# The Gas Law Equations, Properties and Relationship

With the help of Boyle's and Charles' laws, a relationship is established between the volume, temperature, and pressure of a fixed mass of a gas, which is called the gas equation.

Matter: Anything that has mass and occupies some space is called matter, matter exists in four states.

1. Gas: the simplest form of matter.
2. Liquid: Least abundant form of matter.
3. Solid: Most abundant state of matter on earth.
4. Plasma: Most abundant state of matter in-universe.

Note:- Only plasma is not the phase transition state of matter. ## Properties of Gases

(I) Volume:- Gases do not have a specific volume and occupy all the available space.

(II) Shape:- Gases do not have a definite shape and take the shape of a container.

(III) Density:- Gases have a low density as compared is liquids and solids, gases bubble through liquid and kind to rise.

(IV) Diffusion and Effusion:- Gases can diffuse and effuse.

(V) Empty Spaces:- Gases can be compressed by applying pressure due to large empty spaces b/w molecules.

(VI) Expansion:- Gases expand on heating or by increasing available volume.

(VII) Joule Thomson Effect:- When the sudden expansion of a high of low-pressure gas occurs cooling takes place. It is the J.T. effect.

(VIII) Motion:- Molecules of a gas are in a state of constant motion. i.e Transnational, Rotational, and vibration.

(IX) Forces:- Gases have very weak molecules forces or attractions.

(X) Kinetic Energy:- Gases have high kinetic energy and show effective collisions.

Gases effuse due to translational motion.

### Pressures of Gases | Law of Gases

Force per unit area is called pressure. S.I unit of pressure Nm-2 or Pascal. Its unit is the atmosphere (atm.) The pressure of air that can support a 760 mmHg column at 0 gratitude of 45० sea level is called the atmosphere.

1atm = 760 mmHg = 76 cmHg = 101325 pascal = 101.325 KPa = 101325 Nm-2 = 14.7 Psi = 1013.25 millibar = 1.01325 bar.

Note:- Uses Pressure unit

1) Atmosphere (atm) is used for scientific work.

2) Pound inch -2 (Psi) is used for engineering work.

3) 1013.25 millibar is used by metrologies.

4) Nm-² and Pascal are S.I units of Pressure.

#### Color and Odor of Gases

NO2 (Nitrogen Dioxide) is of reddish-brown color, and hydrogen sulfide (H2S) has a rotten egg smell, H2, N2, O2, He are colorless and odorless.

## The Gases Law Definition

The relationship between the volume of a given amount of gas and the prevailing conditions of temperature and pressure are called gas laws. Gas laws describe the uniform behavior of gases. Gases show uniform behavior forwards extend conditions.

### Boyle's law

The volume of a given mass of gas, at constant temperature is inversely proportional to the pressure applied. V∝ 1 / P (T and n are constant)

The value of R is different for a different amounts of some gases. Temperature increases continually K with increases. The product of pressure and volume of a gas at constant temperature is a constant quantity.

P1V1 = P2V2

### Charles's law

The volume of a given mass of a gas is directly proportional to the absolute temperature when the pressure is constant. It is a quantitative relationship b/w the temperature and volume of a gas given by French scientist J. Charles in 1787.

V ∝  T

V = KT   ( Pressure and no. of moles is constant)

K = V / T

The ratio of volume to temperature remains constant for the same amount of gas.

V1 / T1   = V2 / T2

Quantitative Definition:- At constant pressure the volume of a given mass of gas increases or decreases by 1 / 273 of its original volume at 0 for every 1 size or fall in temp.

Vt = V0 ( 1+ t / 273)

Where  Vt = Volume at temp. T

t = Temp. on Celsius scale

V0 = Volume at 0

The equal volumes of all ideal gases at the same temp. and pressure contains equal numbers of moles.

V ∝ ղ

V = Rղ (Temperature and pressure are constant)

V1 / ղ1        =        V2 / ղ2

Ek ∝ T

Tk. E ∝ NT

Absolute temp. is the measure of average translational kinetic energy. T ∝ K.E liquids translational + vibrant  + rat + solids ⟶ Vibrational

## Ideal gas law Definition and Formula

The gas obeys all gas laws under all values of temperature and pressure. Practically no gas exists.

Real Gas:- The gas which obeys all gas laws at a specific value of temperature and pressure.

#### Ideal gas equation | General gas Equation

V ∝ 1/P

V ∝ T

V  ∝  η

V ∝ ηT / P

V = RηT / P ( R is called the general gas constant)

### Ideal Gas Constant (R)

The gas constant value of R depends upon. Units of pressure, Units of volume, and units of temperature.

R = PV / nT

Values and units of R can be calculated easily by using Avogadro's principle. units of Gas constant R= 0.0821  dm3atm /k mole (dm3 atm k-1 mol-1)

Significance:- The amount of energy that is required to change the temperature of one mole of gas by 1K. OR If we have one mole of an ideal gas at 273.16 k and one atm pressure and its temp. is increased by 1K, it will absurdly be 0.0821 dm3 atm of energy. dm3 atm is the unit of energy in this situation.

Note:- When pressure is given in Nm-2 and volume in m-3 the value of R used must be 8.3143 Jk-1mol-1.

Application of Ideal Gas Constant:- There is two major application of the ideal gas constant. 1- To determine the density of a gas. 2- To determine the molecule's mass of gas.

1. Density: density of H2O then decrease

PV = nRT            ( n= mass / M. mass)

PV = m RT
Mr
PMr = m RT
V
PMr = dRT
d = PMr        (M,R constant)
RT

2. Molar Mass:- 22.414 dm3 = 6.02x1023 molecules, 1 dm3 = 2.68x1022 molecules.

Mr = dRT
P

## Ideal and non-ideal behavior of gases

#### Ideal Gas:

* Ideal gas obeys all gas laws strictly under all conditions.

* Actual volume of an ideal gas is negligible as compared to the volume occupied by gas.

* No intermodular attraction or repulsion among gas molecules.

* It can not be liquefied.

Conditions for Ideal gas (Graph). High temperature and low pressure.

### Non-Ideal Gas Behavior:

* If a graph is plotted between pressure on-axis and the comprehensibility factor Z = PV / KT on Y-axis.

*For ideal gas straight line parallel to the pressure axis is obtained.

* For non-ideal gases, the graph is no more parallel to the pressure axis.

Conditions for Non-ideality (Graph). High pressure and low temperature.

Non-ideality x I.M.F x Polar Gas

### Kinetic Molecular Theory of Gases

In order to illustrate the behavior of gases quantitatively, Bernoulli (1738) put a kinetic molecular theory of gases. This theory leads Clausius 1857 to derive kinetic equations and gas laws. The theory was later on elaborated and extended by Maxwell, who gave the law of distribution of velocities-According to this.

" Molecules are in the form of groups having definite velocity range"

Boltzmann also contributed and studied disdain of energy among the gas molecules. van der walls are also an important scientist in this field.

### Postulates of Gas

1. Every gas consists of a large number of tiny particles called molecules.

2. Molecules move haphazardly, colliding with themselves and the walls of a container and changing their directions.

3. Pressure exerted on the walls of the container is due to collisions of molecules with walls collisions that are perfectly elastic.

4. Molecules have no forces of attraction.

5. Actual volume of gas is negligible as compared to the total volume of gas.

6. Effect of gravity is negligible due to repeated collisions of molecules.

7. Average K.E of the gas molecules varies directly from the absolute temperature of a gas.

#### Kinetic Energy Equation or Kinetic Equation

Kinetic energy formula  PV = 1/3mNc2

C2 is the average of Squares of possible velocities.

Root Mean Square Velocity: This equation is the quantitative relation between absolute temp. and gas molecules.

## The PVT Relationship

With the help of Boyle's and Charles' laws, a relationship is established between the volume, temperature, and pressure of a fixed mass of a gas, which is called the gas equation. And also called PVT Relationship.

Let the constant volume of gas be V, temperature T, and pressure P.

By Boyle's law

V ∝ 1/P (at constant temperature) ....(i)

By Charles' laws

V ∝ T ( at constant pressure) ......(ii)

By equations (i) and (ii)

V ∝ T/P

V = RT/P

PV = RT

Where R = 1 gm mole gas is the gas constant. If the number of gas molecules is n.

PV = nRT

This equation is called the gas equation of an ideal gas. From the gas equation, if a gas has volume V₁ at temperature T₁ and pressure P₁ and pressure P₂ and volume V₂ at temperature T₂.

P₁V₁/T₁ = P₂V₂/T₂

### Gas Standard Conditions

The condition of temperature and pressure at which the volume of 1 gm mole gas is 22.4 liters is called the standard condition.

Temperature     Pressure

0 °C                     1 atm

273°C.                 760 mm Hg

32°F.                    29.93 Hg

491.69°R.           14.7 Psi

### Partial Pressure Definition

The pressure exerted by a gas in a mixture of gases is called the partial pressure of that gas.

### Daltons Law of Partial Pressure

When two or more two gases that do not interact chemically are closed in a vessel at a certain temperature, the total pressure of the mixture of gases is equal to the sum of the partial pressures of those gases at the same temperature.

P = P1 + P2 + P3 + P4 ..........Pn

Partial pressure (P) = Mole fraction x Total pressure

### Amagets Law of Partial Volume

Amaget's law of volume addition is in agreement with Dalton's law of pressure addition.

According to this, when two or more gases that do not react with each other are sealed in a vessel at the same temperature and pressure, the total volume of the mixture of gases is equal to the sum of the partial volumes of those gases at the same temperature and pressure.

V = V1 + V2 + V3 +.........

Suppose two or more gases that do not react chemically with each other at the same temperature and pressure are closed in a container. In that case, each gas occupies the same volume as it alone occupies in that container at the same temperature and pressure.

Also Read: What are Reactants in Chemistry

What is Gas Saturation?

Determination of saponification value | significance of ester value

### What is called partial pressure?

The pressure exerted by a gas in a mixture of gases is called the partial pressure of that gas.

### What is the partial volume of the gas?

The volume occupied by a gas alone in a gaseous mixture is called its partial volume.

### What is the standard of atmospheric pressure?

The pressure which is equal to 14.696 Psi or 760 mm Hg at standard gravitational field temperature (°C) or other equivalent temperatures is called standard atomic pressure. Whereas atomic pressure is a variable quantity that is obtained by Barometer.

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