Dalton’s Law of Partial Pressure | Gases | Physics Grade XI

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Dalton’s Law of Partial Pressure | Gases | Physics Grade XI

Dalton’s Law of Partial Pressure | Gases

Dalton’s Law of Partial pressure
It states that "the total pressure exerted by a mixture of gases is equal to the sum of the partial pressure of the individual gas when there is no chemical interaction between them".
Dalton's law of partial pressure diagram
Consider two bulbs A and B separated by a tap key T. Let the bulb A has volume V1 and gas at pressure P1. At bulb B let the volume be V2 and the pressure is P2. When the tap is opened, the final volume occupied by the gas is (V1 + V2). Experimentally, it is found that total pressure exerted by the mixture of gases is
     P = {P1V1/(V1+V2) + P2V2/(V1+V2)} …… (i)
 
If P1' and P2' are the pressure exerted by first and second gas when they are mixed, then the total pressure of the mixture can be written as
     P = P1P2' …………… (ii)
 
For the first gas,
     P1V1 = P1' (V1 + V2)
    or P1' = P1V1/ (V1 + V2)
 
For second gas,
     P2V2 = P2' (V1 + V2)
   or, P2' = P2V2/ (V1 + V2)
 
Putting values of P1' and P2' in (ii), we get
     P = {P1V1/(V1+V2) + P2V2/(V1+V2)} …… (iii)
 
Since from equation (i) and (ii), the total pressure exerted by the mixture of gases is same, which is the sum of partial pressure exerted by a mixture of gases. Hence it proves Dalton’s law of partial pressure.

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