# Heat of Combustion & Respiratory Quotient Calculation

A Javascript that calculates the the Heat of Combustion and Respiratory Quotient (RQ) for fats and carbohydrates.

Carbon     Hydrogen     Oxygen

C=O     C-O-C     Rings

RQ      Mol Wt

Heat of Combustion kJ/mol      kcal/g

How to use
Type in the number of carbon, hydrogen and oxygen atoms in the molecule of interest, and the number of carbonyl and ether linkages, then press the Calculate! button.

For example, glucose has 6 carbons, 12 hydrogens, 6 oxygens and 1 carbonyl group (in the linear form). The respiratory quotient is 1.0. In metabolic measurements made via indirect calorimetry, the respiratory quotient is the ratio of the carbon dioxide produced to the oxygen consumed. An RQ of 1.0 indicates carbohydrates are being burned, while an RQ of 0.7 indicates that fats are being burned.

The molecular weight of glucose is 180 g/mol. The calculated heat of combustion is 2830 kJ/mol, or 3.8 kcals/g. Note that the common unit of calories used in nutrition actually refers to kilocalories.

Many other values are given in the Table.

How the calculation works
The respiratory quotient is the ratio of the carbon dioxide produced to the oxygen consumed in a complete combustion of the organic material. In the equation,

CnHmOq + rO2 --> nCO2 + (m/2) H2O

the value r can be determined from the other values, and the RQ is calculated as n/r.

For the heat of combustion calculation, the algorithm calculates the difference in the bond energies between the products and reactants. Based on the formula and the number of aldehyde and ether bonds, the number and type of all bonds can be derived for the reactant molecule. Likewise, the number of oxygen, carbon dioxide and water molecules and their bond energy can be calculated. The difference between the carbon dioxide/water bond energies and the reactant molecule/oxygen bond energies gives the heat of combustion.

By examining the Javascript source of this page, you can see the method used to determine the number and the bond energy for each type of bond. The values for the bond energies were optimized for the basis set in the Table. These bond energies are close to those given in physical chemistry texts, except for oxygen. The bond energy of molecular oxygen is usually quoted as about 500 kJ/mol, whereas the value optimized for calculation of fat/carbohydrate combustion is 390 kJ/mol. Using 500 kJ/mol, the accuracy of the calculation would only be about 20%, while with 390 kJ/mol the accuracy of almost all the results is within 2%. If you can figure out the source of this discrepancy, please let me know.

Thanks to Ksenia Nadkina for pointing out that previous versions of this page did not perform the calculation correctly for structures containing rings. This has now been fixed and the results for cycloalkanes seem to be fairly good. There is no adjustment for resonance energy, so for aromatic rings like benzene the values are an overestimate. You can try to adjust for this by subtracting 200 kJ/mol for each aromatic ring in your structure.

Version No. 5, July 22, 2009. Please send comments to Jeffrey Clymer
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