Determine the mass of propane in a 10 L
tank if a temperature gauge on the tank reads 20^{o}C and a pressure gauge
on the tank reads 10 kPa.
Assume propane behaves
as an ideal gas, but verify this assumption. 


Read : 
Apply the Ideal Gas EOS to determine the
molar volume of the propane in the tank. If this value is greater than 20 L/mol, the IG EOS is accurate to within 1%.
Use the molar volume, the molecular weight and the volume of the tank to
determine the mass of propane in the tank. 










Given: 
V 
10 
L 



P_{gauge} 
10 
kPa 

T 
20 
^{o}C 
















Find: 
M_{C3} 
??? 
g 


























Assumptions: 
1 Assume the propane behaves as an ideal gas. Be sure to verify this
assumption. 










Equations
/ Data / Solve: 


















We could use the
following equation to determine the mass of propane in the tank if we knew the specific volume. 









Eqn 1 











Equations of state are
written in terms of the molar volume. So we need the following equation to
get from molar volume to the specific volume that we need to make use of Eqn 1. 








Eqn 2 











Now, we need to us the
Ideal Gas EOS to determine
the molar volume. 











Ideal
Gas EOS : 





Eqn 3 











Let's solve for the
molar volume because we know we will need this value to test whether the Ideal Gas EOS is applicable. 


















Eqn 4 











We need to be careful
with our units in Eqn 2. Let's
begin by looking up the Universal Gas Constant in my favorite units, J/molK. 







R 
8.314 
J/molK 











Next we need to
convert the temperature to Kelvins and the gauge pressure to absolute pressure in Pascals. 















T 
253.15 
K 















Assume: 
P_{atm} 
101.325 
kPa 







P_{abs} 
111.325 
kPa 








111,325 
Pa 











Plugging values into Eqn 2 yields: 


V 
0.018906 
m^{3}/mol 








18.91 
L/mol 











We can now look up the
molecular weight of propane: 

MW 
44.1 
g/mol 











Now, we can plug values
into Eqn 2 and then Eqn 1 to complete this solution. 


















( Watch the units here! ) 
V 
0.42870 
m^{3}/kg 

















M_{C3} 
0.02333 
kg 








23.33 
g 










Verify: 
Propane is not a
diatomic molecule. Therefore, it cannot be accurately treated as an ideal gas
unless its molar volume is greater than 20 L/mol. 











Above, we found the
molar volume of propane under the conditions in this problem is 18.91 L/mol. 











Therefore we conclude
that it may not be accurate to use the Ideal Gas EOS to solve this problem. 











You should probably
try a more sophisticated EOS such as the Generalized Compresibility EOS in this lesson or one of the equations of state in the next lesson. 










Answers : 
M_{C3} 
23.33 
g 

















(But this result is
not reliable because the Ideal Gas assumption is not valid. A more accurate analysis yields M_{C3} = 24.1 g.) 









