculate the volume of \(\mathrm{CO}_{2}\) produced by this power plant. (b) If the \(\mathrm{CO}_{2}\) is stored underground as a liquid at \(10^{\circ} \mathrm{C}\) and $12.16 \mathrm{MPa}\( and a density of \)1.2 \mathrm{~g} / \mathrm{cm}^{3},$ what volume does it possess? (c) If it is stored underground as a gas at \(30^{\circ} \mathrm{C}\) and \(7.09 \mathrm{MPa}\), what volume does it occupy?

A \(4.00-\mathrm{g}\) sample of a mixture of \(\mathrm{CaO}\) and \(\mathrm{BaO}\) is placed in a 1.00-L vessel containing \(\mathrm{CO}_{2}\) gas at a pressure of \(97.33 \mathrm{kPa}\) and a temperature of \(25^{\circ} \mathrm{C}\). The \(\mathrm{CO}_{2}\) reacts with the \(\mathrm{CaO}\) and \(\mathrm{BaO},\) forming \(\mathrm{CaCO}_{3}\) and \(\mathrm{BaCO}_{3}\). When the reaction is complete, the pressure of the remaining \(\mathrm{CO}_{2}\) is \(20.0 \mathrm{kPa}\). (a) Calculate the number of moles of \(\mathrm{CO}_{2}\) that have reacted. (b) Calculate the mass percentage of \(\mathrm{CaO}\) in the mixture.

Suppose you are given two 2 -L flasks and told that one contains a gas of molar mass 28 , the other a gas of molar mass 56 , both at the same temperature and pressure. The mass of gas in the flask \(A\) is $1.0 \mathrm{~g}\( and the mass of gas in the flask \)\mathrm{B}\( is \)2.0 \mathrm{~g}$. Which flask contains the gas of molar mass 28 , and which contains the gas of molar mass 56 ?

Consider a mixture of two gases, \(\mathrm{A}\) and \(\mathrm{B}\), confined in a closed vessel. A quantity of a third gas, \(\mathrm{C}\), is added to the same vessel at the same temperature. How does the addition of gas \(\mathrm{C}\) affect the following: (a) the partial pressure of gas \(A,(\mathbf{b})\) the total pressure in the vessel, (c) the mole fraction of gas B?

Consider the combustion reaction between \(1.00 \mathrm{~L}\) of liquid methanol (density \(=0.850 \mathrm{~g} / \mathrm{mL}\) ) and \(500 \mathrm{~L}\) of oxygen gas measured at STP. The products of the reaction are \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) Calculate the volume of liquid \(\mathrm{H}_{2} \mathrm{O}\) formed if the reaction goes to completion and you condense the water vapor.
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free