# Can I calculate the amount (mol or mass) of water in a gas, in a heat exchanger, if I know the partial pressure of the water?

Is it possible to calculate the amount of water (mol, mass...) in a gas, in a heat exchanger, if I know the partial pressure of the water? The stream through the tubes is mainly benzene and hydrocarbons. Partial pressure of the water and the temperature is assumed constant.

I first tried to use the ideal gas law with the compressibility factor, but most people told me this equation is meant for closed systems (like in a tank) and not open systems like the one described. (If I'm wrong and it can be used, give me a good reason why so I understand).

Extra info: I need to calculate how much water is in the gas that will cause a relative humidity of 10 %. After taking the coldest temperature in the heat exchanger (because the RH would be highest here) as a constant, with the formula of relative humidity I can calculate the max partial pressure of water in the tubes thats would cause RH of 10 %. But I need the amount (mass, mol) that would be in the gas.

If you have any more questions, please ask.

## 1 Answer

To your challenge: Most people tell you ... is not a sound working principle for analysis. Molar volume (the inverse of molar density) does not care whether the gas is in an open system or a closed system. Recast your thought process in terms of either a molar volume (density) or take a basis of a certain (enclosed) volume of gas.

To your main question:

• Use Dalton's law $$y_{H_2O} = p_{H_2O}/p_T$$

• Assume a volume of the heat exchanger tubing or TAKE A BASIS of volume $$V_T$$

• Assume ideal gases: $$m_{H_2O} = y_{H_2O}(p_T V_T/RT)M_{H_2O}$$

Yes, you will not be able to determine $$m_{H_2O}$$ without a basis volume. That is however not the same as saying that you cannot use a gas law in an open system.