What is the mole fraction of water in the air and the dew point?

The weather man on channel 5 says the following: The temperature is 78 degrees F, the barometric pressure is 29.9 inches, and the relative humidity is 87%." What is the mole fraction of water in the air and the dew point?What is the mole fraction of water in the air and the dew point?
Get a Psychrometric Chart.

Following the abscissa (horizontal coord.) go to 87 deg. F (this is Dry Bulb) go then up along the ordinate (vertical coord.) until intersects 87% Relative Humidity, from that point, go right again along the abscissa until intersect water content, if units are given in pounds of water per pound of air, get the percentage by weight and transform to the proper values of molecular weights, the answer must come as % of moles of water to moles of air.

If the Psychrometric chart gives you the values in grains per pound of air. divide grains by 700 to get pounds.What is the mole fraction of water in the air and the dew point?
Below is a code for Engineering Equation Solver (EES). Get said software and execute this code.







BTW: I assume by "inches" as a pressure unit, you intend to say "inches of mercury". You need to be specific about this, because "inches of water" is also a pressure unit.



"!---Begin EES"

{Units:

kPa, mass basis, kg, Celsius, }



"Data (notice I convert all to the metric unit system...since I like it better)"

P1 = 29.9 [inHg] * convert(inHg, kPa)

T1 = converttemp(F, C, 78 [F])

phi1 = 0.87



"Assumptions:"

"1. Air is assumed defined as oxygen and nitrogen...and the water associated with the humidity. NOTHING ELSE"

"2. Standard Molar ratio of Nitrogen to Oxygen in air" J = 3.76

"3. Molar Mass of Nitrogen" Mn2 = 28 [kg/kmol]

"4. Molar Mass of Oxygen" Mo2 = 32 [kg/kmol]

"5. Molar Mass of Water" Mh2o = 18 [kg/kmol]



"Strategy:"

"Use EES's built in psychrometric functions to determine the mass mixing ratio (omega1) and the dew point (DP1)"

omega1 = HumRat(AirH2O, T=T1, r=phi1, P=P1)

DP1 = HumRat(AirH2O, T=T1, r=phi1, P=P1)



"Assume 1 kilogram of total dry air constituents in a particular parcel (it will not really matter how much you assume).



Use the definition of omega (mass of water/mass of dry air) along with definition of J and definition of molar mass to find:

1. the mass of water vapor in said parcel (mass_h2o)

2. the kilomoles of water vapor in said parcel (N_h2o)

3. the kilomoles of nitrogen in said parcel (N_n2)

4. the kilomoles of oxygen in said parcel (N_o2)



Remember, EES will autosolve your equations...so no need to do algebra"



mass_dry = 1 [kg]



"definition of omega"

omega1 = mass_h2o/mass_dry



"definition of molar mass, for each constituent"

M_h2o = mass_h2o/N_h2o

M_o2 = mass_o2/N_o2

M_n2 = mass_n2/N_n2



"Definition of mass of dry air:"

mass_dry = mass_o2 + mass_n2



"Definition of J:"

J = N_n2/N_o2



"Now to get molar fraction of water vapor, by its definition:"

X_h2o = N_h2o/(N_h2o + N_n2 + N_o2)



"!---End EES"