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Interstellar space can be considered as having 10 atoms of hydrogen per cubic centimeter and an average temperature (far away from stars!) of 2.7 K . Determine (a) the pressure of hydrogen in interstellar space and (b) the average speed of the hydrogen atoms. Compare these answers with values under normal Earth conditions.

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Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

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Chapter
Section
BuyFindarrow_forward

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 19, Problem 19.12E
Textbook Problem
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Interstellar space can be considered as having 10 atoms of hydrogen per cubic centimeter and an average temperature (far away from stars!) of 2.7 K . Determine (a) the pressure of hydrogen in interstellar space and (b) the average speed of the hydrogen atoms. Compare these answers with values under normal Earth conditions.

Interpretation Introduction

(a)

Interpretation:

The pressure of hydrogen in interstellar space is to be calculated.

Concept introduction:

The pressure of a gas is calculated by the formula,

p=2NEavg3V

Where,

N is the number of atoms.

V is the volume.

Eavg is the average energy of the atoms.

Explanation of Solution

The pressure of a gas is calculated by the formula,

p=2NEavg3V … (1)

Where,

N is the number of atoms.

V is the volume.

Eavg is the average energy of the atoms.

The average energy of the atoms is calculated by the formula,

Eavg=3nRT2N … (2)

Where,

n is the number of moles.

R is the universal gas constant.

T is the temperature.

The number of moles is calculated by the formula,

n=numberofatomsinagivenvolumenumberofatomsinonemole

The number of atoms present in 1cm3 is 10.

The number of atoms present in 1mol is 6.02×1023.

Substitute the number of atoms present in 1cm3 and number of atoms present in 1mol in the above formula.

n=106.02×1023=1.66×1023mol

The value of universal gas constant is 8.205×105m3atmK1mol1.

Substitute the value of number of moles, universal gas constant, and temperature in equation (2).

Eavg=3×1

Interpretation Introduction

(b)

Interpretation:

The average speed of hydrogen atoms is to be calculated.

Concept introduction:

A gas is made up of atoms or molecules that move with very high speeds. The kinetic energy of gases is very high. Every molecule or atom present in a gas can have a different energy. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

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Chapter 19 Solutions

Physical Chemistry
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