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.

 

 

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