   Chapter 20, Problem 95CWP

Chapter
Section
Textbook Problem

# The atmosphere contains 9.0 × 10−6% Xe by volume at 1.0 atm and 25°C.a. Calculate the mass of Xe in a room 7.26 m by 8.80 m by 5.67 m.b. A typical person takes in about 2 L of air during a breath. How many Xe atoms are inhaled in each breath?

(a)

Interpretation Introduction

Interpretation: The percent volume fraction of xenon, atmospheric pressure and temperature and dimensions of the room are given. The mass of the xenon in the room is to be determined. Also the number of xenon atoms inhaled in the given volume of air is to be calculated.

Concept introduction: The ideal gas equation is given as,

Pressure×Volume=Numberofmoles×Gasconstant×Absolutetemperature

One mole of a substance is equivalent to 22.4dm3 .

To determine: The mass of xenon in the room of the given dimension.

Explanation

Given

The percent volume fraction of xenon gas is 9.0×106% .

The atmospheric pressure is 1atm .

The absolute temperature is 25C+273=298K .

The dimension of the room is 7.26m×8.80m×5.67m .

The volume of the room is,

7.26m×8.80m×5.67m=362.24m3=3.622×105dm3

The volume of the xenon is calculated by the formula,

Volumeofxenon=Percentvolumefraction100×Volumeoftheroom

Substitute the value of percent volume fraction and the volume of the room in the above formula.

Volumeofxenon=9.0×106%100×3.622×105dm3=0.033dm3

The ideal gas equation is given as,

Pressure×Volume=Numberofmoles×Gasconstant×Absolutetemperature

The value of universal gas constant is 0

(b)

Interpretation Introduction

Interpretation: The percent volume fraction of xenon, atmospheric pressure and temperature and dimensions of the room are given. The mass of the xenon in the room is to be determined. Also the number of xenon atoms inhaled in the given volume of air is to be calculated.

Concept introduction: The ideal gas equation is given as,

Pressure×Volume=Numberofmoles×Gasconstant×Absolutetemperature

One mole of a substance is equivalent to 22.4dm3 .

To determine: The number of xenon atoms inhaled in the 2L volume of air during a breath.

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