Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 29

Find the mass (in \(\mathrm{kg}\) ) of one molecule of \(\mathrm{CO}_{2}\)

Short Answer

Expert verified
Answer: The mass of one CO2 molecule is approximately \(7.310 \times 10^{-26} kg\).

Step by step solution

01

Find the molar mass of CO2

To find the molar mass of CO2, we need to know the molar mass of each element and their respective number of atoms in a CO2 molecule. A CO2 molecule is composed of one carbon (C) atom and two oxygen (O) atoms. The molar mass of carbon is 12.01 g/mol, and the molar mass of oxygen is 16.00 g/mol. To find the molar mass of CO2, multiply the molar mass of each element by the number of its atoms in the molecule and then add the results: Molar mass of CO2 = (1 × 12.01 g/mol) + (2 × 16.00 g/mol) = 12.01 g/mol + 32.00 g/mol = 44.01 g/mol.
02

Convert g/mol to kg/mol

Since we need to find the mass in kg, we first need to convert the molar mass from grams to kilograms. We know that 1 kg = 1000 g, so divide the molar mass by 1000: Molar mass of CO2 = 44.01 g/mol ÷ 1000 = 0.04401 kg/mol.
03

Use Avogadro's number to find the mass of one molecule

Now, we'll use Avogadro's number (6.022 × 10^{23} ) to find the mass of a single CO2 molecule. Since there are 6.022 × 10^{23} molecules in a mole, we can divide the molar mass by Avogadro's number to find the mass of one molecule: Mass of one CO2 molecule = \(\frac{0.04401 kg/mol}{6.022 \times 10^{23} molecules/mol}\).
04

Calculate the mass of one molecule

Now, you can perform the operation to find the mass of a single CO2 molecule: Mass of one CO2 molecule = \(\frac{0.04401 kg/mol}{6.022 \times 10^{23} molecules/mol} \approx 7.310 \times 10^{-26} kg\). So, the mass of one CO2 molecule is approximately \(7.310 \times 10^{-26} kg\).

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

A diver rises quickly to the surface from a 5.0 -m depth. If she did not exhale the gas from her lungs before rising, by what factor would her lungs expand? Assume the temperature to be constant and the pressure in the lungs to match the pressure outside the diver's body. The density of seawater is $1.03 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$
How many hydrogen atoms are present in \(684.6 \mathrm{g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\)
The mass of \(1 \mathrm{mol}\) of \(^{13} \mathrm{C}\) (carbon- 13 ) is $13.003 \mathrm{g}$. (a) What is the mass in \(u\) of one \(^{13} \mathrm{C}\) atom? (b) What is the mass in kilograms of one \(^{13} \mathrm{C}\) atom?
A bubble with a volume of \(1.00 \mathrm{cm}^{3}\) forms at the bottom of a lake that is \(20.0 \mathrm{m}\) deep. The temperature at the bottom of the lake is \(10.0^{\circ} \mathrm{C} .\) The bubble rises to the surface where the water temperature is \(25.0^{\circ} \mathrm{C}\) Assume that the bubble is small enough that its temperature always matches that of its surroundings. What is the volume of the bubble just before it breaks the surface of the water? Ignore surface tension.
Air at room temperature and atmospheric pressure has a mass density of $1.2 \mathrm{kg} / \mathrm{m}^{3} .$ The average molecular mass of air is 29.0 u. How many molecules are in \(1.0 \mathrm{cm}^{3}\) of air?
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Wave Optics

Read Explanation

Quantum Physics

Read Explanation

Rotational Dynamics

Read Explanation

Waves Physics

Read Explanation

Turning Points in Physics

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