
Concept explainers
(a)
Interpretation:
The percentage of atoms having velocity within
Concept introduction:
The probability distribution function of the velocities of the gas molecules in each dimension is given by
The Maxwell-Boltzmann distribution is shown below.
This distribution depends on the mass of the particle and absolute temperature.

Answer to Problem 19.73E
The percentage of atoms having a velocity within
Explanation of Solution
The given temperature is
The molar mass of the helium gas is
The graph of
Figure 1
The formula to calculate the root-mean-square speed is given below.
Where,
•
•
•
Substitute the values the value of the molar mass of helium,
The corresponding value of the percentage of atoms having
Figure 2
Therefore, the percentage of atoms having velocity within
The percentage of atoms having velocity within
(b)
Interpretation:
The percentage of atoms having velocity within
Concept introduction:
The probability distribution function of the velocities of the gas molecules in each dimension is given by
The Maxwell-Boltzmann distribution is given by,
This distribution depends on the mass of the particle and absolute temperature.

Answer to Problem 19.73E
The percentage of atoms having velocity within
Explanation of Solution
The given temperature is
The molar mass of the helium gas is
The graph of
Figure 1
The formula to calculate the most probable speed is given below as,
Where,
•
•
•
Substitute the values the value of the molar mass of helium,
The corresponding value of the percentage of atoms having
Figure 3
Therefore, the percentage of atoms having velocity within
The percentage of atoms having velocity within
(c)
Interpretation:
The percentage of atoms having velocity within
Concept introduction:
The probability distribution function of the velocities of the gas molecules in each dimension is given by
The Maxwell-Boltzmann distribution is given by,
This distribution depends on the mass of the particle and absolute temperature.

Answer to Problem 19.73E
The percentage of atoms having velocity within
Explanation of Solution
The given temperature is
The molar mass of the helium gas is
The graph of
Figure 1
The formula to calculate the mean speed is given below as,
Where,
•
•
•
Substitute the values the value of molar mass of helium,
The corresponding value of percentage of atoms having
Figure 4
Therefore, the percentage of atoms having velocity within
The percentage of atoms having velocity within
The percentage of atoms having velocity within
Therefore, all the percentages have a relative same value.
The percentage of atoms having velocity within
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Chapter 19 Solutions
Physical Chemistry
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