Comprehensive WBBSE Class 10 Physical Science Notes Chapter 2 Behaviour of Gases can help students make connections between concepts.

## Behaviour of Gases Class 10 WBBSE Notes

Matter: It is classified into three States: Solid, liquids and gases.

Some Physical properties of gases:

Motion of gas molecules: A gas is composed of infinite number of molecules. Molecules of gaseous substances move almost freely and exhibit random motion in all directions.

Shape and Volume: A gas has niether a definite shape nor a definite volume. It takes the shape and volume of the container in which it is kept.

Density: Gases have lower density than the liquids and solids.

Diffusion: When two or more gases which do not react with each other, are brought in contact, they intermix with one another forming a homogeneous mixture. This spontaneous mixing of gases with one another is known as diffusion.

Expansibility: Gases exhibit unlimited power of expansion.

Compressibility: The compressibility of a gas is very high.

Temperature of a gas: Temperature of any gas is the measure of average kinetic energy of the gas molecules.

Pressure of a gas: The force exerted by the gaseous molecules per unit area of the wall due to continuous collision of the gas molecules with the walls of the container is called the pressure of the gas.

- Unit of area: CGS unit : cm
^{2} - SI unit : m
^{2} - Unit of force: CGS unit : dyne
- SI unit : Newton

Unit of pressure:

- The pressure of gas is generally expressed in the unit of atmosphere (atm).
- Torr: Pressure exerted by exactly 1 mm of mercury column at 0°C and at standard gravity is termed as 1 torr.
- Bar: The commonly used unit of pressure = bar

1 atm = 1.01325 bar

Pascal (Pa) : SI unit of pressure is pascal. The pressure exerted when a force of 1 newton acts on 1 m^{2} area is called 1 pascal.

1 atm = 76.0 cuHg = 760 mm Hg = 760 torr

psi : The pressure is also expressed in the unit of pound per square inch or psi.

1 atm = 14.7 psi

Measurement of pressure exerted by a gas : Very common instrument used for measuring the pressure of gas is manometer.

Pressure (P) = \(\frac{\text { Force }}{\text { Area }}\) = \(\frac{\mathrm{A} \times \mathrm{h} \times \mathrm{d} \times \mathrm{g}}{\mathrm{A}}\) = hdg

Unit of volume : At a particular temperature and pressure the volume of a gas closed in a container is equal to the volume of that container at the same temperature and pressure.

- Units : SI units of volume : m
^{3} - Smaller units : dm
^{3}, cm^{3} - The symbol used for litre is : L
- The symbol used for millilitre is : mL

The relationship among different units are :

1 L = 10^{3} mL=10^{3} cm^{3}=10^{3} ×(10^{-1})^{3} dm^{3 }= 1 dm^{3}

1 m^{3}=10^{6} cm^{3}=10^{3} dm^{3}=10^{3} L.

NTP or STP (Normal or Standard Temperature and Pressure): It is defined as the pressure exerted by column of mercury 76 cm in height at 0°C at 45° latitude and mean sea-level.

Boyle’s law (1662): At constant temperature, the volume of a given mass of a gas in inversely proportional to the pressure of the gas.

Mathematical expression of Boyle’s law: Let the pressure of a definite mass of a gas be P and the volume be V. If the temperature of T K (kelvin), then according to Boyle’s Law,

V ∝ \(\frac{1}{P}\)

when temperature T and the mast.

remain constant.

or, V = K.\(\frac{1}{P}\) when temperature T and the mass of the gas ‘m’ remain constant.

or, V = K.\(\frac{1}{P}\) (K = Proportionality Constant)

∴ PV = K, this equation is the mathematical expression of Boyle’s law.

Graphical representation of Boyle’s Law :

At constant temperature plot of P vs. V for a definite mass of gas.

At constant temperature plot of P V vs. P for a definite mass of gas.

At constant temperature plot of \(\frac{I}{V}\) vs. P and V vs. \(\frac{1}{P}\) for a definite mass of gas

At constant temperature plot of log P vs. log V for a definite mass of gas

Isotherms: These are the pressure volume curves obtained at constant temperature.

Charle’s Law (1787): At constant pressure, the volume of a given mass of a gas increases or decreases by \(\frac{1}{273}\) of its volume at 0° C for each one degree rise or fall in temperature.

Mathematical expression of Charle’s law :

(V_{0} = Volume of a given mass of gas at Constant pressure at 0°C

V_{t} = Volume of the gas after t°C rise of temperature)

Absolute zero : According to Charle’s law: At constant pressure, the temperature (-273°C) at which, theoretically a gas would have no volume, is known as absolute zero. A temperature below this cannot be conceived of in the universe.

Absolute scale of temperature : It is a thermometric scale where -273°C is the starting point i.e. on this scale 0 K is equal of -273° C and each degree is equal to that in the celsius scale.

Alternative Statement of Charle’s law : The volume of a given mass of a gas is directly proportional to the absolute temperature if the pressure remains constant.

Mathematical expression of Charle’s law with respect to absolute temperature.

V ∝ T at constant pressure and a definite mass of gas.

or, V = KT

or, [\(\frac{V}{T}\) = K = const

Graphical representation of Charle’s law

At constant pressure, plot of \(\frac{V}{1}\) vs. T for a definite mass of gas.

At constant pressure plot of V vs. t°C for vs. T for a definite mass of gas. definite mass of gas plot of V vs. t°C

At constant pressure plot of log V vs. log T for a definite mass of gas.

Graphical representation of P vs T at constant volume and for a definite mass of gas- According to Gay-Lussac’s law.

Combined form of Boyle’s and Charle’s law :

Let us consider for a definite mass of a gas the pressure, temperature and volume are P, T and V respectively.

According to Boyle’s Law

V ∝ \(\frac{1}{P}\) (at constant temperature and for a given mass of the gas)

According to Charle’s law

V ∝ T (at constant pressure and for a given mass of the gas)

According to the laws of joint variation,

V ∝ \(\frac{T}{P}\) when the mass of the gas remains constant but both pressure and temperature of the gas vary.

∴ V = K.\(\frac{T}{P}\)

(K = proportionality constant and it depends upon the amount of gas)

or, PV = KT

This equation is the combined form of Boyle’s law and Charle’s law.

Ideal gas: A gas which obeys Boyle’s law, Charle’s law and Avogadro’s law for all volumes of temperature and pressures and which obeys the equation of state P V=n R T under all conditions of temperature and pressure is called an ideal gas.

Real gases: The gases which do not obey PV=n R T equation are called real gases.

The compressibility factor (Z)

\(\left(Z=\frac{P V}{n R T}\right)\) of an ideal gas = 1

All gases approach the ideal behaviour as the temperature goes further from their boiling points i.e. at high temperature and low pressure.

Gay-Lussac’s Law: Under the same conditions of temperature and pressure two or more gases combine chemically in simple ratios by volumes of and the volumes of the products if gaseous also bear a simple relation to the volumes of the reacting gases.

Berzelius hypothesis: Under the same conditions of temperature and pressure equal volumes of all gases contain the same number of atoms.

Avogadro’s Law: Under the same conditions of temperature and pressure, equal volumes of all gases (element or compound) contain the same number of molecules.

Avogadro’s Number: Avogadro’s number may be defined as the number of molecules present in one gram-mole of any substance, element or compound (solid, liquid or gas).

N = 6.022 × 10^{23}, R.A. Millikan determined the value by oil drop experiment in 1913.

Molar volume: The volume occupied by one gram-molecule of any gaseous substance (elementary or compound) at a fixed temperature and pressure is known as the molar volume.

At standard conditions of temperature and pressure (STP), the volume equal to 22.4 litres is the molar volume of all gases.

Substance | Molecular mass |

H_{2}O |
2 × 1 + 16 = 18 |

N_{2} |
14 × 2 = 18 |

O_{2} |
16 × 2 = 32 |

Pressure of dry gas = Atmospheric pressure – Aqueous tension

Equation of state for an ideal gas :

According to Boyle’s law, V ∝ \(\frac{1}{P}\) (T and n are constant)

According to Charle’s law, V ∝ T (P and n are constant)

According to Avogadro’s law, V ∝ n (P and T are constant)

By method of compound variation

V ∝ \(\frac{n T}{P}\) when P, T and n of the gas vary

or V = \(\frac{R n T}{P}\) (R = molar gas constant )

or, PV = nRT

This equation is called ideal gas equation.

Calculation of molar mass from equation of state

PV = nRT

[Let the mass of the gas = wg

Molecular mass of the gas = M

Dimension of Molar gas constant R

R = energy K^{-1} mol^{-1}

Values of R in different units

Unit | Volume of R |

L-atm | 0.0821 L_{–}atm mol ^{-1}K^{-1} |

Cal 1 | 1.987 Cal^{-1} K^{-1} |

SI | 8.314 J mol^{-1} K^{-1} |

CGS | 8.314 × 107 erg^{-1} mol^{-1} K^{-1} |

Dm^{3}.torr |
62.36 dm3 .torr. mol ^{-1} K^{-1} |

Dm^{3}.kPa |
8.314 dm3.Pa.mol^{-1} K^{-1} |

Boltzmann constant (K)

Determination of density and molar mass of an ideal gas : For n moles ideal gas, the equation of state is :

PV = nRT, n = \(\frac{m}{\bar{M}}\)

(If ‘m’ and ‘M’ are the mass of the gas in gram and molar mass of the gas respectively, then the number of moles of gas n = \(\frac{m}{\bar{M}}\))

The above equation indicates the relation among the density, pressure, absolute temperature and moiar mass of an ideal gas.

Dalton’s law of partial pressure: At constant temperature, when two or more non-reacting gases are er:closed together in a container of definite volume, the total pressure of a mixture of gases is equal to the sum of the partial pressures of the constituent gases.

P_{Total}= P_{1} + P_{2} + P_{3} +…

Diffusion of gas: The process of the property by virtue of which two or more gases without any external help intermix with each other spontaneously to form a homogeneous gas mixture irrespective of their densities or molar masses is termed as diffusion of gas.

Effusion: The process of out-flow of a gas confined in a closed vessel under high pressure through a fine orifice (hole) made in the well of the vessel is called effusion.

Graham’s Law of diffusion: At constant temperature and pressure, the rate of diffusion of any gas in inversely proportional to the square root of its density.

\(r ∝ [latex]\frac{1}{\sqrt{d}}\) or, r = \(\frac{K}{\sqrt{d}}\)

(r = the rate of diffusion or effusion of gas,

d = the density of gas, K = proportionality constant)

Postulates of kinetic theory of gases:

- All gases consist of very large number of tiny particles called molecules that are in constant rapid motion.
- The gas molecules are perfectly round, very hard and separated by large distances. Their actual volume is thus, negligible as compared to the total volume of the gas.
- The gas molecules collide with one another and with the walls of the container. The pressure exerted by a gas is due to the bombardment of its molecules on the walls of the vessel.
- The collisions between the gas molecules are perfectly elastic, i.e. there is no loss of energy during these collisions.
- The distance between the gas molecules being very large, there is no effective force of attraction or repulsion between them.
- The gas molecules move freely in all directions. Their speed and direction change continuously due to collisions among them. As a result, their motion becomes zig-zag or random.
- The average kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas.

Influenre of pressure on volume occupied by a gas; effect of temperature on the spond of gas molecules and on the pressure exerted by the gas:

- If the velocities of the molecules increase, the magnitude of pressure increases and if velocities of them decrease, pressure decreases.
- The motion of gas molecules depends on temperature of the gas. If the temperature is increased, the velocity of the gas molecules or the kinetic energy of the gas molecules increases.

Deviation from Ideal behaviour :

The modified equation put forward by Vander Waals’ for one mole of a real gas as:

\(\left(P+\frac{a}{V^2}\right)\) (V-b) = RT

and for ‘n’ moles of the gas it is expressed as

\(\left(P+\frac{a n^2}{V^2}\right)\) (V-nb) = nRT

where ‘a’ and ‘b’ are constants called Vander Waals’ constants. The values of constants ‘a’ and ‘b’ depend upon the nature of the gas.