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Density and Molar Masses of Gases

Finding the Molar Mass of a Gas

Moles of  a gas    n=

grams of a gas   =   mass   =      m
molar mass of a gas molar mass molar mass

in the Ideal gas Law equation

P=

nRT

=

(m/molar mass)RT

=

mRT

<--Look m/v...=density

V V V(molar mass)

Substitute in density
 P= dRT (molar mass) So,     molar mass= dRT P So,     d= (molar mass)P RT R= 0.0821 atm L mol-1K-1
Example-

What is the density (g/L) of CO2 at 25oC, 1.8 atm ?

 d= (molar mass)P RT d= (44.0g/mol)(1.8atm) (0.0821 atm L mol-1K-1)298K d= 3.24g/L

 Example-Nitrogen is dissolved in water with the total pressure of gas (Nitrogen + water vapor) over the water being 3.00 atm. The temperature is 25oC. What is the concentration of Nitrogen in the water? Give your answer in g/L . The vapor pressure of water at 25.0oC is 23.8 mm Hg.

convert the pressure to mmHg to get the pressure of pure N2

3.00atm x 760mmHg=2280mmHg

subtract the water vapor pressure Ptot =PN2 +PH2O      2280mmHg Tot -23.8mmHg H2O=2256.2mmHg N2-->2.97atm

mm=dRT/P

so mmP/RT=d

(28g/mol x 2.97 atm)/ (0.0821 atmLmol-1K-1)(298K)=

3.40g/L   Does this make sense well at STP 28g/22.4L= 1.25g/L but the pressure is tripled so yes.