State Boyle's law, Charles' law and Avogadro's law and derive ideal gas equation.

Explanation

Boyle.s law : At constant temperature, the volume of a given mass of gas is inversely proportional to pressure of the gas.
V is the volume of a given mass of the gas and .P. its pressure, then the law can be written as
` V prop (1)/(P )` at constant temperature
` V= (k )/(p )`
` therefore PV = K`
or ` P_1 V_1 = P_2 V_2 = K`
Boyle.s law may also be stated as, .at constant temperature the product of the pressure and volume of a given mass of gas is constant."
Charles. law : At constant pressure, the volume of a given mass of gas is directly proportional to absolute temperature.
`V prop T ` at constant pressure
` V = KT`
` (V )/(T ) = k`
Where V is the volume and T is the absolute temperature. `V_1 and V_2` are the initial and final volumes of a given mass of the gas at the absolute temperatures `T_1 and T_2` respectively at constant pressure.
` (V_1)/(T_1 ) = K , (T_2)/(T_2) =K`
` or (V_1)/(T_1) = (V_2)/(T_2) = K`
Avogadro.s law : Equal volumes of all gases contain equal number of moles at constant temperature and pressure.
`V prop n` (pressure and temperature are constant).
Ideal gas equation : The combination of the above gas laws leads to the development of an equation which relates to the four parameters volume, pressure, absolute temperature and number of moles. This equation is known as ideal gas equation.
In this Boyle.s law and Charles. law combined together and an equation obtained called the gas equation.
`V prop (1)/( P)` (Boyle.s law)
` V prop T` (Charles law)
` V prop n` (Avogadro.s law)
Combining above three laws, we can write
` V prop (1)/(P ) prop T prop n (or) V=R xx (1)/(P ) xx T xx n`
` (or) PV = nRT `
Where V = volume of the gas
`P=` pressure of the gas
n = no. of moles of gas
T = absolute temperature
R - Universal gas constant