Chemistry In Focus
Chemistry In Focus
6th Edition
ISBN: 9781305084476
Author: Tro, Nivaldo J., Neu, Don.
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 56E

Calculate the number of atoms in the universe. The following steps will guide you through this calculation:

a. Planets constitute less than 1% of the total mass of the universe and can, therefore, be neglected. Stars make up most of the visible mass of the universe, so we need to determine how many atoms are in a star. Stars are primarily composed of hydrogen atoms and our Sun is an average-sized star. Calculate the number of hydrogen atoms in our Sun given that the radius of the Sun is 7 × 10 8 m and its density is 1 .4 g/cm 3 . The volume of a sphere is given by

V = ( 4 3 ) × π r 3

(Hint: Use the volume and the density to get the mass of the Sun.)

b. The average galaxy (like our own Milky Way galaxy) contains 1 × 10 11 stars, and the universe contains 1 × 10 9 galaxies. Calculate the number of atoms in an average galaxy and finally the number of atoms in the entire universe.

c. You can hold 1 × 10 23 atoms in your hand (five copper pennies constitute 1 .4 × 10 23 copper atoms.) How does this number compare with the number of atoms in the universe?

Expert Solution & Answer
Check Mark
Interpretation Introduction

Interpretation:

The number of hydrogen atoms in the sun and the number of atoms in a random galaxy are to be determined. Also, the number of hydrogen atoms in the universeis to be compared with the number of atoms that can be held in a hand.

Concept Introduction:

Density is the ratio of the mass of a substance to its volume.

Density of element  = Mass of element in solutionVolume of solutions

The volume of a sphere is 43πr3.

Mole is the unit of the amount of a substance. It relates number of particles to the molar mass.

One mole of a substance contains Avogadro’s number (6.022×1023) of particles. The number remains constant regardless of the nature of the substance. One mole of an atom contains 6.022×1023 atoms. One mole of a molecule contains 6.022×1023 molecules.

It also relates to the molar mass of a substance in grams. The weight of one mole of a substance is equivalent to its molar mass in grams.

It is known that 1m = 100 cm, hence, conversion factor is as:

100 cm1 m

Answer to Problem 56E

Solution: a) 6 × 1056 atoms b) 6 × 1076 atoms c) The number of atoms that can be held in a hand is minuscule compared to the number of hydrogen atoms present in the universe.

Explanation of Solution

a) The number of hydrogen atoms present in the sun.

The radius of the sun is 7×108 m and its density is 1.4 g/cm3.

The number of hydrogen atoms present in the sun is calculated as:

Conversion of the radius of the sun from m to cm is as:

Radius of sun= 7×108 m Radius of sun = 7×108 m × 100 cmm                                   = 7×1010 cm

The volume of a sphere is 43πr3

Substitute the values in the above equation:

Volume of sphere = 43×3.14×(7×1010 cm)3                             = 1×1033 cm3

Thus, the volume of the sphere is  1×1033 cm3.

The mass of hydrogen in sun using the values of density and volume is calculated as:

Density of hydrogen  = Mass of hydrogen in sunVolume of sunMass of hydrogen in sun = Density of hydrogen× Volume of sun

Substitute the values in the above equation:

 Mass=1.4 gcm3× 1× 1033cm3Mass=1 × 1033 g

Therefore, the mass of hydrogen in sun is 1 × 1033 g.

The number of atoms of hydrogen is calculated as follows:

6.022 ×1023 atoms of H = 1 mole of H = 1 g1 g of H contains = 6.022 ×1023 atoms of H1×1033 g of H  contains = 6.022×1023 atoms1g×1×1033g                                         =  6 × 1056 atoms (approx.)

Hence, the number of atoms in hydrogen are 6 × 1056 atoms

b) The number of hydrogen atoms present in one galaxy and in universe.

The average galaxy consists of 1×1011 stars and a universe consists of 1×109 galaxies

The number of hydrogen atoms in one galaxy (Ng) is calculated as follows:

Ng= Number of hydrogen atoms in one star × Number of stars in a galaxyNg= (6 × 1056 atoms)× (1×1011)Ng=× 1067 atoms

Therefore, hydrogen atoms present in one galaxy are × 1067 atoms.

The number of hydrogen atoms in the universe (Nu) is calculated as follows: Nu= Number of hydrogen atoms in one galaxy × Number of galaxies in universeNu= (6 × 1067 atoms)× (1×109)Nu=6 × 1076 atoms

Thus, the number of hydrogen atoms in universe is 6 × 1076 atoms.

c) Compare 1×1023 number (can hold in hand) with number of atoms in the universe.

The atoms which can be held in a hand are 1×1023.

The number of atoms that can be held in a hand are 1×1023. It is minuscule in comparison to the number of hydrogen atoms present in the universe, which is 6 × 1076 atoms.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Chemistry In Focus

Ch. 3 - Prob. 5SCCh. 3 - Which pair of elements do you expect to be most...Ch. 3 - Which statement is true of the quantum mechanical...Ch. 3 - Why is it important to understand atoms?Ch. 3 - Prob. 2ECh. 3 - What defines an element? How many naturally...Ch. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 7ECh. 3 - Prob. 8ECh. 3 - Prob. 9ECh. 3 - Prob. 10ECh. 3 - Explain the quantum mechanical model for the atom....Ch. 3 - Give two examples of each: a. alkali metal b....Ch. 3 - Which elements exist as diatomic molecules?Ch. 3 - Explain the difference and similarity between...Ch. 3 - Prob. 15ECh. 3 - Determine the charge of each of the following: a...Ch. 3 - Determine the number of protons and electrons in...Ch. 3 - Determine the number of protons and electrons in...Ch. 3 - Give the atomic number (Z) and the mass number (A)...Ch. 3 - Prob. 20ECh. 3 - The following isotopes have applications in...Ch. 3 - The following isotopes are important in nuclear...Ch. 3 - 14C is used in carbon dating of artifacts....Ch. 3 - 40K is used to measure the age of Earth. Determine...Ch. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Give electron configurations according to the Bohr...Ch. 3 - Give electron configurations according to the Bohr...Ch. 3 - Prob. 29ECh. 3 - How many valence electrons are in each element of...Ch. 3 - Prob. 31ECh. 3 - Draw electron configurations for each of the...Ch. 3 - Which two of the following elements would you...Ch. 3 - Group the following elements into three similar...Ch. 3 - We have seen that the reactivity of an element is...Ch. 3 - What is the electron configuration of Mg2+? How...Ch. 3 - Classify each of the following elements as a...Ch. 3 - Classify each of the following as a metal, a...Ch. 3 - Calculate the atomic mass of neon (Ne), which is...Ch. 3 - An element has two naturally occurring isotopes....Ch. 3 - A fictitious element has two naturally occurring...Ch. 3 - Copper has two naturally occurring isotopes. Cu-63...Ch. 3 - How many moles of titanium are present in 124 g of...Ch. 3 - Prob. 44ECh. 3 - How many moles are there in each sample? a. 45 mg...Ch. 3 - How many moles are there in each sample? a. 55.0 g...Ch. 3 - What is the mass of each sample? a.1.8 mol S...Ch. 3 - What is the mass of each sample? a.2.75 mol Fe...Ch. 3 - Determine the number of atoms in each sample....Ch. 3 - Determine the number of atoms in each sample....Ch. 3 - How many Ag atoms are present in a piece of pure...Ch. 3 - How many platinum atoms are in a pure platinum...Ch. 3 - A pure gold necklace has a volume of 1.8cm3. How...Ch. 3 - A titanium bicycle component has a volume of...Ch. 3 - An iron sphere has a radius of 3.4 cm. How many...Ch. 3 - Calculate the number of atoms in the universe. The...Ch. 3 - The introduction to this chapter states that...Ch. 3 - Suppose the absolute value of the charge of the...Ch. 3 - When we refer to doughnuts or cookies, we often...Ch. 3 - Prob. 60ECh. 3 - Why does Avogadros number have such an odd value?...Ch. 3 - Prob. 62ECh. 3 - Prob. 63ECh. 3 - Prob. 64ECh. 3 - Here are three fictitious elements and a molecular...Ch. 3 - Prob. 66ECh. 3 - Gather any two of the following items, measure...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry In Focus
Chemistry
ISBN:9781337399692
Author:Tro, Nivaldo J.
Publisher:Cengage Learning,
Text book image
World of Chemistry, 3rd edition
Chemistry
ISBN:9781133109655
Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Publisher:Brooks / Cole / Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry by OpenStax (2015-05-04)
Chemistry
ISBN:9781938168390
Author:Klaus Theopold, Richard H Langley, Paul Flowers, William R. Robinson, Mark Blaser
Publisher:OpenStax
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Introductory Chemistry: A Foundation
Chemistry
ISBN:9781337399425
Author:Steven S. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Atomic Number, Atomic Mass, and the Atomic Structure | How to Pass ChemistryThe Nucleus: Crash Course Chemistry #1; Author: Crash Course;https://www.youtube.com/watch?v=FSyAehMdpyI;License: Standard YouTube License, CC-BY