State and explain Dalton's law of partial pressures.

Explanation

Dalton.s law of Partial pressures : The total pressure exerted by a mixture of chemically non reacting gases at given temperature and volume, is equal to the sum of the partial pressures of the component gases.
Explanation: Consider a mixture of three gases in a vessel. Let `P_1 , P_2 , P_3`, be the partial pressures of the three gases in the mixture. According to Dalton.s law of partial pressures, the pressure (P) of the gaseous mixture is at the same temperature.
` P=P_1 +P_2 +P_3`
Let `n_1 , n_2 , n_3`, be the number of moles of three gases respectively in the mixture. Let "V be the volume of the mixture of gases at T K temperature
According to ideal gas equation,
`P_1 = (n_1 RT)/( V ) , P_2 = (n_2 RT)/(V ) , P_3 = (n_3 RT )/(V)`
` therefore ` Total pressure of the mixture `P = P_1 + P_2 + P_3`
` P= (n_1 RT)/(V ) ,P_2 = (n_2 RT)/(V ) , P_3 = (n_3 RT)/( V)`
` P = (RT)/(V ) ( n_1 +n_2 +n_3)`
since ` n_1 +n_2 +n_3 =n`
` therefore P=(nRT)/( V )`
` or (P_1)/(P ) = (n_1 RT)/( nRT) = (n_1)/(n ) = x_1`
Where `x_1` is the mole fraction of the first gas and given by
` x_1 = ("number of moles of the first gas .")/("total number of moles in the mixture of gases")`
` therefore P_1 = x_1 P `
In a similar way `P_2 = x_2 P and P_3 = x_3 P`.
` therefore `Partial pressure = mole fraction `xx` total pressure