Ask A Scientist© Chemistry Archive

name         Nick
status       educator
age          30s
Question -
One liter of air containing 4% water vapor by volume(saturated),
contains how much liquid water?
How can this be empirically demonstrated?
I have been unable to find this concept discussed in any chemistry
references looked up so far. Perhaps you could direct me to a
source where this is talked about.
------------------------------------------------
Nick
It all falls out of the ideal gas law and the law of additive gas volumes:

PV,i = n,i*RT   and      V,gas = V,water +V,air    where i is some component
'i' and take M,water = 18 and M,air = 28.8.    The comma ',' is used to
identify the component. And n,i = g,i/M,i where g,i is the mass of component
'i'.

It goes like this:  0.04 = V,water / [V,water + V,air] = n,water/ [n,water
+n,air].

The common term RT/P in each term cancels out in numerator and denominator.
So:

0.04 = (g,water / 18) / [ g,water / 18 + g, air / 28.8 ]

Then fix either g, total or g, air to some convenient amount and solve for
the remaining unknown
g, water -- messy but straightforward in principle.

Vince Calder
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