EBK PHYSICAL CHEMISTRY
EBK PHYSICAL CHEMISTRY
2nd Edition
ISBN: 8220100477560
Author: Ball
Publisher: Cengage Learning US
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Chapter 19, Problem 19.15E
Interpretation Introduction

Interpretation:

The temperature required to have an rms-average speed of 200,400,600,800 and 1000m/s for Cs atoms is to be calculated. The pattern of the calculated temperatures is to be predicted.

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 different energies. Therefore, root mean square speed, most probable velocity, and mean velocity are calculated for a gas.

Expert Solution & Answer
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Answer to Problem 19.15E

The temperature required to have an rms-average speed of 200,400,600,800 and 1000m/s is 213.15K, 852.61K, 1918.36K, 3410.42K and 5328.79K, respectively. The rate of increase in temperature is exponential to the rate of increase in root-mean-square speed of Cs atoms.

Explanation of Solution

The root-mean-square speed is calculated by the formula,

vrms=3RTM…(1)

Where,

R is the universal gas constant.

T is the temperature.

M is the molecular mass of a sample.

The molecular mass of Cs is 0.1329kg/mol.

The value of universal gas constant is 8.314J/molK.

The value of vrms is 200m/s.

Substitute the value of universal gas constant, molecular mass and vrms in equation (1).

200m/s=3×8.314J/molK×T0.1329kg/mol(200m/s)2=24.94J/molK×T0.1329kg/mol40000m2/s2×0.1329kg/mol=24.94J/molK×TT=213.15K

The value of vrms is 400m/s.

Substitute the value of universal gas constant, molecular mass and vrms in equation (1).

400m/s=3×8.314J/molK×T0.1329kg/mol(400m/s)2=24.94J/molK×T0.1329kg/mol160000m2/s2×0.1329kg/mol=24.94J/molK×TT=852.61K

The value of vrms is 600m/s.

Substitute the value of universal gas constant, molecular mass and vrms in equation (1).

600m/s=3×8.314J/molK×T0.1329kg/mol(600m/s)2=24.94J/molK×T0.1329kg/mol360000m2/s2×0.1329kg/mol=24.94J/molK×TT=1918.36K

The value of vrms is 800m/s.

Substitute the value of universal gas constant, molecular mass and vrms in equation (1).

800m/s=3×8.314J/molK×T0.1329kg/mol(800m/s)2=24.94J/molK×T0.1329kg/mol640000m2/s2×0.1329kg/mol=24.94J/molK×TT=3410.42K

The value of vrms is 1000m/s.

Substitute the value of universal gas constant, molecular mass and vrms in equation (1).

1000m/s=3×8.314J/molK×T0.1329kg/mol(1000m/s)2=24.94J/molK×T0.1329kg/mol1000000m2/s2×0.1329kg/mol=24.94J/molK×TT=5328.79K

Therefore, the temperature required to have an rms-average speed of 200,400,600,800 and 1000m/s is 213.15K, 852.61K, 1918.36K, 3410.42K and 5328.79K, respectively.

It is clear that the rate of increase in temperature is exponential to the rate of increase in root-mean-square speed of Cs atoms.

Conclusion

The temperature required to have an rms-average speed of 200,400,600,800 and 1000m/s is 213.15K, 852.61K, 1918.36K, 3410.42K and 5328.79K, respectively. The rate of increase in temperature is exponential to the rate of increase in root-mean-square speed of Cs atoms.

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Chapter 19 Solutions

EBK PHYSICAL CHEMISTRY

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