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How much water can evaporate?

  1. Jul 6, 2012 #1
    1. The problem statement, all variables and given/known data
    If the humidity in a room of volume 680m^3 at 25C is 80%, what mass of water can still evaporate from an open pan?


    2. Relevant equations

    RH = actual VP/Saturated VP
    Density = mass/volume

    3. The attempt at a solution

    I have no idea. I'm assuming there is some external information I'm supposed to use, but I don't know what it is. The answer to this problem is apparently 3.1kg.

    RH = actual/saturated, so Actual vapor pressure = saturated*RH = 23.8 torr * 0.8 = 19.04torr.

    Now I'm assuming you use the density equation, but do I use the density of water? Water vapor? dry air?

    How do I relate density back to the actual pressure?

    EDIT: Another thought.... using PV=nRT?
    If I do a whole lot of converting I get P=0.025atm, V = 680,000L, and T = 298K, where R = 0.0821 L*Atm/Mol*K.
    Even at that, I still end up with 12.6kg of water, which is still wrong...

    Considering in my review section this is labeled as a "beginner review" problem, I have to believe I'm missing something major here...
     
    Last edited: Jul 6, 2012
  2. jcsd
  3. Jul 6, 2012 #2

    phyzguy

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    Science Advisor

    Can the humidity in the room go above 100%?
     
  4. Jul 6, 2012 #3
    no. . . .
     
  5. Jul 6, 2012 #4
    to get to maximum saturation I still need an additional 4.76 torr of pressure, but I've run it through using those numbers and I'm getting further away from the right answer.
     
  6. Jul 6, 2012 #5

    phyzguy

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    Science Advisor

    I think your 4.76 torr partial pressure is correct. Check your conversion of this into atmospheres. How did you do this?
     
  7. Jul 6, 2012 #6
    4.76 torr / 760 = 0.006 atm

    I'm about 90 minutes into this problem and finally figured out how to do it about 5 minutes ago. Part of it was that I was looking for an answer of 3.1kg when I should have been looking for 3100 on the calculator since the conversion from moles turns it into grams. I ended up with 174 moles of water after a couple of attempts (both in units of atmospheres and liters as well as a shot with units of pascals and cubic meters). when I multiplied that by 18g/mol for water I would end up with 3132 kilograms (or so I thought)...but I still needed to convert that.

    I look at this and wonder why the heck I couldn't see this obvious mistake from the get-go....it's really not that hard.
     
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