Ideal Gas Law

Mass (m), volume (V), pressure (p), and temperature (T) is of a gas are the measureable properties. The laws which inter-relate these properties are called gas laws.

Perfect Gas or Ideal Gas

The gas whose molecules are point masses (mass without volume) and do not attract each other, is called ideal or perfect gas. It is a hypothetical concept which can not exist in reality. The gases such as hydrogen, oxygen or helium which can not be liquefied, are called parmanent gases.

Properties of ideal Gas are as follows

1. It strictly obeys Boyle’s law, Charle law and the law of pressure under all consitions of temperature and pressure.
2. Its pressure coefficient and the volume coefficient are exactly equal to each other.
3. A perfect gas can not be converted into liquid or solid state, because a force of attraction is necessary between the molecules in case of liquid or solid state.

Ideal Gas law or Equation

The tree laws (Boyle’s law, Charles law and Avogardo’s law) can be combined together in a single equationn which is known as ideal gas equation.

Gas law

1. Boyle’s Law (pressure-voulme relationship) According to this law, at constant temperature, pressure of a fixed amount of gas varies inversely with its volume, i.e.,

p∝1/V(at constant T) or pV = k (constant) or p1V1=p2V2

at constant temperature, pressure of the gas is directly proportional to the density of a fixed mass of the gas.

i.e.,    p ∝ d

2. Charles’ Law (Temperature-Volume relationship) According to this law, at constant pressure, the volume of a fixed mass of a gas is directly proportional to its absolute temperature i.e., decreases with a decrease in temperature.

V∝T (at constant p) or V1/T1 = V2/T2

The lowest hypotheticcal or imaginary temperature at which gases are supposed to occupy zero volume, is called absolute zero.

3. Gay Lussac’s Law (Pressure-Temperature relationship) According to this law, at constant volume, pressure of a fixed amount of a gas varies directly with the temperature, i.e.,

p ∝ T or p/T= constant or p1/T1=p2/T2

4. Avogadro’s Law (Volume-Amount relationship) According to this law, equal volumes of all the gases under the same conditions of temperature and pressure contain the equal number of molecules, i.e.,

V ∝ n (at constant T and p)

where, n=number of molecules

at STP, gram molecular mass or 1 mole of gas occupies volue of 22.4 L.

Number of molecules in one mole of a gas has been determined to be 6.022 x 10²³ This number is known as Avogadro’s constant

5. Combined Gas Law This is the relationship for the simultaneous variation of the variables. If temperature, volume and pressure of a fixed amount of gas vary from T1, V1 and p1 to T2, V2 and p2 then we can write

pV/T=nR or p1V1/T1=p1V2/T2

6. Dalton’s Law of Partial Pressure It states that the total pressure exerted by gaseous mixture of two or more non-reacting gases is equal to the sum of the partial pressure of each individual component in a gas mixture, i.e.,

p_total= p₁+p₂+p₃…..p_n (at constant T, V)

where, p₁, p₂, p₃ … are the partial pressures of individual gases.

7. Graham’s Law of Diffusion According to this law, at constant temperature and pressure, the rate of diffusion (r) of a gas is inversely proportional to the square root of its density (d) i.e.,

(Diffusion is the process of spontaneous mixing of different gases and the volume of a gas diffused per unit time, is called rate of diffusion)

This law is applicable 

1. In the production of marsh gas
2. In the separation of gaseous mixture
3. In the determination of vapour densities of gases
4. In the Separation of Isotopes

Indeal Gas Equation

At constant T and n;

V ∝ 1/p (Boyle’s Law)

At constant p and n;

V ∝ T (Charles’ Law)

At constant p and T;

V ∝ n (Avogadro’s law)

V ∝ nT/p or V = RxnT/p

where, R is proportionality constant, On rearranging the above equation, we obtain

pV=nRT (ideal gas equation)

R=pV/nT

R is called universal gas constant and has vol. 8.314 J mol^-1 K^-1 or 0.0821 L atm mol^-1 K^-1

Ideal gas equation is a relation between four variables and it describes the state of any gas, therefore, it is also called equation of state.