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 TV 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 ) +(n_2 RT)/(V ) + (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 //V )/(n RT //V ) = (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 roles 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