Numerical Value of the Gas Constant

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.

Boyle’s Law – Boyle’s Law is a fundamental law of thermodynamics that was first proposed by Robert Boyle, the same scientist who first proposed the ideal gas law. Boyle’s Law is a corollary of the ideal gas law, and states that the pressure, temperature, and volume of a sample of a gas are in direct proportion to the amount of heat added to the system and in proportion to the number of moles of gas present. This means that if you double the number of moles of gas in a container, the temperature of the gas will double, its pressure will be doubled, and its volume will be cut in half. On the other hand, if you cool the container of gas, its volume will be cut in half, its pressure will be halved and its temperature will be lowered to the new, lower temperature.

Boyle’s Law formula

       P1V1 = P2V2

P1 = first pressure

P2   = second pressure

V1 = first volume

V2   = second volume

Charles’s Law: Charles’ Law is a law describing the thermodynamic behaviour of gases. It was first described by the British chemist and physicist Charles, in 1798. It is often referred to as the \“Charles-Charles Law\” or \”Charles’ Law.\”:pressure, volume, and temperature are in direct proportion to the amount of heat added to the system, and inversely proportional to the amount of work done on the system.This means that, if you double the amount of heat added to a system, pressure will be reduced in half, volume will be reduced in half, and the temperature will be increased to the new, higher temperature.

Charles’s Law formula

   PV = K

   k ~   constant.

   P= Pressure.

   V= Volume.

Gay-Lussac’s Law

“Gay-Lussac’s law: it is a valid refinement of the ideal gas law. It is used in chemistry to describe interactions between two or more gases and says that the ratio of the volume of a gas to its pressure is constant. Gay-Lussac’s Law also shows that more heat is needed to make a gas hotter and less heat is needed to increase gas pressure compared to that needed to decrease gas temperature.

Gay-Lussac’s Law formula

                                                        P1/T1=P2/T2.

P1 is the initial pressure

T1 is the initial temperature

P2 is the final pressure

T2 is the final temperature

Avogadro’s Law

Avogadro’s Law, also known as Avogadro’s constant, is a formula that relates the number of atoms in a sample of ideal gas to the mass of that sample. It states that the number of particles in an ideal gas is equal to the number of molecules in the gas multiplied by the constant Avogadro, which is 6.022×1023 particles per mole. This means that if you double the number of particles in an ideal gas, its mass will be doubled, and its pressure will be raised to the new, higher number of particles. On the other hand, if you cool an ideal gas, its volume will be cut in half, its pressure will be cut in half, and its temperature will be

Avogadro’s Law formula

                                                  V1/n1= V2/n2  

Combined Gas Law 

The combined gas law states that the pressure, volume, and temperature of a sample of ideal gas are in proportion to the amount of heat added to the system. This law is useful for determining the behaviour of gases in equilibrium, such as at equilibrium temperatures and pressures. The law of combining gases is also a useful tool when determining the behaviour of gases under conditions of change, such as when the temperature of an ideal gas is changed.

Combined Gas Law / Ideal Gas Law 

   PV = nRT

P = pressure

V = volume

n = amount of substance

R = Numerical Value of the Gas Constant

T =      Temperature

This formula is known as an ideal gas formula.

Numerical Value of the Gas Constant

This is also called the ideal gas constant or molar gas constant or universal gas constant. It can be represented by the symbol R.

This gas constant R can be combined derived from all the gas laws like Charle’s Law, Boyle’s Law, Gay-Lussac’s Law, Avogadro’s Law etc. 

The numerical value of R can be derived by 1 mole of a gas at a given pressure and a given temperature. 

 R=8.314Joulemol −1K −1

We know that P V = nRT

So R  = PVnT

Numerical Value of the Gas Constant in various units

R = 8.3144598 J⋅K−1⋅mol−1

R = 1.9872036(11)×10−3  kcal.K-1.mol-1

R = 8.2057338(47)×10−5 m3.atm.K-1.mol-1

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