Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 26

Describe 1 mole of \(\mathrm{CO}_{2}\) in as many ways as you can.

Short Answer

Expert verified
1 mole of \(\mathrm{CO}_{2}\) contains \(6.022\times10^{23}\) molecules, has a molecular composition of \(6.022\times10^{23}\) carbon atoms and \(2\times(6.022\times10^{23})\) oxygen atoms, and has a mass of 44 grams. At STP, it occupies a volume of 22.4 liters with a density of approximately \(1.964\) g/L. Its standard enthalpy of formation is \( -393.5 \) kJ/mol, and it participates in various chemical reactions, such as photosynthesis, where it reacts with water to form glucose and oxygen gas.

Step by step solution

01

1. Define a mole in terms of particles

A mole is the unit of measurement in chemistry that represents \(6.022\times10^{23}\) particles of a substance. In this case, 1 mole of \(\mathrm{CO}_{2}\) contains \(6.022\times10^{23}\) molecules of carbon dioxide.
02

2. Molecular composition

Each molecule of carbon dioxide (\( \mathrm{CO}_{2} \)) is composed of one carbon atom (C) and two oxygen atoms (O). So, in 1 mole of \(\mathrm{CO}_{2}\), there are \( 6.022\times10^{23} \) carbon atoms and \( 2\times(6.022\times10^{23}) \) oxygen atoms.
03

3. Molar mass

The molar mass of \(\mathrm{CO}_{2}\) can be calculated using the atomic masses of carbon and oxygen. The atomic mass of carbon is approximately 12 grams per mole, and the atomic mass of oxygen is approximately 16 grams per mole. Thus, the molar mass of \(\mathrm{CO}_{2}\) is \(12 + 2\times16=44 \) grams per mole. So, 1 mole of \(\mathrm{CO}_{2}\) has a mass of 44 grams.
04

4. Volume at STP

At standard temperature and pressure (STP), which is defined as 0°C (273.15 K) and 1 atmosphere (atm) pressure, the volume of 1 mole of any ideal gas is equal to 22.4 liters. Therefore, at STP, 1 mole of \(\mathrm{CO}_{2}\) occupies a volume of 22.4 liters.
05

5. Density at STP

The density of a substance can be calculated using the formula: density = mass/volume. At STP, the mass of 1 mole of \(\mathrm{CO}_{2}\) is 44 grams and the volume is 22.4 liters. Therefore, the density of 1 mole of \(\mathrm{CO}_{2}\) at STP is \( \frac{44 \text{g}}{22.4 \text{L}} \approx 1.964 \) g/L.
06

6. Partial pressure

The partial pressure of \(\mathrm{CO}_{2}\) in a gas mixture can be determined using Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of all the individual gases. If we know the total pressure and the mole fraction (concentration) of \(\mathrm{CO}_{2}\) in the mixture, we can calculate its partial pressure.
07

7. Energy content

The energy content of \(\mathrm{CO}_{2}\) can be described in terms of its enthalpy of formation, which is the heat released or absorbed when 1 mole of a compound is formed from its constituent elements under standard conditions. The standard enthalpy of formation of \(\mathrm{CO}_{2}\) is \( -393.5 \) kJ/mol, meaning that 393.5 kJ of heat is released when 1 mole of \(\mathrm{CO}_{2}\) is formed from its elements.
08

8. Chemical reactions involving \(\mathrm{CO}_{2}\)

One mole of \(\mathrm{CO}_{2}\) can also be described in terms of the chemical reactions it participates in. For example, during photosynthesis, 1 mole of \(\mathrm{CO}_{2}\) reacts with 1 mole of water (H₂O) to produce 1 mole of glucose (C₆H₁₂O₆) and 6 moles of oxygen (O₂) gas. In this case, the balanced chemical equation for photosynthesis is: \( \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} + \mathrm{O}_{2} \).

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

DDT, an insecticide harmful to fish, birds, and humans, is produced by the following reaction: $$2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}+\mathrm{C}_{2} \mathrm{HOCl}_{3} \longrightarrow \mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}+\mathrm{H}_{2} \mathrm{O}$$ In a government lab, 1142 g of chlorobenzene is reacted with 485 g of chloral. a. What mass of DDT is formed, assuming \(100 \%\) yield? b. Which reactant is limiting? Which is in excess? c. What mass of the excess reactant is left over? d. If the actual yield of DDT is \(200.0 \mathrm{g},\) what is the percent yield?

A 2.25-g sample of scandium metal is reacted with excess hydrochloric acid to produce 0.1502 g hydrogen gas. What is the formula of the scandium chloride produced in the reaction?

A compound contains \(47.08 \%\) carbon, \(6.59 \%\) hydrogen, and \(46.33 \%\) chlorine by mass; the molar mass of the compound is 153 g/mol. What are the empirical and molecular formulas of the compound?

An ionic compound \(\mathrm{MX}_{3}\) is prepared according to the following unbalanced chemical equation. $$\mathbf{M}+\mathbf{X}_{2} \longrightarrow \mathbf{M X}_{3}$$ A \(0.105-\mathrm{g}\) sample of \(\mathrm{X}_{2}\) contains \(8.92 \times 10^{20}\) molecules. The compound \(\mathrm{MX}_{3}\) consists of \(54.47 \%\) X by mass. What are the identities of \(\mathrm{M}\) and \(\mathrm{X}\), and what is the correct name for \(\mathrm{MX}_{3} ?\) Starting with 1.00 g each of \(M\) and \(X_{2}\), what mass of \(M X_{3}\) can be prepared?

The reusable booster rockets of the U.S. space shuttle employ a mixture of aluminum and ammonium perchlorate for fuel. A possible equation for this reaction is $$\begin{aligned}3 \mathrm{Al}(s)+3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s) & \longrightarrow \\ \mathrm{Al}_{2} \mathrm{O}_{3}(s)+& \mathrm{AlCl}_{3}(s)+3 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\end{aligned}$$ What mass of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\) should be used in the fuel mixture for every kilogram of Al?
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Nuclear 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