ICSE Class 9 Chemistry Chapter 07 Study of Gas Laws

Study Of Gas Laws

Syllabus

The behaviour of gases under changes of temperature and pressure; explanation in terms of molecular motion (particles, atoms, molecules); Boyle's Law and Charles' Law; absolute zero; gas equation; simple relevant calculations.

The behaviour of gases under changes of temperature and pressure, explanation in term if molecular motion (particles, atoms, molecules)

Boyle's Law: statement, mathematical form, simple calculations.

Charles' Law: statement, mathematical form, simple calculations.

Absolute zero Kelvin scale of temperature.

Gas equation P₁V₁/T₁ = P₂V₂/T₂; simple relevant calculations based on gas equation.

Relationship Between Kelvin Scale And Celsius Scale Of Temperature; Standard Temperature And Pressure

Conversion of temperature from Celsius Scale to Kelvin scale and vice versa.

Standard temperature and pressure. (Simple calculations)

Introduction

The state of matter in which inter-particle attraction is weak inter-particle space is so large that the particles become completely free to move randomly in the entire available space is known as Gas. Gas occupies the entire space of the vessel in which it is kept and so takes the shape of the vessel. All gases show uniform behaviour under similar conditions of temperature and pressure irrespective of their chemical nature or color or odour.

Behaviour And Characteristic Properties Of Gases

Gases are composed of molecules (particles) that are in constant random motion. Kinetic theory helps in explaining the simple relationship that exists between the pressure, the volume, and the temperature of a gas.

The kinetic molecular theory, explains the behaviour and characteristic properties of gases:

(1) Composition of gases: Gases are made up of tiny particles (molecules) moving in all possible directions at all possible speeds. The molecules are negligibly small in size as compared to the volume occupied by the gas.

(2) Gases have neither a fixed volume nor a fixed shape: There is negligible force of attraction between the particles (gas molecules). Therefore, the particles (gas molecules) are free to move in the entire space available to them, their movement is restricted only by the walls of the container. Thus, they attain the shape of the containing vessel.

(3) Gases exert pressure in all directions: The moving particles (molecules) of a gas collide with each other and also with the walls of the container. Due to these collisions, gas molecules exert pressure. It has been found, that at a given temperature, time and area, the same number of molecules of a gas strike against the walls of the container. Thus, gases exert the same pressure in all directions.

(4) Gases are highly compressible: There are large inter-particle (inter-molecular) spaces between gas molecules, and this accounts for the high compressibility of gases. On applying pressure, the molecules come closer, thus decreasing the volume of the gas.

(5) Gases are highly expansible: Gases increase in volume on decrease in pressure and increase in temperature.

When pressure on an enclosed gas is reduced, its particles (molecules) move apart, thus increasing their inter-molecular spaces. As a result, the volume of the gas increases.

When an enclosed gas is heated, kinetic energy of its molecules increases. Thus, the molecules start moving faster and further apart from each other, resulting in an increase in the volume of the gas.

(6) Gases have low density: The number of molecules per unit volume in a gas is very small as compared to solids and liquids. Gases have large inter-molecular space between their molecules. Therefore, gases have very low density.

(7) Gases have a natural tendency to mix with one another (diffusion): Inter-particle (inter-molecular) spaces in a gas are very large. When two gases are brought in contact with each other, their molecules mix with each other in such a manner that a homogeneous gaseous mixture is formed.

Diffusion is the process of gradual mixing of two substances, kept in contact, by molecular motion.

If you open a jar of chlorine or ammonia in a large room, the odorous presence of the gas can be detected in every part of the room within a few seconds. Although chlorine is heavier than air, it does not remain at the floor but spreads throughout the room.

The particles (molecules) of chlorine coming out of the jar collide with air particles (molecules) and due to the collisions of the particles, they start moving in a haphazard manner in all possible directions. This process continues till there is an equal concentration of chlorine particles (molecules) throughout the room.

(8) Gases can be liquefied: On cooling, the kinetic energy of the molecules of a gas is reduced and on applying pressure on a cooled gas, the molecules come closer. Hence, the inter-molecular space gets reduced and there is an increase in the number of molecules per unit volume. Thus, the gas liquefies.

Molecular Motion: Relationship Of Temperature, Pressure And Volume

According to the kinetic model, particles (molecules) of a substance are in constant random motion, so they possess kinetic energy.

The average kinetic energy of a particle (molecule) is directly proportional to its absolute temperature.

As temperature increases, molecular motion increases, and when temperature decreases, molecular motion also decreases. This suggests that when the temperature is zero, molecular motion ceases (theoretical concept). This fact is applied in defining a scale of temperature called Kelvin scale.

Kelvin scale is also called the absolute scale of temperature.

The temperature at which the molecular motion completely ceases (theoretical concept), on the Kelvin scale, is called absolute zero.

Absolute zero or zero kelvin is equal to -273 degrees C. Obviously, temperatures lower than absolute zero, i.e., -273 degrees C are not possible.

When a gas is enclosed in a vessel, it exerts uniform pressure on the walls of the containing vessel. The reason is that the particles (molecules) of the gas collide with each other and with the walls of the containing vessel. Since a large number of particles (molecules) suffer collisions with the wall, an appreciable force acts on the wall. The force exerted on a unit area of the wall of the vessel is equal to the pressure of the gas.

But, when the temperature of the gas is increased, keeping its volume constant, the average kinetic energy of the gas molecules increases and therefore average speed of the molecules also increases. The molecules now strike the walls of the container with greater momentum (momentum is the product of mass and velocity) and the rate of collision of the particles (molecules) also increases. Thus, the force exerted on the walls of the container increases, which results in an increase in the pressure exerted by the gas.

If one of the walls of the container is movable, then, due to the increased pressure, that wall is pushed back and the gas expands. Thus, volume also increases with the increase in molecular motion.

The Gas Laws

The behaviour of a gas under known conditions of pressure, volume and temperature is described by laws known as Gas Laws.

Standard variables for gas laws:

The physical behaviour of gases can be described by three standard variables:

(i) volume (V) (ii) pressure (P) (iii) temperature (T).

All gases are similar in their physical behaviour; they expand and contract equally under similar conditions of temperature and pressure. For a given mass of a gas, a change in one or more than one variable, i.e., pressure, volume and temperature, results in a change in the remaining variables.

(a) The Volume (V) Of A Gas Is The Space Occupied By That Gas

The space occupied by a gas is equal to the volume of its container.

Units of volume:

In S.I. system, volume of a gas is measured in cubic metre (m³). Other units are:

(i) cubic centimetre (cm³)

(ii) millilitre (mL)

(iii) cubic decimetre (dm³)

(iv) litre (L)

Relationship between units:

1 m³ = 1000 dm³ = 1000 litres

1 Litre = 1000 mL = 1000 cm³

(b) The Pressure (P) Of A Gas Is The Force That The Gas Exerts Per Unit Area On The Walls Of Its Container

Our planet is surrounded by a thick blanket of air known as atmosphere. The pressure exerted by air (present in the atmosphere) on the surface of the earth is called atmospheric pressure.

Standard pressure of one atmosphere (1 atm) is defined as the pressure exerted by 76 cm of mercury at 0 degrees C and at standard gravity of 9.8 m s-2 (density of mercury = 13.5951 g cm-3).

The S.I. unit of pressure is Pascal (Pa)

Pascal (Pa) is defined as the pressure exerted when a force of 1 Newton acts on an area of 1 m².

Units of pressure:

(i) Pascal (Pa)

(ii) Atmosphere (atm)

(iii) (a) in centimetre (cm Hg),

(b) in millimetre (mm Hg),

(c) in torr (named after Torricelli).

Relationship between these units:

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

(c) The Temperature (T) Of A Gas Is Defined As The Degree Of Hotness Of That Gas

The more commonly used scale of temperature is Celsius scale, formerly known as the Centigrade scale. The zero on Celsius scale is purely arbitrary. In other words, temperature of a substance may go below zero i.e. a substance can have negative temperatures too. The behaviour of gases show that it is not possible to have temperature below -273 degrees C. This fact has led to the formulation of another scale known as Kelvin scale. The zero on this scale corresponds to -273 degrees C.

Relationship between Kelvin (K) and degree Celsius (degrees C)

Celsius scale values can be converted to Kelvin scale values by adding 273 to degree Celsius values.

Kelvin (K) = degrees C + 273.

Pressure And Volume Relationship In Gases

Experiment - Take a 10 mL syringe fitted with a piston. Raise the latter to the 10 mL mark and wrap an adhesive tape over its nozzle. Fit the wrapped nozzle tightly into a hole, bored half way through a rubber stopper (Fig. 7.1).

Observation: On placing some weight on the piston (to put pressure), it moves downward and reduces the volume of air. Gradually, put some more weight. The piston moves further downward and the volume of the air is further reduced.

Now remove the weights one by one. You will notice that, on decreasing the pressure, piston moves upward, as such, the volume of the air increases.

Conclusion:

1. An increase in pressure at constant temperature causes a decrease in the volume of a gas; conversely, if the volume of a fixed mass of a gas at constant temperature is decreased, the pressure of the gas increases.

2. A decrease in pressure at constant temperature causes an increase in the volume of a gas; conversely, if the volume of a fixed mass of a gas at constant temperature is increased, the pressure of the gas decreases.

Boyle's Law

Robert Boyle systematically studied the relationship between pressure and volume of gases.

In 1662, he found that, at constant temperature, the volume of a fixed mass of a dry gas decreased by half when the pressure on it was doubled, and it became four times its original volume when its pressure was decreased to one-fourth. He described this behaviour in the form of a law, known as Boyle's law.

Boyle's law: Volume of a given mass of a dry gas is inversely proportional to its pressure at constant temperature.

Mathematical expression of Boyle's law:

Suppose a gas occupies volume V₁ when its pressure is P₁; then

V₁ ∝ 1/P₁ or V₁ = k/P₁

or P₁V₁ = k = constant

If V₂ is the volume occupied when the pressure is P₂ at the same temperature, then

V₂ ∝ 1/P₂ or V₂ = k/P₂

or P₂V₂ = k = constant

Therefore, P₁V₁ = P₂V₂ = k; at constant temperature.

This is called Boyle's law equation.

Boyle's law may also be stated as: the product of volume and pressure of a given mass of a dry gas at a constant temperature is constant.

Graphical Verification Of Boyle's Law

The law can be verified by plotting a graph

(i) V vs 1/P (ii) V vs P (iii) PV vs P

(i) V vs 1/P: a straight line passing through the origin is obtained (Fig. 2.2).

(ii) V vs P: a hyperbolic curve in the first quadrant is obtained (Fig. 7.3).

Note: The term isotherm (meaning at constant temperature) is used to describe such graphs.

(iii) PV vs P: a straight line is obtained parallel to the pressure axis (Fig. 7.4).

Explanation Of Boyle's Law In Terms Of Molecular Motion (Kinetic Theory)

According to the kinetic theory of gases, number of particles (molecules) present in a given mass and the average kinetic energy possessed by the particles is constant.

If volume of a given mass of a dry gas is reduced to half its original volume, the same number of particles (molecules) will have half the space to move. As a result, the number of molecules striking at unit area of the walls of the container at a given time will get doubled and so the pressure also gets doubled. Conversely, if the volume of a given mass of a gas is doubled at constant temperature, the same number of molecules will have double the space to move about. Consequently, the number of molecules striking at unit area of the walls of the container at a given time will become one half of the original value. Thus, pressure of the gas will be reduced to half of its original pressure. Hence it is seen that if pressure increases, the volume of a given mass of gas decreases at constant temperature (BOYLE'S LAW).

Significance Of Boyle's Law

On increasing pressure, volume decreases. The gas becomes denser. Thus, at constant temperature, the density of a gas is directly proportional to its pressure.

Atmospheric pressure is low at high altitudes, so air is less dense. Hence, a lesser quantity of oxygen is available for breathing. This is the reason why mountaineers have to carry oxygen cylinders with them.

Note: When air is blown into a balloon, volume and pressure inside the balloon increase. Here, Boyle's law is not violated as the law is valid for a definite mass, whereas mass increases when more air is blown into the balloon.

Solved Examples

Example 1: A gas occupies 800 cm³ under 760 mm Hg pressure. Find under what pressure the gas will occupy 380 cm³, the temperature remaining constant.

Solution:

P₁ = 760 mm Hg; V₁ = 800 cm³

P₂ = ? mm Hg; V₂ = 380 cm³

By Boyle's law, P₁V₁ = P₂V₂

Substituting the values,

760 × 800 = P₂ × 380

Therefore, P₂ = (760 × 800) / 380 = 1600 = 1600 mm Hg = 160 cm Hg

Ans.: The required pressure is 160 cm Hg.

Example 2: A gas occupies 600 cm³ under a pressure of 700 mm Hg. Find under what pressure the volume of the gas will be reduced by 20 per cent of its original volume, the temperature remaining constant throughout?

Solution:

20% of 600 cm³ = (600 × 20) / 100 = 120 cm³

Therefore, The new volume of the gas = 600 - 120 = 480 cm³

P₁ = 700 Hg; V₁ = 600 cm³

P₂ = ? mm Hg; V₂ = 480 cm³

By Boyle's law, P₁V₁ = P₂V₂

Substituting the values,

700 × 600 = P₂ × 480

Therefore, P₂ = (700 × 600) / 480 = 875 mm Hg

Ans.: The required pressure is 875 mm Hg.

Example 3: Two cylinders, both containing carbon dioxide, are connected together by a tube fitted with a tap. The capacity of one cylinder is 4 dm³ and that of the other is 1 dm³; the pressure in the first cylinder is 560 mm Hg and that in the second is 1000 mm Hg. What will be the final pressure in either cylinders on opening the tap if the temperature remains constant?

Solution:

Total volume of carbon dioxide (after opening the tap) = 4 + 1 = 5 dm³.

For the first cylinder

P₁V₁ = P₂V₂

560 × 4 = P₂ × 5

Therefore, P₂ = (560 × 4) / 5 = 448 mm Hg

For the second cylinder

P₁V₁ = P₂V₂

1000 × 1 = P₂ × 5

Therefore, P₂ = (1000 × 1) / 5 = 200 mm Hg

Ans.: Final pressure = 448 + 200 = 648 mm Hg

Example 4: The volume of a given mass of a gas with some pieces of marble in a container at 760 mm Hg pressure is 100 mL. If the pressure is changed to 1000 mm Hg, the new volume is 80 mL. Find the volume occupied by the marble pieces, if the temperature remains constant.

Solution: Let the volume occupied by the marble pieces = V mL

At 760 mm Hg, the volume occupied by the gas = (100 - V) mL

At 1000 mm Hg, the volume occupied by the gas = (80 - V) mL

By Boyle's law, P₁V₁ = P₂V₂

Therefore, 760 × (100 - V) = 1000 × (80 - V)

or 24 V = 400 mL

or V = 16.6 mL

Ans.: The required volume = 16.6 mL.

Teacher's Note

In everyday life, when you compress air in a bicycle pump, you're applying Boyle's Law - as the volume decreases, the pressure increases, making it easier to inflate tires.

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