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The Gaseous State

Table of Contents

Introduction to the Gaseous State

Gaseous State is the simplest state of matter. In fact, the lowermost part of the atmosphere (called troposphere) in which we live is a mixture of gases like Dioxygen, Dinitrogen, Carbon Dioxide, Water Vapour etc.
If we look at the periodic table, we observe that there are only eleven elements which exist in the gaseous state under normal conditions of temperature and pressure as shown in figure no. 1.

Classification of elements as per their statesFig. No 1 Classification of elements as per their states

General Characteristics of Gases

  • Molecules are sufficiently apart from one another (Intermolecular molecular distance are of order 10-7 to 10-5 cm)
  • Negligible amount of intermolecular forces of attraction is present.
  • Densities of gases is much lower than solids and liquid.
  • Molecules of a gas have large rotatory, Vibratory and translatory motions.
  • Gas molecules are most energetic.
  • Gases have neither definite shapes nor definite volumes.
  • Gases possess high compressibility ‘and thermal expansion

As already explained above, gases possess the following General Characteristics:
(i) Shape and volume: Gases have neither definite shape nor definite volume. They take up the shape and volume of the container.

(ii) Density: They have lower density than liquids and solids.

(iii) Compressibility: They are highly compressible.

(iv) Diffusability: Gases intermix completely in all proportion without any mechanical aid.

(v) Pressure: They exert pressure equally in all direction

The above properties are due to the fact that intermolecular forces of attraction among the molecules of a gas are negligible.

In addition to the various properties of gases listed above, gases obey certain laws, called ‘Gas Laws’ which have been discovered as a result of experimental studies These laws give quantitative relationships between mass, volume, pressure and temperature of the gas. To understand the gaseous state, liquid state and the various gas laws we need to know the measurement of various properties of a gas, liquids like mass, volume. Pressure, temperature.

Measurement of Mass, Volume, Pressure and Temperature

Measurement of Mass

The mass of a gas can be easily determined by weighing the container containing the gas, and then emptying the container by taking out the gas and weighing the empty container again. The difference between the two masses gives the mass of the gas. The amount of the gas is usually expressed in terms of moles which can be obtained by dividing the mass of the gas by its molar mass, that is,

Molar Mass

The moles can be converted into the number of molecules using the relationship 1 mole = 6.022 x 1023 molecules

Measurement of Volume

As a gas fills the whole of the vessel in which it is put, hence the volume of the gas is equal to the volume of its container which in turn can be calculated from the dimensions of the container.
The SI unit of volume is m3. But this is too big a unit. Hence, the units commonly employed are cm3 or dm3. However, the unit like ml and liters are also used, generally in expressing the volumes of liquids and solutions. These units are interrelated as follows:

1m3 = 103 dm3 = 106 cm3

1 ml = 1 cm3

1 liter = 103 cm3 = 1dm3 = 10-3 m3

The symbol generally used for liter is ‘L’ and that for milliliter is ‘ml’ ​

Measurement of Pressure

The instrument used for the measurement of atmospheric pressure is called a Barometer. The principle of a barometer is illustrated in figure no. 2. It consists of inverted tube filled with mercury in a dish of mercury. The height of the mercury column above the level of mercury in the dish is a measure of the atmospheric pressure at that place.

BarometerFig. No. 2 Barometer

Why is mercury used as a barometric liquid?

This is on account of the following two reason:
(i) The height of the column in a barometer is inversely proportional to the density of the liquid. A mercury has very high density, the height of the column set up is very convenient for study.

(ii) Mercury is non-volatile at room temperature. Hence, the vapour pressure due to mercury vapours is negligible.

The instrument used for the measurement of the pressure of a gas is called a Manometer. It simply consists of a U-shaped tube containing mercury usually. One side of the tube is longer than the other. Two types of manometers are used:
(i) Those in which the longer tube is closed. Fig. No. 3

Closed Tube ManometerFig. No. 3 Closed Tube Manometer

(ii) Those in which the longer tube is open. (Figure no 4)

Open Tube ManometerFig. No. 4 Open Tube Manometer

Closed tube manometer is used only for gases at pressures less than the atmospheric pressure. The open tube manometer is used for all cases. In case the gas pressure is greater than atmospheric pressure, mercury stands at a higher level in the longer limb. In such a case, the difference of levels is added to the atmospheric pressure to get the pressure of the gas.

As pressure is force per unit area, the pressure obtained in terms of the height of the mercury column can be converted into force per unit area as follows:
Suppose height of the mercury column = h cm

Area of cross-section of the tube = A cm2

Volume of the mercury column = A x h cm3

If density of mercury at room temperature = g cm-3

then mass of the mercury column = A x h x gram

Weight of the mercury column = (A x h x ) x g

where g is the acceleration due to gravity.

This weight of the mercury column is the force acting on A cm2

Hence,

A standard or normal atmospheric pressure is defined as the pressure exerted by a mercury column of exactly 76 cm at 0°C. This is the pressure exerted by the atmosphere at the sea level.
The smaller unit commonly employed in expressing the pressures of gas is mm or torr (after the name of Torricelli, who invented the barometer). Hence
1atm = 76cm = 760mm or 760torr 

However, the unit of pressure now commonly used is ‘bar’.
1 atm = 1.01325 bar or 1 bar = 0.986923 atm
The SI unit of pressure is pascal (Pa) which is defined as the pressure exerted by a force of 1 newton on an area of 1 m2.
1Pa = 1 N m-2 = 1kgm-1s-2

The two units are related as

1 atm = 101325 Pa or N m-2 = 1.01325 x 105 Pa or N m-2

1bar = 105 Pa or Nm-2

A bigger unit, called Kilopascals (kPa) is also sometimes used. Thus,

1 bar = 102 kPa
Also, remember that 1 atm (at sea level) = 14.7 lb/sq. inch

Measurement of Temperature

Temperature is a measure of the extent of hotness or coldness of body. The measurement of temperature is based upon the principle that substances expand on heating. The most common substance whose expansion is made use of in the measurement of temperatures is ‘mercury’. There are three different scales on which the temperatures are measured. These are

(i) Centigrade or Celsius scale (after the name of Anders Celsius)
(ii) Fahrenheit scale (after the name of Daniel Fahrenheit, a German instrument maker)

(iii) Kelvin scale (after the name of Lord Kelvin)
The Kelvin scale of temperatures has emerged as a result of study on gases. It is possible to cool a substance below 0°C and thus we can have negative temperatures. But experimentally it is found that it is not possible to cool a gas below -273.15°C as after that the gas ceases to exist. Thus, this is the lowest temperature that can be attained and hence is taken as 0 K on the Kelvin scale. Negative Kelvin temperatures are as impossible as negative volumes or negative lengths. Thus, 273.15°C = O K or 0°C = 273.15 K

The size of Kelvin degree is same as that of Celsius degree. Hence, to convert °C into Kelvin the formula used will be

K = °C + 273.15

Gas Laws

Boyle’s Law

For constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure.

Mathematically, Boyle’s law may be stated as V ∝ 1/P

For a given mass of a gas at constant temperature.

or

that is, PV = constant at constant temperature

Where P and V represent the pressure and volume of the gas while k is a constant which depends upon the mass of the gas and temperature. The constant value obtained for PV is called Boyle Constant.

Thus, Boyle’s law may also be stated as follows:

At constant temperature, the product of volume and pressure of a given mass of a gas is constant.

Charles Law

At constant pressure, for every one degree centigrade rise or fall in temperature, volume of gas increases or decreases by the ratio of 1/273 of its volume at 0°C 

Mathematically,

where Vt, is the volume of the gas at t°C and V0 is its volume at 0°C.

Gay-Lussac’s Law

“At constant volume for every 1°C rise or fall in temperature, the pressure of a given mass of a gas increases or decreases by the ratio of 1/273 of its pressure at 0°C.”

Mathematically,

where Pt and P0 are the pressures of a certain amount of a gas at 1°C and 0°C respectively.

The above law may also be defined as follows:

Pressure of a given mass of a gas is directly proportional to its temperature in degrees Kelvin at constant volume.

Avogadro’s Law

Avogadro’s Law states that

All gases having equal volumes under the same conditions of temperature and pressure contain equal number of molecules.
As 1 mole of a gas contains Avogadro’s number of molecules (6.022 x 1023), this means that one mole of each gas at the same temperature and pressure should have the same volume.

Dalton’s Law of Partial Pressures

If in an enclosed vessel, two or more gases (which do not react chemically) are present then the total pressure exerted by the gaseous mixture is equal to the sum of all the partial pressures that each gas would exert when present alone in the same vessel at the same temperature.

The pressure which that gas would exert when present alone in the same space at the same temperature is called Partial Pressure of a particular gas in a gaseous mixture enclosed in a given space. Let p1, p2, p3...pn be the partial pressures of n gases enclosed in a given vessel and P be the total pressure of the gaseous mixture. Then by Dalton’s Law of Partial Pressures, we have

P = p1+ p2+ p3+…...pn:
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