[Needaask]

Here is the question: 5.​You have two l-liter containers connected to each other by a valve which is closed. In one container, you have liquid water in equilibrium with water vapor at 25°C. The other container contains a vacuum. Suddenly, you open the valve.  Discuss the changes that take place, assuming temperature is constant with regard to
(a) the vapor pressure,
(b) the concentration of the water molecules in the vapor,
(c) the number of molecules in the vapor state.
 
Answer: Vapour pressure and concentration of the gaseous molecules of the system remains essentially unchanged. Number of molecules doubled.

For (a) I agree that the vapour pressure remains the same. However, for (b) this was my thought process: Since P=F/A, and since the volume was doubled, the containers being of the same shape would have the same surface area. Hence the the surface area is doubled when the valve is opened. Since pressure remains the same, the force is also doubled. Hence the number of collisions per unit time would be the same. This would mean that the concentration is the same.

But thinking about it more deeply, if I double the volume it is not necessary that the surface area is doubled right? Because the piston adds to some surface area before removing it. So taking it away doesn't cause the surface area to double exactly right?

Then if it is not doubled then the frequency of collision would not be doubled and hence the concentration of the gas wouldn't be doubled too right?

So why can we simply say that the concentration would double? Are we assuming that the piston has a negligible surface area? Or is my concept here wrong?

Thanks

[Corribus]

I'm sorry, maybe I'm not following, but where was a piston mentioned in the problem?

The problem makes some assumptions (namely: the container(s) are in rapid thermal equilibrium with the external environment and that there is enough liquid water to fill both chambers with vapor but little enough that the volume of liquid can be ignored).

[Needaask]

I'm sorry, maybe I'm not following, but where was a piston mentioned in the problem?

The problem makes some assumptions (namely: the container(s) are in rapid thermal equilibrium with the external environment and that there is enough liquid water to fill both chambers with vapor but little enough that the volume of liquid can be ignored).

Oops sorry I meant that the valve was opened. But if we say that there is enough water to fill the entire space but not enough to reduce the surface area there is still that surface area of the valve there? Like after opening it up, the volume is doubled but the volume is not exactly doubled cos now the initially closed valve is now an open space. So wont the force not be doubled exactly?

And since temperature is a constant here, force is directly proportional to the frequency of collision. So now the frequency of collisions isn't exactly doubled. And the frequency of collision is proportional to the number of moles of the vapour, the number of moles won't be exactly doubled too. So now that concentration is number of moles/volume and volume is doubled while number of moles isn't exactly doubled (it's a little less depending on the surface area of the valve) won't the concentration of gas molcules be smaller than before?

[Corribus]

You are technically right but in problems like this it is convention to ignore the volume of the valve.

[Needaask]

You are technically right but in problems like this it is convention to ignore the volume of the valve.

Hi do you mean surface area of it too? Thanks but this question makes a lot of assumptions like the 2 you mentioned and this.

[Corribus]

Most homework problems do.   The goal isn't to represent reality.  It's to help teach you concepts.  That you are recognizing what assumptions are being made is a great sign - it's indicative of someone who is really thinking about what they're doing.  This is an important aspect of any experimental science.

[Needaask]

Most homework problems do.   The goal isn't to represent reality.  It's to help teach you concepts.  That you are recognizing what assumptions are being made is a great sign - it's indicative of someone who is really thinking about what they're doing.  This is an important aspect of any experimental science.

Haha thanks for the help