# Total pressure of saturated solution of air and Benzene [closed]

The question asked for me is - A sample of air is saturated with benzene (vapour pressure =100 mm Hg at 298 K) at 298 K, 750 mm Hg pressure.If it is isothermally compressed to one third of its initial volume, the final pressure of the system is -

In the solution part Total pressure is taken as Vapor Pressure of Benzene + Pressure of air. By this equation, Pressure of air is found. And by using PV = nRT air pressure after compression is found. And then the final pressure of the system is given as air pressure after the compression plus vapour pressure of the benzene.

Can you explain:

why can't we use total pressure of the container in PV=nRT that is P(initial)V(initial) = P(final)V(initial)/3 But rather the solution involves finding the pressure exerted by air and then using PV=nRT to find the final air pressure and adding the vapor pressure of benzene with the final air pressure. Also i was unclear how total pressure = Vapor pressure of benzene + Air pressure. And I was also unclear how vapor pressure of benzene does not change with the change in the volume of the container.

• You should explain what is unclear to you particularly and what you did to understand it, before asking here. Commented May 15 at 14:41
• why can't we use total pressure of the container in PV=nRT that is P(initial)V(initial) = P(final)V(initial)/3 But rather the solution involves finding the pressure exerted by air and then using PV=nRT to find the final air pressure and adding the vapor pressure of benzene with the final air pressure. Also i was unclear how total pressure = Vapor pressure of benzene + Air pressure. And I was also unclear how vapor pressure of benzene does not change with the change in the volume of the container. Commented May 15 at 14:48
• Consider condensation of saturated vapor when compressed. Commented May 15 at 14:49
• Oh! when we compress the system, some of the saturated benzene gets condensed thus making the vapor pressure same as it was in initial system. Commented May 15 at 14:53

## 1 Answer

The vapor pressure of a volatile substance in its saturated state does not change with change in volume at constant temperature. It is like when volume decreases isothermally, some of the saturated benzene condenses making vapor pressure the same as earlier. If the volume is increased (again isothermally and assuming enough benzene liquid in the system) some more benzene evaporates, and again the vapor pressure is the same as earlier. So vapor pressure does not change with the volume change.

That is the reason why we find only the change in air pressure due to change in volume and then add the vapor pressure of benzene to it.

NOTE: Here air pressure is not like vapor pressure. It changes with a volume change even if temperature is constant (Boyle's law).