Q. how to calculate enthalpy of combustion

Definition. The enthalpy of combustion is the enthalpy change when one mole of a substance undergoes complete combustion with oxygen under specified conditions. It is usually reported as the standard molar enthalpy of combustion, written as \( \Delta H^\circ_{\text{comb}} \). A negative value means the reaction is exothermic, and a positive value would mean endothermic.

General method using standard enthalpies of formation. Follow these steps exactly.

Step 1. Write and balance the chemical equation for the complete combustion of one mole of the fuel. Make sure all coefficients are the smallest whole numbers. For example, the balanced combustion equation for methane as one mole of fuel is
\[ \text{CH}_4 + 2\,\text{O}_2 \rightarrow \text{CO}_2 + 2\,\text{H}_2\text{O} \]
In this equation one mole of methane reacts with two moles of oxygen to give one mole of carbon dioxide and two moles of water.

Step 2. Use the standard enthalpies of formation, \( \Delta H_f^\circ \), for every substance in the balanced equation. By Hesss law the enthalpy of combustion per mole of fuel equals the sum of the standard enthalpies of formation of the products (each multiplied by its stoichiometric coefficient) minus the sum of the standard enthalpies of formation of the reactants (each multiplied by its stoichiometric coefficient). Write this as a formula.
\[ \Delta H^\circ_{\text{comb}} = \sum_{\text{products}} \nu_i \, \Delta H_f^\circ(i) \;-\; \sum_{\text{reactants}} \nu_j \, \Delta H_f^\circ(j) \]
Here \( \nu \) denotes stoichiometric coefficients and \( \Delta H_f^\circ \) are standard molar enthalpies of formation, usually in kJ mol^{-1}.

Step 3. Look up numerical values for \( \Delta H_f^\circ \) of each species in the equation, using consistent standard states and units. Standard values commonly used are, for example: carbon dioxide gas \( \Delta H_f^\circ(\text{CO}_2,g) = -393.5\ \text{kJ mol}^{-1} \), liquid water \( \Delta H_f^\circ(\text{H}_2\text{O},l) = -285.8\ \text{kJ mol}^{-1} \), methane gas \( \Delta H_f^\circ(\text{CH}_4,g) = -74.8\ \text{kJ mol}^{-1} \), and oxygen gas \( \Delta H_f^\circ(\text{O}_2,g) = 0\ \text{kJ mol}^{-1} \). Ensure you use water liquid or gas consistently with the equation and data source.

Step 4. Substitute the values into the formula and evaluate the sums. For the methane example substitute the coefficients and values:
\[ \Delta H^\circ_{\text{comb}} = \bigl[1\cdot \Delta H_f^\circ(\text{CO}_2) + 2\cdot \Delta H_f^\circ(\text{H}_2\text{O},l)\bigr] – \bigl[1\cdot \Delta H_f^\circ(\text{CH}_4) + 2\cdot \Delta H_f^\circ(\text{O}_2)\bigr] \]
Now insert numbers:
\[ \Delta H^\circ_{\text{comb}} = \bigl[1\cdot (-393.5) + 2\cdot (-285.8)\bigr] – \bigl[1\cdot (-74.8) + 2\cdot 0\bigr]\ \text{kJ mol}^{-1} \]
Compute the sums step by step: first the products sum is \( -393.5 + 2(-285.8) = -393.5 -571.6 = -965.1\ \text{kJ mol}^{-1} \). The reactants sum is \( -74.8 + 0 = -74.8\ \text{kJ mol}^{-1} \). Therefore
\[ \Delta H^\circ_{\text{comb}} = -965.1 – (-74.8) = -965.1 + 74.8 = -890.3\ \text{kJ mol}^{-1} \]
So the standard molar enthalpy of combustion of methane is \( -890.3\ \text{kJ mol}^{-1} \), using the above standard formation values and liquid water.

Step 5. Interpret the sign and units. The negative sign indicates the reaction is exothermic. The units are energy per mole of fuel, typically kJ mol^{-1}. If you used one mole of fuel in the balanced equation, the result is per mole. If your equation used a different reference amount, divide or scale to get per mole.

Alternative approximate method using bond energies. If standard formation data are not available, you can estimate the enthalpy change by summing bond enthalpies. Use the approximation
\[ \Delta H \approx \sum \text{(bond energies broken)} \;-\; \sum \text{(bond energies formed)} \]
This gives a rough estimate because bond energies are average values and depend on molecular environment. To use this: count every bond broken in reactants and every bond formed in products, multiply by the appropriate average bond enthalpy, perform the subtraction, and report the result in kJ per mole of reaction as written. Expect larger uncertainty than the formation enthalpy method.

Practical checklist before reporting a final value. Always ensure the chemical equation is balanced, use consistent reference states and units, use reliable data for \( \Delta H_f^\circ \) or bond energies, and specify whether water is liquid or gas. State whether the reported number is per mole of fuel and whether values are standard (\( \Delta H^\circ \) at 1 bar and a specified temperature, typically 298.15 K).