Answer :

Let the partial pressure of gas A and B be P’A and P’B respectively.


Given:


Pressure, temperature and volume of gas A PA TA, V


Pressure, temperature and volume of gas B PB, TB, V


We know that ideal gas equation


PV=nRT


Where V= volume of gas


R=gas constant =8.3JK-1mol-1


T=temperature


n=number of moles of gas


P=pressure of gas.


In a mixture of non-interacting ideal gases, the pressure that a gas in a mixture of gases would exert if it occupied the same volume as the mixture at the same temperature is called the partial pressure of that gas.


Using this definition volume of gas, A when gas B in not present, is 2V and temperature T.


So, from ideal gas equation


P’A2V=nRT


Also


PAV=nRTA


Equating nR from both the above equation




Doing the same above procedure for gas B


P’B2V=nRT


Also


PBV=nRTB




According to Dalton’s law of partial pressure, the total pressure of a mixture of ideal gas is the sum of partial pressures.





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