Chapter 5, Problem 5.30P

Interpretation Introduction

Interpretation:

The density of $\text{Xe}$ gas at STP should be calculated.

Concept Introduction:

Ideal gas law equation is shown as:

  $\text{PV= nRT}$

Where,

P = Pressure

V = Volume

n = Number of moles

R = Universal gas constant

T = Temperature

Number of moles is defined as the ratio of mass to the molar mass.

The mathematical expression is given as:

  $\text{Numnber of moles =}\frac{\text{Mass}}{\text{Molar mass}}$

Density is defined as the ratio of mass to the volume.

The mathematical expression is given as:

  $\text{Density = }\frac{\text{Mass}}{\text{Volume}}$

Put the value of number of moles in ideal gas law:

  $\text{PV= }\frac{\text{Mass}}{\text{Molar mass}}\text{RT}$

Rearrange the above formula,

  $\text{P= }\frac{\text{Mass}}{\text{Molar mass}\times \text{V}}\text{RT}$

  $\text{P = }\frac{\text{d}}{\text{Molar mass}}\text{RT}$

Now, rearrange the above expression in terms of density:

  $\text{d = }\frac{\text{Molar mass}\times \text{P}}{\text{RT}}$