State and explain Dalton's law of partial pressures.Derive the relation between partial pressure and total pressure.

Explanation

Dalton's law of partial pressure: "At constant temperature , the total pressure exerted by a gaseous mixture which do not react chemically with each other is equal to the sum of partial pressures of the component gases."
Consider a mixture of three gases in a vessel. Let `p_1,p_2p_3` be the partial pressures of the three gases in the mixture . Then according to Dalton'a law of partial pressure,
`P=p_1+p_2+p_3`
Consider a mixture of three gases in a vessel of a volume V at constant temperature T. Let the number of moles of these gases be `n_1,n_2` and `n_3`, Then according to Ideal gas equation
`P_1=(n_1RT)/V`......(1)
` P_2=(n_2RT)/V`......(2)
`P_=(n_3RT)/V`......(3)
According to Dalton's law of partial pressure,
Total pressure `(P)=P_1+P_2+P_3`
(or) (or)`P=(n_1RT)/V+(n_2RT)/V+(n_3RT)/V`
(or)`P=(RT)/V(n_1+n_2+n_3)`
(or)` P=(nRT)/V(where n=n_1+n_2+n_3)`......(4)
Dividing (1) by (4) `P_1/P=(n_1RT//V)/(nRT//V)=n_1/n=x_1`
(or)`P_1=Ptimesx_1`
Similarly by dividing (2) by (4) and (3) by (4) we get
`P_2=Ptimesx_2&P=P_3timesx_2` Now we can write
Total pressure =Partial pressure `times` mole fraction