   # Using the kinetic molecular theory (see Section 8.6), calculate the root mean square velocity and the average kinetic energy of H 1 2 nuclei at a temperature of 4 × 10 7 K. (See Exercise 50 for the appropriate mass values.) ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 69AE
Textbook Problem
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## Using the kinetic molecular theory (see Section 8.6), calculate the root mean square velocity and the average kinetic energy of H 1 2 nuclei at a temperature of 4 × 107 K. (See Exercise 50 for the appropriate mass values.)

Interpretation Introduction

Interpretation: The root mean square velocity and the average kinetic energy of 12H at given temperature are to be calculated.

Concept introduction: Root mean square velocity is used to calculate the average velocity of gas particles.

The average kinetic energy of gases depends only on the temperature. It increases with the increase in temperature.

To determine: The root mean square velocity and the average kinetic energy of 12H at given temperature.

### Explanation of Solution

Explanation

Given

The temperature is 4×107K .

The atomic mass of 12H is 2.01410amu .

The conversion of amu into kg is done as,

1amu=1.66×1027kg

Therefore, the conversion of 2.01410amu into kg is,

2.01410amu=2.01410×1.66×1027kg=3.3434×1027kg

The mass of one mole of 12H is calculated by the formula,

M=NAm

Where,

• M is the molar mass.
• NA is the Avogadro’s number (6.022×1023permole) .
• m is the atomic mass.

Substitute the values of NA and m in the above equation.

M=6.022×1023×3.3434×1027=20.13×104kg/mole_

Explanation

The root mean square velocity is calculated by the formula,

urms=3RTM

Where,

• urms is the root mean square velocity.
• R is the universal gas constant (8.314J/mol×K) .
• M is the molar mass.
• T is the temperature.

Substitute the values of R , M and T in the above equation.

urms=3RTM=3×8

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