# Properties of Ideal Gases

Although gases are simple, both to describe and in terms of their internal structure, they are of immense importance. We spend our whole lives surrounded by gas in the form of air and the local variation in its properties is what we call the ‘weather’. To understand
the atmospheres of this and other planets we need to understand gases. As we breathe, we pump gas in and out of our lungs, where it changes composition and temperature. Many industrial processes involve gases, and both the outcome of the reaction and the design of the reaction vessels depend on a knowledge of their properties.

Equations of state

We can specify the state of any sample of substance
by giving the values of the following properties (all of
which are defined in the Introduction):
• V, the volume of the sample
• p, the pressure of the sample
• T, the temperature of the sample
• n, the amount of substance in the sample
However, an astonishing experimental fact is that
these four quantities are not independent of one
another.

p = f (n,V,T)
This expression tells us that the pressure is some function of amount, volume, and temperature and that if we know those three variables, then the pressure can have only one value.

## Ideal gas

While various gases will differ in their behaviours due to small differences in intermolecular forces and molecular size, they still tend to behave much like one another; thus the concept of an ideal gas was created. An ideal gas is an imaginary gas which has no intermolecular forces and no molecular volume. Its properties closely approximate those of real gasses under most conditions.

Ideal Gas Law

When we describe an ideal gas we are intrestaed in four variables. These varables are listed below along with common conversions factors.

P, pressure ( 1 atm = 760 mm Hg) , ( 1 atm = 760 torr ) , ( 1 atm = 1x 10^5 Pa )

V , volume ( 1 L = 1000 mL ) , ( 1 L = 1000 cm ^3 ) , ( 1 m^3 = 1000 L ).

n , moles ( # moles = # grams /MW).

T , temparature. ( K = o C + 273 ), where K is the temparature expressed in Kelvin.

The relationship of the above variables is given in the ideal gas equation below:

PV = n RT

where P is in atm, V is in L, T is in Kelvin. R is the gas constant which is equal tp 0.082 L.atm/mol.K. ( When SI units are used R = 8.3 J/mol.K )

An ideal gas is de¯ned as a hypothetical substance that obeys the ideal gas equation of state. We will see later that all real gases behave more and more like an ideal gas as the pressure approaches zero. A pressure of only 1 atm is su±ciently close to zero to make this relation useful for most gases at this pressure.

## Boyle,s law

Boyle's law states that a sample of gas at a constant temperature will have a volume which is inversely proportional to its pressure.

PV = k or P1V1 = P2V2

## Charles's law

Charles's Law states that a sample of gas at a constant pressure will have a volume which is directly proportinal to its temparature.

V/T = k   or V1/T1 = V2/T2