9th Edition
Steven S. Zumdahl
ISBN: 9781133611097




9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

The noble gas with the largest atmospheric abundance is argon. Using the data in Table 20.22, calculate the mass of argon at 25°C and 1.0 atm in a room 10.0 m × 10.0 m × 10.0 m. How many Ar atoms are in this room? How many Ar atoms do you inhale in one breath (approximately 2 L) of air at 25°C and 1.0 atm? Argon gas is inert, so it poses no serious health risks. However, if significant amounts of radon arc inhaled into the lungs, lung cancer is a possible result. Explain the health risk differences between argon gas and radon gas.

Interpretation Introduction


The temperature, pressure and dimension of a room is given. The mass and number of argon atoms in the room is to be calculated. Also, the number of argon atoms inhaled in one breath is to be calculated. The difference in the health risk between argon gas and radon gas is to be explained.

Concept introduction:

The expression to calculate the number of moles of an atom is,





Dimension of room is 10.0m×10.0m×10.0m .

Temperature is 25°C .

Pressure is 1.0atm .

Refer to Table 19-22 .

Atmospheric abundance of argon is 9.0×101 .

Volume of room is equal to the dimension. The volume of room is,


The conversion of cubic meter (m3) into liter (L) is done as,


Hence, the conversion of 1.0×103m3 into liter is,


Volume of argon in the room is 1.0×106L . But, the percentage of atmospheric abundance of argon is 9.0×101 .

Hence, the overall volume of argon is,


The conversion of degree Celsius (°C) into Kelvin (K) is done as,


Hence, the conversion of 25°C into Kelvin is,



Number of moles of argon is calculated using the formula,



  • P is the total pressure.
  • V is the volume.
  • n is the total moles.
  • R is the universal gas constant (0.08206Latm/Kmol) .
  • T is the absolute temperature.

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


The number of moles of argon is 368mol .

The atomic mass of argon is 39.95g/mol .


The mass of argon is calculated using the formula,

m = nM


  • m is the mass of argon.
  • M is the atomic mass of argon.
  • n is the number of moles of argon.

Substitute the values of M and n in the above equation.

m = nM=386mol×39

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