Fuel values, reported in units of KJ/g, are useful in comparing the efficiency of various energy sources on a mass basis. Determine the fuel value of the glucose and the tristearin. Which one, carbohydrates or fats, have the highest fuel value (and hence is the most efficient energy source on a mass basis)?
Glucose C6H12O6, DHf -1260.04 KJ/mol
Tristearin C57H110O6, DHf -390.70 KJ/mol
C6H12O6 + 6O2 ==> 6CO2 + 6H2O
dHrxn = (n*dHf products) - (n*dHf reactants) and dHrxn will be in kJ/mol.
Divide by 1 and divide by molar mass C6H12O6 to get kJ/gram. To convert to fuel value change the negative sign to a + sign.
Do the same for tristearin. The equation is
2C57H110O6 + 163O2 ==> 114CO2 + 110H2O
Here the answer is in kJ/mol so you divide by 2 (to convert from 2 mols to 1 mol) the divide by molar mass of trisearin. Then change the - number to + number.
Compare the two. The larger + number wins.
To determine the fuel value of glucose and tristearin, we need to calculate their energy released per gram.
First, let's convert the given enthalpy of formation (DHf) values from kilojoules per mole to kilojoules per gram.
For glucose:
Molar mass of glucose (C6H12O6) = 180.16 g/mol
DHf of glucose = -1260.04 KJ/mol
To convert KJ/mol to KJ/g, we divide by the molar mass:
Fuel value of glucose = (-1260.04 KJ/mol) / (180.16 g/mol) = -7.0 KJ/g
For tristearin:
Molar mass of tristearin (C57H110O6) = 885.57 g/mol
DHf of tristearin = -390.70 KJ/mol
Again, to convert KJ/mol to KJ/g, we divide by the molar mass:
Fuel value of tristearin = (-390.70 KJ/mol) / (885.57 g/mol) = -0.4 KJ/g
Comparing the fuel values, we see that glucose has a higher fuel value (-7.0 KJ/g) compared to tristearin (-0.4 KJ/g). Therefore, carbohydrates (glucose) have a higher fuel value and are more efficient energy sources on a mass basis compared to fats (tristearin).