Chapter 8, Problem 30Q

(a)

Interpretation Introduction

Interpretation:

For the given sample of gases at the same temperature, it should be arranged in the increasing order of pressure, average kinetic energy, density and root mean square velocity.

Concept introduction:

• The container with lowest pressure will be the one that has the fewest moles of gas present in the large volume. The smallest container with the most moles of gas present will have the highest pressure.

To arrange: The given sample of gases in increasing order of pressure

(b)

Interpretation Introduction

Interpretation:

For the given sample of gases at the same temperature, it should be arranged in the increasing order of pressure, average kinetic energy, density and root mean square velocity.

Concept introduction:

• Kinetic molecular theory explains the properties of ideal gas. From the postulates of kinetic molecular theory it is clear that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas.

    Average kinetic energy of gas can be determined as,  $K{E}_{avg}=\left(3/2\right)RT$

To arrange: the given sample of gases in increasing order average kinetic energy.

(c)

Interpretation Introduction

Interpretation:

For the given sample of gases at the same temperature, it should be arranged in the increasing order of pressure, average kinetic energy, density and root mean square velocity.

Concept introduction:

• The root mean square velocity $\mu$ is defined as the measure of velocity of particle in gas. It is the method to determine the single velocity value for particles.

          Root mean square velocity can be determined,

${\mu }_{rms}={\left(\frac{3RT}{M}\right)}^{1/2}$ (1)

$\begin{array}{l}R=\frac{8.314J}{Kmol}\\ M=Molarmassinkg\end{array}$

To arrange: the given sample of gases in increasing order of root mean square velocity

(d)

Interpretation Introduction

Interpretation:

For the given sample of gases at the same temperature, it should be arranged in the increasing order of pressure, average kinetic energy, density and root mean square velocity.

Concept introduction:

• Equation for density is,

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

To arrange: the given sample of gases in increasing order of density

Increasing order of density is 2<1=4=6<3=5=8=<7