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The Gas Laws: Charle’s Law, Boyle’s Law and Gay-Lussac’s law

Gas Laws

Matter is found in three physics states –

Solid: A solid is a substance whose shape and volume are fixed.

In the solid state of matter, the molecules of matter are very close to each other, that is, they have very little intermolecular space. Due to less intermolecular space, intermolecular attraction is very high in them and their freedom to move is very less.

Solid State of matter

In this way, their potential energy is very high and kinetic energy is very less and they keep on vibrating both in their mean position and in limited space. Due to this the size and volume of the solid remain fixed.

Liquid: A liquid is a substance whose volume remains fixed but the shape becomes like that of the vessel in which it is kept. The intermolecular space between the molecules of a liquid is greater than that of a solid. Due to this, the intermolecular attraction between the molecules of the liquid is less and the freedom of movement of the molecules of the liquid is more.

Thus the molecules of a liquid have less potential energy and more kinetic energy. Due to the high kinetic energy of liquid molecules, they keep on colliding with each other while moving randomly and they do not have any definite shape.

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Because of this, the vessel in which the liquid is kept, therefore the liquid has the property of flowing and it does not have any definite shape. Due to this, the liquid assumes the shape of the vessel in which it is kept.

The kinetic energy of the liquid molecules is not more than the potential energy produced by their earth’s gravity and due to intermolecular attraction, so they cannot leave their plane and the volume of the liquid remains fixed.

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Gas: A gas is a substance whose volume and shape are not fixed, but the volume and shape of the vessel in which it is kept becomes similar. The intermolecular space between gas molecules is much larger than that of solid and liquid.

Due to the large space between the gas molecules, the intermolecular attraction between them is very less and the freedom of movement of their molecules is very high. In this way, the potential energy of the gas molecules is very low and the kinetic energy is very high and they remain almost completely free.

Due to the high kinetic energy, the gas molecules collide with each other and with the walls of the vessel and move at an irregular speed in all directions. Because of this, gases also have the property of flowing like liquids and their shape is not fixed. The kinetic energy of gas molecules is so high that they can leave their plane. Therefore, the volume of gases is also uncertain.

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Due to the high kinetic energy, the gas molecules collide with each other and with the walls of the vessel and move at an irregular speed in all directions. Because of this, gases also have the property of flowing like liquids and their shape is not fixed. The kinetic energy of gas molecules is so high that they can leave their plane. Therefore, the volume of gases is also uncertain.

Boyle’s law

Boyle introduced this rule in 1662.

According to this rule :-

The volume (V) of a fixed amount of a gas at constant temperature is inversely proportional to its pressure (P).

V 1/P

V = k x 1/P (where k is a constant)

PV = k

Therefore, the product of pressure and volume of a gas at a constant temperature is always constant.

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If a certain quantity of a gas at the same temperature has volume V1 and pressure P1 and its volume is changed from V1 to V2, then its pressure from P1 to P2 will be in such a way that –

P1V1 = P2V2

P1         =             first pressure

P2         =             second pressure

V1         =             first volume

V2         =             second volume

Charles Law

Charles introduced this rule in 1787. According to this law –

The volume of a fixed amount of a gas at constant pressure is directly proportional to its absolute temperature.

Absolute temperature = 273 + temperature in °C

The absolute temperature is represented in A° (°absolute) or K (kelvin). If the temperature of a gas is 25 °C, then its absolute temperature will be 273 + 25 = 298 K.

If the volume V and absolute temperature T of a certain amount of a gas at constant pressure is –

V T

V = k’ T (k is a constant)

If a fixed volume of a gas at constant pressure has volume V1 and absolute temperature T1 and its temperature is raised from T1 to T2, then its volume from V1 to V2 will be such that –

V1/T1 = V2/T2

Putting the value of T1 as 273°A and the value of T2 as 274°A (1°C) –

V1/V2 = T1/T2 = 273/274

V1/V2 = 273/274 = 1 + 1/273

V2 = V1 + V1/273

Therefore, the volume of a certain amount of a gas at constant pressure increases by 1/273 of its volume on increasing its temperature from 0°C to 1°C. Similarly, on reducing the temperature from 0°C to -1°C, the volume of a gas decreases by 1/273 of its volume.

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According to this law, the volume of gas will become 0 at absolute zero temperature. It is not possible to generate absolute temperature.

Gas Equation

By combining the laws of Boyle and Charles, these two laws can be represented by only one equation.

Boyle’s law                         V 1/P

 Charles Law:                    V T

There for                            V T/P

                                                PV ∝ T

                                           PV = KT (K is a constant)

It is clear that both the above rules are included in the above equation. If T is constant then PV = KT = k, which is Boyles law. If P is constant then V = (KP) T = kT which is Charles law.

The value of K depends on the amount of gas and the units of P, V and T. According to Avogadro’s law, the volume of one gram molecule of all gases under the same conditions of temperature and pressure is also the same.

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