Ideal Gas equation

The Ideal Gas Law is an equation in thermodynamics describing the relationship between temperature, pressure, and volume of gases. The Ideal Gas Law equation is PV = nRT, where P is the pressure, V is the volume, ‘n’ is the number of moles of gas molecules, R is the universal gas constant, and T is the absolute temperature. 

Practically, there is no such thing as an ideal gas. However, in conditions like high temperatures and low pressures where individual particles are moving so fast and are too much away from each other such that their interaction is almost zero, gases behave like an ideal gas. Ideal Gas Law is a useful approximation.

Ideal Gas Law:

In thermodynamics, Ideal gas law is a well-defined approximation of the gases under different conditions. Ideal Gas Equation combines Charle’s Law, Boyle’s Law, Gay-Lussac’s Law, and Avogadro’s Law.

• Charles’s Law-

Charles’ Law, sometimes called the Law of volumes, gives a detailed account of how gas expands when the temperature increases. And, when there’s a drop in temperature, it leads to a decrease in the volume of gases.

When we compare a substance under two different conditions, with the help of the above statement, we can write:

              V2/V1 = T2/T1  

OR 

V1.T2 = V2.T1

The above-mentioned equation shows that as the absolute temperature increases, the volume of the gas also increases in the same proportion.

Also, Charles’s Law is a special case of the ideal gas law. This Law applies to the ideal gases that are held at constant pressure, but the volume and temperature go on changing.

• Boyle’s Law-

Boyle’s Law explains that the pressure exerted by the gas of a particular mass, when kept at a constant temperature, is inversely proportional to the volume occupied by it. For a gas, the relationship between pressure and volume (at constant mass and temperature) can be expressed mathematically as-

                       P ∝ (1/V)

Where P is the pressure exerted by the gas and V is its volume. This proportionality can be converted into an equation by adding a constant, k.

                     P = k*(1/V) ⇒ PV = k

• Gay-Lussac’s Law-

Gay-Lussac’s Law describes that the pressure exerted by a gas of a particular mass, when kept at a constant volume, varies in a direct proportion with the absolute temperature of the gas. In simpler terms, we can say that the pressure exerted by a gas is directly proportional to the temperature of the gas when the volume is constant, and the mass is of a fixed quantity.

The mathematical expression of Gay-Lussac’s Law can be written as follows:

                          P ∝ T or P/T = k

Where,

             P is the pressure exerted by the gas

             T is the absolute temperature of the gas

             k is a constant.

• Avogadro’s Law-

Avogadro’s Law, otherwise called Avogadro’s guideline or Avogadro’s speculation, states that different gases with equal volume contain an exact number of molecules when the temperature and pressure are constant.

Avogadro’s Law is related to the ideal gas condition since it has temperature, tension, volume, and measure of substance for a given gas.

At steady tension and temperature, Avogadro’s Law can be presented by the following equation:

                       V ∝ n or V/n = k

Where V is the volume of the gas, n denotes the amount of gaseous substance (which is expressed in moles), and k is a constant. When the amount of gaseous substance is increased, the volume occupied by the gas also gest increased that can be calculated with the help of the following formula:

                      V1/n1 = V2/n2 = k

Derivation Of Ideal Gas Equation:

Let us consider,

The pressure exerted by the gas: P

The volume of the gas: V

Temperature: T

The number of moles of gas: n

Universal gas constant: R

According to Boyle’s Law, At constant n & T, the volume makes an inverse relation with the pressure exerted by a gas.

i.e. 

      v ∝ 1/P ————————-(i)

According to Charles’ Law, When P & n are constant, the volume of gas directly relates to the temperature.

i.e. 

       v ∝ T     ————————-(ii)

According to Avogadro’s Law, When P & T are constant, then the volume of gas makes a direct relation with the number of moles of gas.

i.e. 

       v ∝ n     ———————–(iii)

Combining all the three equations, we have-

V ∝ nT/P 

or 

PV = nRT

Where R is the Universal gas constant, which has a value of 8.314 J/mol-K

Conclusion:

Any gas is known as an ideal gas when its particles are too far away from each other that they do not exert any force of attraction on each other. In such a gas, the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

An ideal gas can be characterised by three state variables: the absolute pressure denoted by P, volume represented by V, and absolute temperature indicated by T.

Ideal gas law: PV = nRT = NkT

Where,

             n: number of moles

             R: universal gas constant = 8.314J/molK

             N: number of molecules

             k: Boltzmann constant = 1.38066×10-23 J/K

            NA: Avogadro’s number = 6.0221 x 1023 /mol