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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?

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Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692

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Section
BuyFindarrow_forward

Chemistry In Focus

7th Edition
Tro + 1 other
Publisher: Cengage Learning,
ISBN: 9781337399692
Chapter 3, Problem 56E
Textbook Problem
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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?

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

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

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Chapter 3 Solutions

Chemistry In Focus
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