Gaseous State : Partial Pressure & Diffusion

 

Dalton’s law of partial pressures

(1)     According to this law, “When two or more gases, which do not react chemically are kept in a closed vessel, the total pressure exerted by the mixture is equal to the sum of the partial pressures of individual gases.”

Thus, Ptotal­ = P1 + P2 + P3 + …..

Where P1, P2, P3…….. are partial pressures of gas number 1, 2, 3 ………

 

(2)     Partial pressure is the pressure exerted by a gas when it is present alone in the same container and at the same temperature.

Partial pressure of a gas (P1) =  \frac { Number\quad of\quad moles\quad of\quad the\quad gas({ n }_{ 1 })\times { P }_{ Total } }{ Total\quad number\quad of\quad moles\quad (n)\quad in\quad the\quad mixture }   =  Mole fraction (X1) × PTotal

 

(3)     If a number of gases having volume V1, V2, V3…… at pressure P1, P2, P3…… are mixed together in container of volume V, then,

PTotal =  \frac { { P }_{ 1 }V_{ 1 }+{ P }_{ 2 }V_{ 2 }+{ P }_{ 3 }V_{ 3 }..... }{ V }

                   or = (n1 + n2 + n3……)  \frac { RT }{ V }   (∴ PV = nRT)   

or = n \frac { RT }{ V }    ( ∴ n = n1 + n2 + n3 …..)

 

(4)     Applications : This law is used in the calculation of following relationships,

(i)      Mole fraction of a gas  in a mixture of gas =  \frac { Partial\quad Pressure\quad of\quad a\quad gas{ (P }_{ 1 }) }{ { P }_{ Total } }

(ii)     % of a gas in mixture =  \frac { Partial\quad Pressure\quad of\quad a\quad gas{ (P }_{ 1 }) }{ { P }_{ Total } }  × 100

(iii)    Pressure of dry gas collected over water : When a gas is collected over , it becomes moist due to water vapour which exerts its own partial pressure at the same temperature of the gas. This partial perssure of water vapours is called aqueous tension. Thus,

Pdry = Pmoist gas or PTotal – PWater Vapour or Pdry gas = Pmoist gas Aqueous tension (Aqueous tension is directly proportional to absolute temperature)

(iv)    Relative humidity (RH) at a given temperature is given by :

RH =  \frac { Partial\quad Pressure\quad of\quad water\quad in\quad air }{ Vapour\quad pressure\quad of\quad water }

                        .

(5)     Limitations : This law is applicable only when the component gases in the mixture do not react with each other. For example,  and O2, CO  and CO2, N2 and Cl2, CO and N2 etc. But this law is not applicable to gases which combine chemically. For example, H2 and Cl2, CO and Cl2, NH3, HBr and HCl, NO and O2 etc.

Note :    N2 (80%) has the highest partial pressure in atmosphere.

 

(6)     Another law, which is really equivalent to the law of partial pressures and related to the partial volumes of gases is known as Law of partial volumes given by Amagat. According to this law, “When two or more gases, which do not react chemically are kept in a closed vessel, the total volume exerted by the mixture is equal to the sum of the partial volumes of individual gases.”

Thus, VTotal = V1 + V2 + V3 +…….

 Where V1, V2, V3…….. are partial volumes of gas number 1, 2, 3…..