What Fraction of Water Vapor Condenses When Room Temperature Drops?

[leena19]

Homework Statement

The temperature of a room is 25 degree Celsius and its relative humidity (RH) is 60%.If the temperature is lowered to 15 degree Celsius,what fraction of water vapor gets condensed?
Saturated Vapour Pressure(SVP₂₅)at 25 degree celsius = 23.7mmHg
S.V.P.₁₅=12.8mmHg

Homework Equations

The Attempt at a Solution

RH= (m₁/M)*100%
where m₁= mass of water vapour present in the room ,at 25 deg celsius
M=mass of water vapour required to saturate the same volume of air

therefore 0.6M=m₁

At 15 degrees Celsius,water vapour present in the room gets condensed,so the room is now saturated(m₂) and RH is now 100% ?
If so fraction of water vapour condensed = (m₁-m₂)/m1?
But I don't know how I'm supposed to find m₂.

Hope someone can help.
Thanks

 

[cepheid]

I'm not sure either, but I find it interesting that you aren't using the information about the vapour pressures in your attempted solution at all. Their presence suggests that they are meant to be used in some way. What if you assumed that the vapour pressure of the water in the room is directly proportional to the amount (or mass) of water that is present in gaseous form? Furthermore, what if you assumed that the constant of proportionality does not change? Under these assumptions, the fractional change in vapour pressure will be the same as the fractional change in amount of water vapour. Can you see why?

 

[leena19]

Yes(I think?).cause at the same temperature and volume , mass is directly proportional to the pressure?

RH = (pressure of water vapour present in the room(P25)/SVP at 25 degrees celsius)*100%
60/100 = P25/23.7
P25 = 14.22mmHg

Now here comes my problem,
can I use the same relationship to find the partial pressure of saturated water vapour at 15 degree celsius?
Or is this partial pressure equal to the SVP at 15 degrees celsius?
If the latter were true,then the answer would be
=14.22-12.8/14.22
=0.1 ?
don't know but this answer just doesn't feel right

Heres another thread on SVPs i find difficult to understand
https://www.physicsforums.com/showthread.php?t=316332&highlight=vapour+pressure"
In this problem,I'm not sure but I think the OP had used the ideal gas equation,to find the mass of saturated water vapour.
Can we do that?Can we use the ideal gas equation for non-ideal saturated vapour as well?

 

[leena19]

I still don't know how to do this.
Hope someone can help.

Thanx

 

[chriscolose]

So the current vapor pressure is (0.6)*(23.7) = 14.22 mmHg. The saturation pressure at 15 C is 12.8 mmHg. So obviously 14.22 - 12.8 = 1.42 mmHg needs to condense out. You just need to find a fraction (or percentage). About 10% of the original vapor content needs to be lost to bring yourself to 100% R.H.

 

[leena19]

Thank you very much for replying

So the current vapor pressure is (0.6)*(23.7) = 14.22 mmHg. The saturation pressure at 15 C is 12.8 mmHg. So obviously 14.22 - 12.8 = 1.42 mmHg needs to condense out. You just need to find a fraction (or percentage). About 10% of the original vapor content needs to be lost to bring yourself to 100% R.H.

OK then the answer is 10%.

I have one more question,
If we were to use the equation ,
RH= (m1/M)*100%
where m1= mass of water vapour present in the room ,at 25 deg celsius
M=mass of water vapour required to saturate the same volume of air
therefore 0.6M=m1

can we use the ideal gas equation to solve this?
SVP₂₅=MrT₂₅ --------(1)
SVP₁₅=M₂rT₁₅----(2)
where m₂ is the mass of saturated vapour at 15 degrees C and r the gas constant.