Gas Laws: Boyle’s Law, Charles’s Law, Gay-Lussac’s Law

#### Boyle’s Law

“The volume of a certain volume of a gas at constant temperature is inversely proportional to its pressure.” That is, the volume decreases when the gas pressure is increased at constant temperature and the volume increases when the pressure is reduced.

If the volume of a certain mass of a gas at constant temperature is V and pressure P, then

[latex] V \ propto \ frac {1} {P} [/ latex]

Or [latex] V = \ frac {1} {P} [/ latex]

Where K is a constant.

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

Again

[latex] {V} _ {1} = \ frac {M} {{D} _ {1}} [/ latex] or [latex] {V} _ {2} = \ frac {M} {{D} _ {2}} [/ latex]

But according to Boyle’s law –

[latex] {P} _ {1} {V} _ {1} = {P} _ {2} {V} _ {2} [/ latex]

Or, [latex] {P} _ {1} \ frac {M} {{D} _ {1}} = {P} _ {2} \ frac {M} {{D} _ {2}} [/ latex]

Or, [latex] \ frac {{P} _ {1}} {{D} _ {1}} = \ frac {{P} _ {2}} {{D} _ {2}} [/ latex]

Or, [latex] \ frac {P} {D} [/ latex] = constant

Or, [latex] P \ propto D [/ latex]

That is, the pressure of a certain amount of a gas at constant temperature is proportional to its density.

Charle’s Law:

“The volume of a certain amount of gas at constant pressure is directly proportional to its ultimate temperature.”

If the volume of a certain mass of a gas at constant pressure is v and the ultimate temperature T, then –

[latex] V \ propto T [/ latex]

[latex] \ frac {V} {T} [/ latex] = constant

Or, [latex] \ frac {{V} _ {1}} {T_ {1}} = \ frac {{V} _ {2}} {{T} _ {2}} [/ latex]

Where, V1 and V2 are the volumes of gas in the initial and final stages respectively and T1 and T2 are the temperatures of the gas in those states.

Pressure’s Law:

“The pressure of a certain mass of a gas at a constant volume is directly proportional to its altitude.” That is, if the temperature of a gas is increased at constant volume, the pressure increases and if the temperature is reduced, the pressure decreases.

If the pressure of a certain mass of a gas at constant volume (V) is P and temperature T, then –

Or, [latex] \ frac {P} {T} [/ latex] = constant

Or, [latex] \ frac {P_ {1}} {T_ {1}} = \ frac {{P} _ {2}} {{T} _ {2}} [/ latex]

Or, [latex] {P} _ {1} {T} _ {2} = {P} _ {2} {T} _ {1} [/ latex]

The Equation of State for Gases:

An equation that describes the relationship between pressure, temperature and volume of a constant magnitude of a substance is called the Equation of State of that substance. For 1 mile of a gas, according to Boyle’s law,

[latex] P \ propto \ frac {1} {V} [/ latex], while T is a constant.

According to Charles’s rules –

P ∝ T, while V is a constant.

On combining the rules of Boyle and Charles –

[latex] P \ propto \ frac {T} {V} [/ latex], while both T and v change. or,

Or, [latex] P = \ frac {RT} {V} [/ latex] where R is a constant, called the gas constant. It is a universal constant.

If a gas has a corresponding volume V1 and pressure P1 at a temperature T1 for 1 mile, then –

[latex] R = \ frac {{P} _ {1} {V} _ {1}} {{T} _ {1}} [/ latex]

Similarly, for 1 mole of a gas at another temperature T2 with its corresponding volume V2 and pressure P2, then

[latex] R = \ frac {{P} _ {2} {V} _ {2}} {{T} _ {2}} [/ latex]

[latex] \ therefore \ frac {{P} _ {1} {V} _ {1}} {{T} _ {1}} = \ frac {{P} _ {2} {V} _ {2} } {{T} _ {2}} = R [/ latex]

That is, PV = RT

For n moles of gas – PV = nRT

Absolute Temperature Scale:

The scale of measuring temperature in which -273 ° C is considered zero is called the ultimate heat scale. -273 ° C is called Absolute Zero Temperature.

According to Charles’s law, the volume of a gas at absolute zero temperature should be zero, but in practice this is not the case, because before this temperature reaches, the gas transforms into a liquid or solid. The ultimate temperature T is called TK or T kelvin.

Hence,

0 ° C = 273K

5 ° C = (273 +5) = 278K

100 ° С = (273 + 100) = 37ЗК

273 is added to the temperature of the centigrade heat to be converted to absolute heat or Kelvin and 273 is subtracted from it to convert the ultimate temperature to the centigrade temperature, ie

t ° C = (T + 273) K

TK = (T-273) ° С

Normal Temperature and Pressure: 0 ° C T 273K is called normal temperature. When the height of mercury (Hg) in a barometer is 760 mm, the atmospheric pressure is called normal pressure. It is also called 1 atmospheric pressure. Therefore, 0 ° C temperature and 760 mm pressure are also known as normal temperature and pressure or abbreviated as SaTa (N.T.P).

Diffusion of Gases: The natural process of mixing of gases against the earth’s gravitational force, even when there is a difference in density, is called diffusion of gases.

Gas Laws: Boyle’s Law

Rate of Diffusion: The volume of a gas that can diffuse through an imperfect vessel in unit time is called the velocity of diffusion of the gas.

Graham’s Law of Diffusion: In 1883 AD, Graham proposed a law regarding the speed of diffusion of gases, called Graham’s law of gaseous diffusion. According to this rule – “The relative velocity of diffusion of different gases at certain temperature and pressure are inversely proportional to the square root of their density.”

If the relative densities of two gases are D1 and D2 respectively and their diffusion velocities are r1 and r2 respectively, according to Graham’s law-

[latex] {r} _ {1} \ propto \ frac {1} {\ sqrt {{D} _ {1}}} [/ latex]

{r} _ {2} \ propto \ frac {1} {\ sqrt {{D} _ {2}}} [/ latex]

or,

[latex] {r} _ {1} = \ frac {k} {\ sqrt {{D} _ {1}}} [/ latex]

[latex] {r} _ {2} = \ frac {k} {\ sqrt {{D} _ {2}}} [/ latex]

[latex] \ frac {{r} _ {1}} {{r} _ {2}} = \ sqrt {\ frac {{D} _ {2}} {{D} _ {1}}} [/ latex]

The density of hydrogen is 1 and the density of oxygen is 16, if their diffusion velocities are rH and rO respectively.

[latex] \ frac {{r} _ {H}} {{r} _ {O}} = \ sqrt {\ frac {16} {1}} [/ latex]

or,

[latex] \ frac {{r} _ {H}} {{r} _ {O}} = 4 [/ latex]

or,

[latex] {r} _ {H} = 4 \ quad \ times \ quad {r} _ {O} [/ latex]

That is, the velocity of diffusion of hydrogen gas is four times the velocity of diffusion of oxygen gas.

Uses of Diffusion of Gases

In Ansel’s Marsh Gas director,
In separating the mixture of gases,
In determining the vapor density of gases,
In separating isotopes.
Dalton’s Law of Partial Pressure: According to this rule, the total pressure of a gaseous mixture of a certain volume is equal to the sum of the partial pressures of the constituent gases.

If the partial pressures of three gases A, B and C are PA, PB, and PC, respectively, according to Dalton’s partial pressure law (if all three gases are filled together in another V liter flask),

Total pressure (P) = PA + PB + PC

Avogadro’s Hypothesis: All gases at the same temperature and pressure have the same number of molecules in the same rectangles.

If the volume of the gas at the same temperature and pressure is V and the number of moles of the gas is n, then

V ∝ n

Gas Laws: Boyle’s Law | Gas Laws: Boyle’s Law | Gas Laws: Boyle’s Law