Hydrogen and methanol (CH3OH) have both been proposed as alternatives to hydrocarbon fuels.
a) Write balanced chemical equations for the complete combustion of hydrogen and the complete combustion of gaseous methanol.
Combustion reaction for hydrogen:
2H2(g)+ O2 --> 2H2O(l)
Combustion reaction for methanol:
2CH3OH(g) + 3O2(g) --> 2CO2(g) + 4H20(l)
b) Now use standard enthalpies of formation to calculate Delta H reaction for each of these reactions.
Delta H reaction for hydrogen combustion= -285.8 Delta H
[(2*0)+(1*0)] - [(-285.8)] = -285.8
Delta H reaction for methanol combustion = -1135 Delta H
[(2*-393.5)+(4*-187.8)] - [(2*-201.0)+(3*0)]=
-1537-(-402)=-1135 Delta H
c) Finally, calculate the amount of heat released per kilogram of the fuel.
I am having troubles with this one. What I am thinking is that I use the Delta H of what I got above which is in kJ/mol so for hydrogen -285.8kJ/mol and since this is hydrogen gas I figured that a molar mass would be appropriate since it has grams and moles but when I looked at it harder I don't see how I am going to get rid of the kJ with a molar mass. There must be a step I am missing?
For hydrogen combustion above. You have calculated that heat released is 285.8 (you don't write a unit; I presume this is kJ/mol) so we go with -285.8 kJ/4 g hydrogen. We want heat 1 kg (1000 g).
-285.8 kJ x (1000 g/4 g) = ??
To calculate the amount of heat released per kilogram of the fuel, you need to convert the molar enthalpy change (ΔH) to a mass-based enthalpy change. Here's how you can do that:
1. Determine the molar mass of the fuel.
- The molar mass of hydrogen (H2) is approximately 2 g/mol.
- The molar mass of methanol (CH3OH) is approximately 32 g/mol.
2. Convert the molar enthalpy change (ΔH) to kilojoules per gram.
- For hydrogen: ΔH/2 g = ΔH/2 kJ/g
- For methanol: ΔH/32 g = ΔH/32 kJ/g
3. Convert the kilojoules per gram to kilojoules per kilogram.
- Multiply the value obtained in step 2 by 1000 (since there are 1000 grams in a kilogram).
- For hydrogen: ΔH/2 kJ/g × 1000 g/kg = ΔH/2 kJ/kg
- For methanol: ΔH/32 kJ/g × 1000 g/kg = ΔH/32 kJ/kg
Now, you can plug in the values of ΔH for each fuel and perform the calculations:
- For hydrogen: ΔH = -285.8 kJ/mol
=> ΔH/2 = -285.8/2 kJ/mol
=> ΔH/2 kJ/mol × (2 g/mol) = -285.8 kJ
Dividing -285.8 kJ by the molar mass of hydrogen (2 g/mol), you get:
-285.8 kJ / 2 g = -142.9 kJ/g.
Now convert to kJ/kg:
-142.9 kJ/g × 1000 g/kg = -142,900 kJ/kg
Therefore, the amount of heat released per kilogram of hydrogen fuel is -142,900 kJ/kg.
- For methanol: ΔH = -1135 kJ/mol
=> ΔH/32 = -1135/32 kJ/mol
=> ΔH/32 kJ/mol × (32 g/mol) = -1135 kJ
Dividing -1135 kJ by the molar mass of methanol (32 g/mol), you get:
-1135 kJ / 32 g = -35.46 kJ/g.
Now convert to kJ/kg:
-35.46 kJ/g × 1000 g/kg = -35,460 kJ/kg
Therefore, the amount of heat released per kilogram of methanol fuel is -35,460 kJ/kg.
Note that the negative sign indicates that heat is released during the combustion process.
To calculate the amount of heat released per kilogram of the fuel, you need to convert the standard enthalpy change (Delta H) from kJ/mol to kJ/kg. Here's how you can do it:
1) Determine the molar mass of the fuel: For hydrogen, the molar mass is 2.016 g/mol, and for methanol, the molar mass is 32.04 g/mol.
2) Convert the Delta H from kJ/mol to kJ/g:
- For hydrogen: -285.8 kJ/mol * (1 mol/2.016 g) = -141.8 kJ/g
- For methanol: -1135 kJ/mol * (1 mol/32.04 g) = -35.41 kJ/g
3) Convert the Delta H from kJ/g to kJ/kg by multiplying by 1000:
- For hydrogen: -141.8 kJ/g * 1000 = -141,800 kJ/kg
- For methanol: -35.41 kJ/g * 1000 = -35,410 kJ/kg
Therefore, the heat released per kilogram of the fuel is approximately -141,800 kJ/kg for hydrogen and -35,410 kJ/kg for methanol.