Chapter 9, Problem 9.107CHP

(c)

Interpretation Introduction

Interpretation:

The gases with respective to average speed has to be ranked.

Concept Introduction:

A gas composed of molecules in a continuous random motion is known as Kinetic theory of gas.

Postulates of Kinetic Theory of Gases

1. 1. All gases composed of some tiny units known as molecules. These tiny units are made up of single or group of atoms depending on the nature of the chemical gas.
2. 2. The molecules stir in arbitrary direction with random speed.
3. 3. These collisions are completely elastic. The molecules go through collisions between themselves and to the sides of the container. The average time spent by a molecule between the collisions and the normal collision time is very small
4. 4. The amount of the molecule is very little compared to the average intermolecular distance. Molecules do not exert any force amongst themselves or to the sides except during collision.
5. 5. The Newton's Law of Motion is followed by the molecules.
6. 6. The density and distribution of different physical parameters are same. The number of gas molecules is so huge that at each point of infinitesimal volume of the container. The above parameters are also independent of direction and time at a steady state.

Average speed:

Average speed is the sum of the objects moving in a certain speed divisible by the time taken by the objects.

(b)

Interpretation Introduction

Interpretation:

The gases with respective to pressure has to be ranked.

Concept Introduction:

A gas composed of molecules in a continuous random motion is known as Kinetic theory of gas.

Postulates of Kinetic Theory of Gases

1. 1. All gases composed of some tiny units known as molecules. These tiny units are made up of single or group of atoms depending on the nature of the chemical gas.
2. 2. The molecules stir in arbitrary direction with random speed.
3. 3. These collisions are completely elastic. The molecules go through collisions between themselves and to the sides of the container. The average time spent by a molecule between the collisions and the normal collision time is very small
4. 4. The amount of the molecule is very little compared to the average intermolecular distance. Molecules do not exert any force amongst themselves or to the sides except during collision.
5. 5. The Newton's Law of Motion is followed by the molecules.
6. 6. The density and distribution of different physical parameters are same .The number of gas molecules is so huge that at each point of infinitesimal volume of the container. The above parameters are also independent of direction and time at a steady state.

Pressure

Pressure or Stress is the force applied perpendicular to the surface of an object per unit area.

SI derived unit of pressure is Pascal (Pa).

The number of moles can be calculated by,

$Numberofmoles=\frac{Massingram}{Molarmass}$

Boyle’s law:

At fixed temperature, the volume of a fixed amount of gas is inversely proportional to the pressure exerted by the gas.

$\begin{array}{l}\text{P}\propto \frac{\text{1}}{\text{V}}\left(\text{n}\text{,}\text{T}\text{will}\text{be}\text{constant}\right)\\ \text{PV}\text{=}\text{constant}\\ {\text{P}}_{\text{1}}{\text{V}}_{\text{1}}\text{=}{\text{P}}_{\text{2}}{\text{V}}_{\text{2}}\end{array}$

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas. Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained. It is referred as ideal gas equation.

$\text{V }\propto \frac{\text{nT}}{\text{P}}$

Where,

$\begin{array}{l}\text{n = moles}\text{of}\text{gas}\\ \text{P = pressure}\\ \text{T = temperature}\\ \text{R = gas }\text{constant}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The gases with respective to collision frequency has to be ranked.

Concept Introduction:

A gas composed of molecules in a continuous random motion is known as Kinetic theory of gas.

Postulates of Kinetic Theory of Gases

1. 1. All gases composed of some tiny units known as molecules. These tiny units are made up of single or group of atoms depending on the nature of the chemical gas.
2. 2. The molecules stir in arbitrary direction with random speed.
3. 3. These collisions are completely elastic. The molecules go through collisions between themselves and to the sides of the container. The average time spent by a molecule between the collisions and the normal collision time is very small
4. 4. The amount of the molecule is very little compared to the average intermolecular distance. Molecules do not exert any force amongst themselves or to the sides except during collision.
5. 5. The Newton's Law of Motion is followed by the molecules.
6. 6. The density and distribution of different physical parameters are same. The number of gas molecules is so huge that at each point of infinitesimal volume of the container. The above parameters are also independent of direction and time at a steady state.

Collision Frequency

In a defined system, the average rate in which two reactants collide and it is used to express the average number of collisions per unit of time

(d)

Interpretation Introduction

Interpretation:

The gases with respective to density has to be ranked.

Concept Introduction:

A gas composed of molecules in a continuous random motion is known as Kinetic theory of gas.

Postulates of Kinetic Theory of Gases

1. 1. All gases composed of some tiny units known as molecules. These tiny units are made up of single or group of atoms depending on the nature of the chemical gas.
2. 2. The molecules stir in arbitrary direction with random speed.
3. 3. These collisions are completely elastic. The molecules go through collisions between themselves and to the sides of the container. The average time spent by a molecule between the collisions and the normal collision time is very small
4. 4. The amount of the molecule is very little compared to the average intermolecular distance. Molecules do not exert any force amongst themselves or to the sides except during collision.
5. 5. The Newton's Law of Motion is followed by the molecules.
6. 6. The density and distribution of different physical parameters are same. The number of gas molecules is so huge that at each point of infinitesimal volume of the container. The above parameters are also independent of direction and time at a steady state.

Density: The amount of substance per unit volume is known as density.

$\begin{array}{l}\text{ ρ = }\frac{\text{M}}{\text{V}}\\ \text{Where,}\\ \text{ρ=density}\\ \text{M=mass}\\ \text{V=Volume}\end{array}$