What is the density of water vapor at room temperature?
1 Answer
Explanation:
The first thing to do here is to pick a temperature that can be considered room temperature. I'll go with
#T["K"] = 20^@"C" + 273.15 = "293.15 K"#
Next, look up the partial pressure of water vapor at
#P = "0.0230 atm"#
http://www.endmemo.com/chem/vaporpressurewater.php
Now, that you have a pressure and a temperature to work with, use the ideal gas law equation to find the density of water vapor.
#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#
Here you have
#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant
#T# - the absolute temperature of the gas
Let's assume that your room contains a mass
#n = m/M_("M H"_2"O")#
Plug this into the ideal gas law equation to get
#PV = m/M_("M H"_2"O") * RT#
As you know, density,
#P = m/M_("M H"_2"O") * 1/V * RT#
#P * M_("M H"_2"O") = m/V * RT#
#m/V = (P * M_ ("M H"_ 2"O"))/(RT) implies color(purple)(|bar(ul(color(white)(a/a)color(black)(rho = M_ ("M H"_2"O") * P/(RT))color(white)(a/a)|)))#
Water has a molar mass of
#rho = "18.015 g"color(red)(cancel(color(black)("mol"^(-1)))) * (0.0230 color(red)(cancel(color(black)("atm"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * "L")/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 293.15 color(red)(cancel(color(black)("K"))))#
#color(green)(|bar(ul(color(white)(a/a)color(black)(rho = "0.0172 g L"^(-1))color(white)(a/a)|)))#