Ideal Gas: Gas Laws, Boyle’s Law, Charles’ Law, Charles’ and Boyle’s Laws combined, The Individual Gas Constant - R, The Universal Gas Constant - Ru, The Molecular weight of a Gas Mixture ~ MECHTECH GURU

# Ideal Gas

Perfect gas, also called ideal gas, a gas that conforms, in physical behaviour, to a particular, idealized relation between pressure, volume, and temperature called the general gas law.

# Gas Laws

## Boyle’s Law

Boyle’s Law Pressure is inversely proportional to volume: p∞ 1/v Robert Boyle noticed that when the volume of a container holding an amount of gas is increased, pressure decreases, and vice versa (while the temperature is held constant). Note that this is not a linear relationship between p and V.

## Charles’ Law

Charles’ Law Volume is directly proportional to temperature: V = cT, where c > 0 is constant. Scientist Jacque Charles noticed that if air in a balloon is heated, the balloon expands. For an ideal gas, this relationship between V and T should be linear (as long as pressure is constant).

## Charles’ and Boyle’s Laws combined

Combine the two laws above:

pV/T = K,

where k is a constant, = pV=mRT

## The Individual Gas Constant - R

The Individual Gas Constant depends on the particular gas and is related to the molecular weight of the gas. The value is independent of temperature. The induvidual gas constant, R, for a gas can be calculated from the universal gas constant, Ru (given in several units below), and the gas molecular weight, Mgas:

R = Ru/Mgas

In the SI system units are J/kg K.

## The Universal Gas Constant - Ru

The Universal Gas Constant - Ru - appears in the ideal gas law and can be expressed as the product between the Individual Gas Constant - R - for the particular gas - and the Molecular Weight - Mgas - for the gas, and is the same for all ideal or perfect gases:

Ru = Mgas R, kJ/(kmol.K) : 8.3144598

## The Molecular weight of a Gas Mixture

The average molecular weight of a gas mixture is equal to the sum of the mole fractions of each gas multiplied by the molecular weight of that particular gas:

Mmixture = Σxi*Mi = (x1*M1 + ......+ xn*Mn)

where

xi = mole fractions of each gas

Mi = the molar mass of each gas

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