Chapter 5, Problem 19DQ

a)

Interpretation Introduction

Interpretation:Average kinetic energies in both containers with 1 mole of xenon gas should be compared.

Concept introduction:In accordance with kinetic molecular theory (KMT), average kinetic energy is dependent on temperature and is function of temperature only. It is represented by ${\left(\text{KE}\right)}_{\text{avg}}$ .

b)

Interpretation Introduction

Interpretation:Force of collision of $\text{Xe}$ atoms with container wallsin both containers should be compared.

Concept introduction:Anything that has mass and accommodates some space is called matter. Three common states of matter are solids, liquids and gases. Gas is state of matter that neither has specific shape and volume. It can take up volume of container in which it is kept. Negligible intermolecular forces arise between molecules of gases.

c)

Interpretation Introduction

Interpretation:Root mean square velocity of $\text{Xe}$ atoms in both containers should be compared.

Concept introduction:Square root of average of square of velocities of different particles is called root mean square velocity. It is denoted by $u_{\text{rms}}$ .

Expression for root mean square velocity is as follows:

  $u_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Where,

• $u_{\text{rms}}$ is root mean square speed.
• $R$ is universal gas constant.
• $T$ is absolute temperature of gas.
• $M$ is molar mass of gas.

d)

Interpretation Introduction

Interpretation:Collision frequency of $\text{Xe}$ atoms with other atoms in both containers should be compared.

Concept introduction:Rate of collisions between different species in particular volume per unit time is called collision frequency.

e)

Interpretation Introduction

Interpretation:Pressure of $\text{Xe}$ atoms in both containers should be compared.

Concept introduction:State of any gas is determined by some of its parameters. These parameters are pressure, amount of gas, temperature and volume. Ideal gas law helps to govern state of gas with help of relationships between these gas parameters.

Expression for ideal gas equation is as follows:

  $PV=nRT$

Where,

• $P$ is pressure of gas.
• $V$ is volume of gas.
• $n$ is amount or moles of gas.
• $R$ is universal gas constant.
• $T$ is absolute temperature of gas.