## Introduction

Gas is the **state of matter** in which molecules are always in random motion. Intermolecular interactions are extremely small (almost negligible) as compared to other states like solid and liquid. Gases are highly compressible state of matter and its state of diffusion is maximum. Gases have their own importance in living world. Air is a gaseous mixture of oxygen, nitrogen, CO_{2}, Ar, etc.

## Intermolecular Forces

**Intermolecular forces** are the forces of attraction and repulsion between interacting particles. This term does not include the electrostatic forces that exist between the two oppositely charged ions.

### Van der Waal's Forces

These are the weak forces of attraction between two molecules with or without any strong bond. These are electrostatic in nature. Types of van der Waal's forces are as follow :

**1. Dipole-dipole interaction** : These forces exist between two molecules which are polar in nature. Opposite charges of two dipoles attract each other and produce interactions called keesom forces. In HCl, dipole-dipole interactions exist.

Dipole-dipole interaction energy is inversely proportional to the sixth power of the distance between the rotating polar molecules.

interaction energy `propto\1/r^{6}`

**2. Dipole-induced dipole interaction** : When a polar molecule comes closer to a non-polar molecule it induces weak polarity (dipole) in that molecule. Now, weak interactions develop between polar molecule and molecule in which polarity is induced. These interactions are known as **Debye interactions**.

**3. London dispersion forces** : This polar molecule produces polarity in other molecule. Weak interaction arises between instantaneous dipoles. These interactions are known as **Dispersion forces** or **London forces**.

**Read also:** Thermodynamics Class 11 Notes Chemistry Chapter 6

## Measurable Properties of Gases

**1. Temperature:** Temperature is a relative measure, or indication of hotness or coldness. At absolute zero on Kelvin scale is equivalent to –273.15°C on the Celsius scale. Both the Celsius and the Kelvin scales have units of equal magnitude that is one degree celsius equivalent to one kelvin.

Thus T(K) = T(°C) + 273.15

**2. Pressure of a gas:** According to laws of motion, pressure is defined as force applied per unit area of surface. It is denoted by P and SI unit of it is pascal (Pa). It is a scalar quantity.

`P=\frac{F}{A}`

**Atmospheric Pressure:** The atmospheric pressure at a point is equal to the weight of a column of air of unit cross-sectional area extending from that point to the top of the atmosphere. Its value is 1.013 × 10^{5} Pa at sea level. Atmospheric pressure is measured using an instrument called barometer.

## Gaseous Laws

### (1). Boyle’s Law (Volume-Pressure Relation)

According to this, "The volume of a given mass of gas is inversely proportional to pressure at constant temperature." This law is given by **Robert Boyle**.

`P\propto\frac{1}{V}` .....(at constant T and n)

`P=k\frac{1}{V}`

where k is the proportionality constant.

If a fixed amount of gas at constant temperature T occupying volume V_{1} at pressure P_{1} undergoes expansion, so that volume becomes V_{2} and pressure becomes P_{2}, then according to Boyle’s law :

p_{1}V_{1} = p_{2}V_{2} = constant

`\frac{P_1}{P_2}=\frac{V_2}{V_1}`

**Read also:** Laws of Motion Class 11 Physics Notes Chapter 5

### (2). Charle’s Law (Volume-Temperature Relation)

According to this, "The volume of a given mass of gas is directly proportional to its absolute temperature at constant pressure." This law is given by **Jacques Charles**.

`V\propto T` .....(at constant P)

`V=kT`

where k is the proportionality constant.

If a fixed amount of gas at constant pressure P occupying volume V_{1} at temperature T_{1} undergoes expansion, so that volume becomes V_{2} and temperature becomes T_{2}, then according to Charle’s Law :

`\frac{V}{T}=` .....constant

`\frac{V_2}{V_1}=\frac{T_2}{T_1}`

### (3). Gay Lussac’s Law (Pressure-Temperature Relation)

It states that at constant volume, the pressure of a fixed mass of a gas is directly proportional to the Kelvin temperature. The law may be expressed mathematically as

`P\propto\ T` .....(at constant V)

`P=kT`

where k is the proportionality constant.

If a fixed amount of gas at constant volume V occupying pressure P_{1} at temperature T_{1} undergoes expansion, so that pressure becomes P_{2} and temperature becomes T_{2}, then according to Gay Lussac’s Law :

`\frac{P}{T}=` constant

`\frac{P_1}{T_1}=\frac{P_2}{T_2}`

**Read also:** Conceptual Questions for Class 11 Physics Chapter 5 Laws of Motion

### (3). Avogadro’s Law ((Volume - Amount Relationship)

According to this, “Equal volumes of all gases at same temperature and pressure contain equal numbers of molecules”.

`V\propto n`

`V=kn`

where k is the proportionality constant.

`\frac{V_1}{n_1}=\frac{V_2}{n_2}`

## Ideal Gas Equation

On combining the Boyle’s law, Charles law and Avogadro’s law we get an equation known as ideal gas equation which correlate P, V, T of a gas.

`V\propto\frac{1}{P}` (according to Boyle’s law at constant T)

`V\propto T` (according to Charle’s law at constant P)

`V\propto n` (according to Avogadro’s law at constant P and T)

`V\propto\frac{nT}{P}`

`PV\propto nT`

PV = nRT

Where R is proportionality constant known as universal gas constant.

### Numerical value of R

R = 0.0821 litre atm K^{–1} mol^{–1}

R = 0.0831 litre bar K^{–1} mol^{–1}

R = 8.314 J K^{–1} mol^{–1}

R = 1.987 ≈ 2 cal K^{–1} mol^{–1}

R = 8.314 × 107 erg K^{–1} mol^{–1}

If temperature, volume and pressure of a fixed amount of gas vary from T_{1}, V_{1} and p_{1} to T_{2}, V_{2} and p_{2} then we can write

`\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}`

This equation is also known as Combined gas law.

## Dalton’s Law of Partial Pressure

Dalton’s law of partial pressure and states that “the total pressure exerted by a mixture of non reacting gases is equal to the sum of partial pressure of each gas present in the mixture”.

P_{Total} = p_{1} + p_{2 }+ p_{3} +......(at constant T, V)

## Kinetic Theory of Gases

The postulates of kinetic theory of gases are as follows:

The gaseous molecules are considered to be point masses.

The volume of a molecule is negligible as compared to total volume of the gas.

The molecules neither attract nor repel each other.

The collisions are perfectly elastic i.e. there is no loss of energy during the molecular collisions.

The average kinetic energy of molecules is directly proportional to the absolute temperature of the gas.

The effect of gravity on molecular motion is negligible.

### The Kinetic Gas Equation

`PV=\frac{1}{3}mnu^2`

where P =Pressure of the gas

V = Volume of the gas

m = Mass of one molecule of a gas

n = number of molecules of gas

u = root mean square speed of the molecule

m × n = M = molecular weight of the gas.

`PV=\frac{1}{3}Mu^2`

## Graham’s Law of Diffusion

According to Graham’s Law “at constant pressure and temperature, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its vapour density or molecular mass”.

`r\propto\sqrt{\frac{1}{d}}`

## Behaviour of Real gases

**Ideal gas** : A gas which obeys the gas laws and the gas equation PV = nRT strictly at all temperatures and pressures is said to be an ideal gas. But actually the concept of ideal gas is hypothetical as there is no gas which practically is ideal. So, the non-ideal gases are the real gases which are the actually existing gases which obey gas equation approximately only under two conditions. (i) Low pressure (ii) High temperature.

### Causes of Deviation

There are two hypothetical postulates in the kinetic theory of gases. These are as follows

The volume of a molecule is negligible as compared to total volume of the gas. Actually, gas molecules do possess some volume which account for the deviation.

There is no intermolecular forces of attraction between gaseous molecules.

By correcting these two postulates, we get an equation which can be applied to the gases which deviate from ideal behaviour. This deviation of a gas from ideal behaviour can also be expressed in terms of **compressiblity factor** (Z).

`Z=\frac{PV}{RT}`

### Van der Waal’s Equation

`(P+\frac{an^2}{V^2})(V-nb)=nRT`

Where **a** and **b** are **van der waal's** constant.

## Liquifaction of Gases

Gases can be liquefied by applying high pressure or by cooling.

**Critical Temperature** : It is the temperature above which gas cannot be liquefied, no matter how high be pressure.

`T_c=\frac{8a}{27Rb}`

**Critical Pressure** : It is the minimum pressure that is required to liquefy a gas at critical temperature.

`P_c=\frac{a}{27b^2}`

**Critical Volume** : It is the volume occupied by gas at critical temperature and critical pressure.

`V_c=3b`

### (i). Liquid State

It is the intermediate state between gaseous and solid states. Liquids possess fluidity like gases but incompressibility like solids.

**Properties of liquid are:**

- A liquid is made up of molecules. Only Hg(l) is in atomic state.
- The intermolecular forces of attraction in a liquid are quite large.
- Liquids have no definite shape but have definite volume as the cohesive forces are strong.
- Liquids diffuses slowly in comparison to gas.
- They have definite volume but irregular shapes or we can say that they can take the shape of the container.

### (ii). Evaporation

The process of change of liquid into vapour state at any given temperature is **evaporation**. Evaporation is accompanied by cooling as average kinetic energy of remaining molecules decreases. **Example:** Ether evaporates faster than alcohol.

### (ii). Vapour Pressure

In a closed vessel when the rate of evaporation become equal to rate of condensation, i.e. equilibrium is established, the pressure exerted by the vapours of liquid on its on surface is known as **vapour pressure**.

### (iii). Boiling Point

**Boiling point** of the liquid is the temperature at which the vapour pressure of the liquid is equal to the atmospheric pressure. Ex- Boiling point of pure water is 100 ℃.

### (iv). Surface tension

“It is the force acting on the surface at right angles to any line of unit length”. The property of surface tension may also be described in terms of the tendency of a liquid to decrease its surface area. It's SI unit is N/m.

Surface tension, `S=\frac{F}{l}`

### (v). Viscosity

The property of the liquids which determines their resistance to flow, is called **viscosity**. The forces between the layers which oppose the relative motion between them are known as the forces of viscosity. Thus viscosity may be thought of as the internal function of a fluid in motion.

This force is proportional to the area of contact of layers and **velocity gradient** i.e.

`F\propto\frac{dv}{dz}` ...[\frac{dv}{dz} is called velocity gradient]

`F\propto A`

`F=ηA\frac{dv}{dz}`

η is the coefficient of viscosity. It is expressed in Nm^{–2}s or poise

1 poise = 0.1 Nm^{–2}s

### (vi). Fluidity(Φ)

The reciprocal of the coefficient of viscosity is called **Fluidity**.

`\phi=\frac{1}{η}`

## Summary

**Three different states of matter (solid, liquid and gas)**: Solid is that state of matter which has a definite shape and a definite volume, liquid has a definite volume but no definite shape whereas gas has neither definite shape nor definite volume.**Two more states of matter**:**(i) Plasma state**which consists of a mixture of electrons and positively charged ions formed due to super heating of gases, e.g., in sun or stars.**(ii) Super cooled solid state**in which atoms lose their identity to form a single super atom.**Triple point**: It is the temperature at which all the three states of matter or phases of the same substance exist together, e.g., ice, water and water vapour exist together at 0.01°C (273.16 K) and 4.58 mm pressure.**Ideal and Real gases**: A gas which obeys ideal gas equation under all conditions of temperature and pressure is called an ideal gas. However, the concept of ideal gas is only hypothetical. The gases obey gas laws only if pressure is low or temperature is high. Such gases are called real gases.**Significance of van der Waal’s constants**: ‘a’ is a measure of the magnitude of attractive forces whereas ‘b’ is a measure of the effective size of the gas molecules. b = 4v where v is actual volume of gas molecules. ‘b’ is called**excluded volume**or co-volume.**Boiling point**: It is the temperature at which vapour pressure of the liquid becomes equal to external pressure. When external pressure = 1 atm = 760 mm, it is called normal boiling point.**Surface tension of liquids**: It is the force acting at right angles to the surface along one centimeter length of the surface. Its units are dynes cm^{–1}or Nm^{–1}.**Vapour pressure of a liquid**: It is the pressure exerted by the vapour present in equilibrium with a liquid in a closed vessel at a particular temperature. Cooling is caused by evaporation because more energetic molecules leave the liquid.**Viscosity of liquids**: It is the internal resistance of a liquid to flow or it is the force of friction which one part of the liquid offers to another part of the liquid.**Factors affecting viscosity**:**(i) Nature of the liquid**: Greater the inter-molecular forces, higher is the viscosity.**(ii) Temperature**: Viscosity of a liquid decreases with increase of temperature because kinetic energy increases and hence inter-molecular forces of attraction decrease.**Boyle’s law**: Temperature remaining constant, volume of a given mass of a gas is inversely proportional to its pressure, i.e., `v\propto 1/P` at constant T or PV = constant.**Dalton’s law of partial pressures**: If two or more gases which do not react chemically with each other are enclosed in a vessel, then total pressure exerted by the gaseous mixture is the sum of their partial pressure.**Graham’s law of diffusion/effusion**: Under similar conditions of temperature and pressure, rates of diffusion/effusion of different gases are inversely proportional to the square root of their densities.**Compressibility factor (Z)**: The extent of deviation of a real gas from ideal behaviour is expressed in terms of compressibility factor (Z) viz. `Z= PV/nRT`