- #1
treddie
- 91
- 2
I have a question about how to calculate the mass/mole of a combustion gas.
In my own research, I came across two methods. The first method is suspect in my opinion. The second I trust, although the discussion left some issues unexplained, so I attempted to fill in the details as best I could.
The following is a non-stoichiometric reaction in a rocket engine combustion chamber:
1C12H23.4 + 12.265O2 --> 11.7H2O + 6.415CO2 + 5.585C
It has an oxidizer to fuel mixture ratio (O/F) = 2.34.
As a check:
O/F =
12.265 * 31.998 g/mol (O2)
---------------------------------------------------------- = 2.34
(1 * 12 * 12.011 g/mol (C)) + (1 * 23.4 * 1.0079 g/mol (H))
Now we can find the total molar mass of the combustion products (NOT the
reactants) that actually create thrust. However, this method seems to miss an
important issue covered by the second method discussed later:
Moles of combustion products:
11.7 mol (H2O) + 6.415 mol (CO2) + 5.585 mol (C) = 23.7 mol
Total mass of combustion products:
(11.7*2*1.0079 g/mol(H)) + (11.7*1*15.999 g/mol(O)) +
(6.415*1*12.011 g/mol (C)) + (6.415*2*15.999 g/mol (O)) + (5.585*1*12.011 g/mol (C))
= 560.17233 g
Total molar mass of the combustion products as a gas mixture:
560.17233 g
------------ = 23.63596 g/mol
23.7 mol
But this seems incorrect, because it does not take into account the PROPORTION of the given mole
amounts with respect to their different molar masses. According to my references on Chemistry and
molar fractions, should not the following, second method be used?
Moles of combustion products:
11.7 mol (H2O)
6.415 mol (CO2)
5.585 mol (C)
Molar masses of the individual combustion products:
MolarMass (H2O) = (2 * 1.0079) + (1 * 15.999) = 18.0148 g/mol
MolarMass (CO2) = (1 * 12.011) + (2 * 15.999) = 44.009 g/mol
MolarMass (C) = (1 * 12.011) = 12.011 g/mol
Mass fractions of the combustion products:
f(H2O) =
11.7 [(2 * 1.0079) + (1 * 15.999)]
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .3763
f(CO2) =
6.415 [( 1 * 12.011) + (2 * 15.999)]
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .504
f(C) =
5.585( 1 * 12.011)
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .1197
Total molar mass of the combustion products as a gas mixture:
MolarMass(mixture) = [tex]\Sigma[/tex]fjMolarMassj = 30.3972 g/mol
Is the second method the correct approach, or am I totally missing the point?
In my own research, I came across two methods. The first method is suspect in my opinion. The second I trust, although the discussion left some issues unexplained, so I attempted to fill in the details as best I could.
The following is a non-stoichiometric reaction in a rocket engine combustion chamber:
1C12H23.4 + 12.265O2 --> 11.7H2O + 6.415CO2 + 5.585C
It has an oxidizer to fuel mixture ratio (O/F) = 2.34.
As a check:
O/F =
12.265 * 31.998 g/mol (O2)
---------------------------------------------------------- = 2.34
(1 * 12 * 12.011 g/mol (C)) + (1 * 23.4 * 1.0079 g/mol (H))
Now we can find the total molar mass of the combustion products (NOT the
reactants) that actually create thrust. However, this method seems to miss an
important issue covered by the second method discussed later:
Moles of combustion products:
11.7 mol (H2O) + 6.415 mol (CO2) + 5.585 mol (C) = 23.7 mol
Total mass of combustion products:
(11.7*2*1.0079 g/mol(H)) + (11.7*1*15.999 g/mol(O)) +
(6.415*1*12.011 g/mol (C)) + (6.415*2*15.999 g/mol (O)) + (5.585*1*12.011 g/mol (C))
= 560.17233 g
Total molar mass of the combustion products as a gas mixture:
560.17233 g
------------ = 23.63596 g/mol
23.7 mol
But this seems incorrect, because it does not take into account the PROPORTION of the given mole
amounts with respect to their different molar masses. According to my references on Chemistry and
molar fractions, should not the following, second method be used?
Moles of combustion products:
11.7 mol (H2O)
6.415 mol (CO2)
5.585 mol (C)
Molar masses of the individual combustion products:
MolarMass (H2O) = (2 * 1.0079) + (1 * 15.999) = 18.0148 g/mol
MolarMass (CO2) = (1 * 12.011) + (2 * 15.999) = 44.009 g/mol
MolarMass (C) = (1 * 12.011) = 12.011 g/mol
Mass fractions of the combustion products:
f(H2O) =
11.7 [(2 * 1.0079) + (1 * 15.999)]
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .3763
f(CO2) =
6.415 [( 1 * 12.011) + (2 * 15.999)]
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .504
f(C) =
5.585( 1 * 12.011)
------------------------------------------------------------------------------------
11.7[(2*1.0079) + (1*15.999)] + 6.415[( 1*12.011) + (2*15.999)] + 5.585[1*12.011)]
= .1197
Total molar mass of the combustion products as a gas mixture:
MolarMass(mixture) = [tex]\Sigma[/tex]fjMolarMassj = 30.3972 g/mol
Is the second method the correct approach, or am I totally missing the point?