Gaseous State: Anything that has mass and occupies space is called matter. The matter is composed of atoms or molecules, and the arrangement of these atoms and molecules gives matter different states, physical and chemical properties. The arrangement of molecules gives matter its physical properties based on which it is classified into solids, liquids, or gases. Out of the three states of matter, it is only in the gaseous state that even the slightest change in physical conditions of temperature or pressure can be observed very easily, which makes this state very interesting. In this article, we will explore a little more about The Gaseous State.

What is a Gaseous state?The state of matter which possesses definite mass, but no definite shape and volume is called a gaseous state.

Pressure, volume, temperature, amount of substance, specific heat, etc., are some of the measurable properties of gases. The amount, volume, pressure, and temperature are the most important properties as these four independent variables describe the state of the gas. The interdependence of these variables leads to different gas laws.

What are Gaseous substances?

There are only eleven elements in the periodic table that exist as a gas under normal conditions. They are hydrogen, nitrogen, oxygen, fluorine, chlorine, helium, neon, argon, krypton, xenon, and radon.

Characteristics of Gases

The characteristics of gases are:

Intermolecular Force

The intermolecular force between the gas molecules is negligible because the molecules are very far from each other.

Compressibility

The molecules in gases are very far from each other as compared to the other two states. Therefore, the molecules can easily be compressed. It can be done by applying pressure, decreasing its volume and bringing the molecules closer to each other. Thus, the gaps between the molecules reduce, and this makes the gases highly compressible.

Density

As the intermolecular forces between the molecules are negligible, gases tend to have a very low density compared to the solid and the liquid states. The density increases with decreasing temperature and increasing pressure.

Pressure

The gas particles are always in constant, rapid, and random motion in all possible directions and collide with each other and with the container’s walls.

The pressure exerted by a gas is due to the collisions of gas molecules with the container’s walls.

Shape

Gases have no shape of their own. Instead, they take the form of the container in which they are filled.

The molecules exert pressure on the container walls and tend to occupy the shape of the container.

Volume

Gases have no volume of their own. Therefore, measuring the volume of the gas is like measuring the volume of the container. It is measured in litres or cubic metres.

Diffusion

Diffusion refers to the movement of particles from an area of higher concentration to a lower concentration area. Gaseous atoms and molecules movely and randomly through space. Thus, they have kinetic energy, and when this energy increases, the rate of diffusion also increases.

Gaseous State of Water

Water exists in all three states. The gaseous state of water is called water vapour. It is one of the states of water within the hydrosphere. It is the amount of moisture present in the air. If we say that the air is moist, we refer that the air contains a large amount of water vapour.

Water vapour can be produced from evaporation or boiling of the liquid water. It is one of the most important greenhouse gases that absorbs the heat radiated from Earth’s surface and radiates it in all directions.

The Gas Laws

The four measurable properties of gases- volume, temperature, pressure and amount of the gas are interrelated, and these relationships are commonly known as gas laws.

Boyle’s Law

According to Robert Boyle, in 1662, the volume of a given mass of gas is inversely proportional to its pressure at a given temperature

\({\rm{i}}{\rm{.e}}{\rm{.,V}}\,{\rm{\alpha }}\,\frac{{\rm{1}}}{{\rm{P}}}\) or

\({\rm{PV}}\,\,{\rm{ = }}\,\,{\rm{constant}}\)

The value of constants depends on the amount of gas and temperature.

If temperature \({\rm{T}}\) remains constant, the process is called the isothermal process.

If \({{\rm{V}}_1}\) is the volume of a certain mass of a gas at a pressure \({{\rm{P}}_1}\) and \({{\rm{V}}_1}\) volume of the same mass of gas at a pressure \({{\rm{P}}_2}\) at the same temperature, then,

\({{\rm{P}}_{\rm{1}}}\,{{\rm{V}}_{\rm{1}}}\,{\rm{ = }}\,{{\rm{P}}_{\rm{2}}}\,{{\rm{V}}_{\rm{2}}}\)

Graphical Representation

Applications

1. It is used in cycle pumps.
2. It is used in a tyre pressure gauge.
3. It is used in an aneroid barometer.

Let us understand the concept through gaseous state examples.

Solved Example on Boyle’s Law

A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds \(0.2\) bar. If at 1 bar pressure the gas occupies \(2.27\,{\rm{L}}\) volume, up to what volume can the balloon be expanded?

Solution: According to Boyle’s Law \({{\rm{P}}_{\rm{1}}}\,{{\rm{V}}_{\rm{1}}}\,{\rm{ = }}\,{{\rm{P}}_{\rm{2}}}\,{{\rm{V}}_{\rm{2}}}\)

If \({{\rm{P}}_1} = 1\) bar, \({{\rm{V}}_1}\, = \,22.7{\rm{L}}\)

If \({{\rm{P}}_2} = 0.2\) bar, then \({{\rm{V}}_{\rm{2}}}{\rm{ = }}\frac{{{{\rm{P}}_{\rm{1}}}{{\rm{V}}_{\rm{1}}}}}{{{{\rm{P}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{1}}\,{\rm{bar}}\,{\rm{ \times 2}}{\rm{.27L}}}}{{{\rm{0}}{\rm{.2}}\,{\rm{bar}}}} = 11.35\,{\rm{L}}\)

Since balloons bursts at \({\rm{0}}{\rm{.2}}\) bar pressure, the volume of the balloons should be less than \({\rm{11}}{\rm{.35}}\,{\rm{L}}\).

Charle’s Law

Jacques Charles, in \({\rm{1787}}\) found that for a fixed amount of gas at constant pressure, the gas expands as the temperature increases.

The law states that the volume of a fixed amount of gas is directly proportional to the absolute temperature at constant pressure.

\({\rm{i}}.{\rm{e}}.,{\mkern 1mu} {\rm{V}}{\mkern 1mu} \alpha \,{\rm{T}}\,{\rm{or}}\)

\(\frac{{\rm{V}}}{{\rm{T}}}\,\, = \,\,{\rm{constant}}\)

The constant pressure process is referred to as an isobaric process.

If \({{\rm{V}}_1}\) is the volume of a gas at a temperature \({{\rm{T}}_1}\) and \({{\rm{T}}_2 }\) is the volume of a gas at a temperature \({{\rm{T}}_2}\) at the same pressure, then according to Charles’ law,

\(\frac{{{{\rm{V}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}}} = \frac{{{{\rm{V}}_2}}}{{{{\rm{T}}_2}}}\)

Graphical Representation

Application

Hot air balloons are used in sports, and meteorological observations follow Charle’s law.

Solved Example on Charle’s Law

On a ship sailing in the Pacific Ocean, where the temperature is \({23.4^ \circ }{\rm{C}}\) a balloon is filled with 2L air. What will be the volume of the balloon when the ship reaches the Indian ocean, where the temperature is \({26.1^ \circ }{\rm{C?}}\)

Solution: \({{\rm{V}}_1} = {\rm{2L}},{{\rm{T}}_2} = 26.1 + 273 = 299.1{\rm{K}}\)

\({{\rm{T}}_1}\, = \,23.4 + 273 = 296.4\,{\rm{K}}\)

From Charle’s law,

\(\frac{{{{\rm{V}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}}} = \frac{{{{\rm{V}}_2}}}{{{{\rm{T}}_2}}}\)

\({{\rm{V}}_2} = \frac{{{{\rm{V}}_{\rm{1}}}{{\rm{T}}_{\rm{2}}}}}{{{{\rm{T}}_{\rm{1}}}}} = \frac{{2{\rm{L}} \times 299.1{\rm{K}}}}{{296.4\,{\rm{K}}}}\)

Gay Lussac’s Law

Gay Lussac’s law states that the pressure of a given mass of a gas is directly proportional to absolute temperature at constant volume.

\({\rm{i}}.{\rm{e}}.,{\rm{P}}{\mkern 1mu} \alpha \,{\rm{T}}\,{\rm{or}}\)

\(\frac{{\rm{P}}}{{\rm{T}}} = {\rm{constant}}\)

If volume remains constant, the process is called the isochoric process.

If \({{\rm{P}}_1}\) is the initial pressure of a gas at an initial temperature \({{\rm{T}}_1}\) and \({{\rm{P}}_2}\) is the final pressure of a gas at a temperatur \({{\rm{T}}_1}\), then according to Gay Lussac’s law,

\(\frac{{{{\rm{P}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}}}{\rm{ = }}\frac{{{{\rm{P}}_{\rm{2}}}}}{{{{\rm{T}}_{\rm{2}}}}}\)

Graphical Representation

Application

The tyres of automobiles are inflated to lesser pressure in summer than in winter – This is done to avoid bursting of tyres.

Avogadro’s Law

Amedeo Avogadro, in \(1811\) stated that an equal amount of all gases under the same conditions of temperature and pressure contain the same number of molecules.

Or

At a given temperature and pressure, the volume of any gas is directly proportional to the number of moles of the gas.

If \({\rm{P}}\) and \({\rm{P}}\) remain constant,

\({\rm{V}}\,{\rm{\alpha }}\,{\rm{n}}\)

or \(\frac{{\rm{V}}}{{\rm{n}}} = {\rm{constant}}\)

Where \({\rm{n}}\) is the number of moles, i.e., \({\rm{n}}\,\,{\rm{ = }}\,\frac{{\rm{W}}}{{\rm{M}}}\)

Ideal Gas Equation

By combining Boyle’s law, Charle’s law and Avogadro’s law, we get a general equation relating pressure, volume, absolute temperature, and the number of moles. The equation so obtained is called the ideal gas equation.

According to Boyle’s law, \({\rm{V}}\,{\rm{\alpha }}\frac{{\rm{1}}}{{\rm{P}}}\)

According to Charle’s law, \({\rm{V}}{\mkern 1mu} {\rm{\alpha }}{\mkern 1mu} {\rm{T}}\)

According to Avogadro’s law, \({\rm{V}}\,{\rm{\alpha }}\,{\rm{n}}\)

By combining the three laws, we get \({\rm{V}}\,{\rm{\alpha }}\frac{{{\rm{nT}}}}{{\rm{P}}}\)

Or \({\rm{PV}}\,{\rm{\alpha }}\,{\rm{nT}}\)

\({\rm{PV}}\, = \,{\rm{nRT}}\), Where \({\rm{R}}\,{\rm{ = }}\) universal gas constant \({\rm{ = }}\,{\rm{8}}{\rm{.314J}}\,{\rm{mo}}{{\rm{l}}^{ – 1}}\,{{\rm{K}}^{ – 1}}\)

Solved Examples on Ideal Gas Equation

At \(25{\,^ \circ }{\rm{C}}\) and \(760\,{\rm{mm}}\) of \({\rm{Hg}}\) pressure, a gas occupies \({\rm{600}}\,{\rm{ml}}\) volume. What will be its pressure at a height where the temperature is \({\rm{1}}{{\rm{0}}^ \circ }{\rm{C}}\) and the volume of the gas is \({\rm{640}}\,{\rm{ml}}\).

Solution: \({{\rm{P}}_1} = 760\,{\rm{mm of Hg,}}\,{{\rm{V}}_1} = 600\,{\rm{ml at }}{{\rm{T}}_1} = 25 + 273 = 298\,{\rm{K}}\)
\({{\rm{V}}_2} = 640\,{\rm{ml at }}{{\rm{T}}_2} = 10 + 273 = 283\,{\rm{K}}\)
According to the combined gas law,
\({{\rm{P}}_{\rm{1}}}\frac{{{{\rm{V}}_{\rm{1}}}}}{{{{\rm{T}}_{\rm{1}}}}}{\rm{ = }}{{\rm{P}}_{\rm{2}}}\frac{{{{\rm{V}}_{\rm{2}}}}}{{{{\rm{T}}_{\rm{2}}}}}\)
\({{\rm{P}}_2}\frac{{{{\rm{P}}_1}{{\rm{V}}_{\rm{1}}}{{\rm{T}}_2}}}{{{{\rm{T}}_{\rm{1}}}{{\rm{V}}_2}}} = \frac{{760\,{\rm{mm}}\,{\rm{of}}\,{\rm{Hg}}\, \times 600\,{\rm{ml}} \times 283\,{\rm{K}}}}{{640\,\,{\rm{ml}}\, \times 298\,{\rm{K}}}} = 676.6\,{\rm{mm of Hg}}\)

Kinetic Molecular Theory of Gases

The macroscopic behaviour of gases can be described by Boyle’s law, Charle’s law, etc. To explain the uniformity in the general behaviour of different gases, Bernoulli proposed the kinetic theory of gases, and it was modified by Maxwell, Boltzmann, Clausius and others. The main assumptions of the kinetic theory of gases are:

1. Gases consist of many identical particles (atoms or molecules) that are so small and so far apart on average that the actual volume of the molecules is negligible compared to the empty space between them.
2. The gas particles are always in constant, rapid, random motion in all possible directions and collide with each other and the container’s walls.
3. The molecular collisions are perfectly elastic.
4. The pressure exerted by the gas is due to the collisions of gas molecules with the container’s walls.
5. There is no intermolecular attraction between gas molecules.
6. The volume of the gas molecules is negligibly small compared with the space occupied by the gas.
7. The average kinetic energy of gas molecules is directly proportional to absolute temperature.

The Behaviour of Real Gases: Deviation from Ideal behaviour

An ideal gas obeys \({\rm{PV}}\,{\rm{ = }}\,{\rm{nRT}}\) under all conditions of temperature and pressure. Real gases deviate from an ideal gas behaviour and hence are known as non-ideal gases. Real gas approaches ideal behaviour only at low pressure and at high temperature. It has been found that gases show small deviation at ordinary temperatures and pressure. As the pressure increases and temperature decreases, the deviation of gases from ideal behaviour also increases.

The cause of deviation from ideal gas behaviour is attributed to the two faulty assumptions of the kinetic theory of gases which are-

1. There is no intermolecular attraction between gas molecules.
2. The volume of the gas molecules is negligibly small compared with the space occupied by the gas.

Vander Waal’s Equation

Vander Waal suggested a modified gas equation that describes the behaviour of real gases over a wide range of pressure and temperature.

The modified equation of state is-

\(\left\{ {{\rm{P + }}\frac{{{{\rm{n}}^{\rm{2}}}{\rm{a}}}}{{{{\rm{V}}^{\rm{2}}}}}} \right\}{\rm{(V}}\,{\rm{ – }}\,{\rm{nb) = nRT}}\,{\rm{for ‘n’}}\) moles of gas.

Vander Waal’s constants depend upon the nature of the gas.

Summary

In this article, we studied the gaseous state of matter, its properties, and the gas laws that are interdependent on the values of pressure, volume, absolute temperature, and amount of the gas. We also studied the equations for each law and their solved examples and how they combine to form an ideal gas equation. We now know the difference between ideal gas and non-idea gas and how Vander Waal’s equation corrected the ideal gas equation.

FAQs on Gaseous State

Q.3. Which metal is in the gaseous state?
Ans: No metal known till now exists in the gaseous state. They occur as solids except for mercury that is liquid at room temperature.

Q.4. Where is water found in the gaseous state?
Ans: Water in its gaseous form in the form of water vapour can be found in the Hydrosphere.