   Chapter 20, Problem 70E

Chapter
Section
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

Interpretation:

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,

PV=nRTn=PVRT

Explanation

Explanation

Given

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,

10.0m×10.0m×10.0m=1.0×103m3

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

1m3=103L

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

1.0×103m3=(1.0×103×103)L=1.0×106L

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,

1.0×106L(9.0×101100)=9.0×103L

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

T(K)=T(°C)+273

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

T(K)=T(°C)+273T(K)=(25+273)K=298K

Formula

Number of moles of argon is calculated using the formula,

PV=nRTn=PVRT

Where,

• 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.

n=PVRT=9.0×103L(1.0atm)(0.08206Latm/Kmol)(298K)=368mol_

The number of moles of argon is 368mol .

The atomic mass of argon is 39.95g/mol .

Formula

The mass of argon is calculated using the formula,

m = nM

Where,

• 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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