Figure shows two vessels A and B with rigid walls containing ideal gases. The pressure, temperature and the volume are pA. TA, V in the vessel A and pB, TB, V in the vessel B. The vessels are now connected through a small tube. Show that the pressure p and the temperature T satisfy.
When equilibrium is achieved.
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.