# Quantity of water in air at saturation

1. Jan 19, 2010

### lesy1

Hi,
I would like to know if somebod knows where I could find a corelation to calculate the quantity of water in air at saturation in g/m3.
I know that many equations exist to calculate saturation pressure of water vapor in air as a function of temperature. Using one of these equations and an ideal gas law the quantity of water in air (in kg/m3) could be calculated, but I think that the asumptions for ideal gas law are not valid in my case.
Regards

2. Jan 19, 2010

### rcgldr

Last edited by a moderator: May 4, 2017
3. Jan 21, 2010

### lesy1

Jeff, thank you for the answer, although I did not find out anything new. The quantity I am looking for is also called saturation vapor density, but I cannot find any suitable model to calculate it. Can anybody please comment validity of using ideal gas law in my case.
Regards

4. Jan 21, 2010

### mgb_phys

If you assume it's an ideal gas then
PV = nRT where n is the number of moles, T is in kelvin

You can get the density from number of moles,
n = M/m = mass of water / molar mass of water (18 g/mole)

P* m / (R*T) = M/V = density

5. Jan 21, 2010

### Redbelly98

Staff Emeritus
The ideal gas law is valid. So your calculations would be correct, assuming no errors were made of course.

6. Jan 22, 2010

### lesy1

Redbelly, Y,
I am sure that ideal gas law could be used if humidity of air would be low, but because I have air with 100% relative humidity, something says to me, that I cannot use ideal gas law in this case.

7. Jan 22, 2010

### Yeti08

What equations are these? The saturation pressure is dependant on more than just temperature - it will change depending on the amount of water in the air. If you meant the saturation pressure of pure water vapor, then, yes, you can determine it from just temperature.

To solve your problem, a simple way is to assume that the air and water form and ideal binary mixture. You can then apply Raoult's law:

$$P=P^{*}_{w}\ x_{w}+P^{*}_{a}\ x_{a}$$

where P is the total apparent pressure, x is the mole fraction, P superscript * denotes the pure fluid pressure, and subscripts w and a are for water and air. For the water you would use the pure saturation pressure and for air I would just assume that the pressure is roughly the total pressure. You can then determine the number of moles and therefore the mass fractions and specific volume ratios using the ideal gas law. Doing a quick calc this returned a value with about a 3% error.

Another option would be to find a psychrometric chart at the pressure in question, though this may be difficult if your pressure is far from atmospheric pressure.

Finally, you can use published relations such as from “Formulations for the Thermodynamic Properties of the Saturated Phases of H2O from 173.15 K to 473.15 K", ASHRAE Transactions, Part 2A,Paper 2793 (RP-216), (1983), or you can use more complicated (i.e. non-ideal) binary mixture relations.

8. Jan 22, 2010

### Staff: Mentor

Best approach IMHO would be to take some engineering handbook and read values from tables - unless you really need them in functional form.