Bond enthalpy measures the energy stored within a chemical bond, indicating its strength and stability. It is defined as the energy required to break one mole of a specific bond in the gaseous state. Calculating total energy changes in chemical reactions relies on these values, as reactions involve breaking old bonds and forming new ones. By comparing the energy required to break reactant bonds with the energy released when product bonds form, chemists determine the overall energy change, known as the enthalpy of reaction (\(\Delta H_{rxn}\)).
Understanding Bond Enthalpy and Necessary Data
The values used for these calculations are typically averaged across many different molecules containing that bond type, referred to as the average bond enthalpy. This differs from the Bond Dissociation Energy (BDE), which is the energy required to break a specific bond in a single molecule. Since surrounding atoms can influence bond strength, using the average value provides a good estimation for a wide range of chemical processes.
The calculation method relies on two principles. Bond breaking is always an endothermic process, requiring energy input from the surroundings, which gives the energy values a positive sign. Conversely, bond formation is an exothermic process, releasing energy into the surroundings, represented by a negative sign. This occurs because atoms move to a lower, more stable energy state when they form a bond, releasing excess energy.
To perform any calculation, a table of standard average bond enthalpies is required, usually expressed in kilojoules per mole (\(\text{kJ/mol}\)). These data points represent the energy needed to break one mole of a given bond, such as C-H or O=O.
The General Formula for Enthalpy Change
The overall enthalpy change for a reaction, \(\Delta H_{rxn}\), is the net difference between the energy absorbed during bond breaking and the energy released during bond formation. The calculation assumes two stages: reactant bonds are broken, and then product bonds are formed. The governing relationship is: \(\Delta H_{rxn} = \sum (\text{Energy of Bonds Broken}) – \sum (\text{Energy of Bonds Formed})\).
The first term (bonds broken) is positive, representing the absorbed energy input. The second term (bonds formed) is subtracted to account for the energy released. Subtracting the released energy from the absorbed energy determines if the overall reaction absorbed energy (positive \(\Delta H_{rxn}\)) or released energy (negative \(\Delta H_{rxn}\)).
Preparatory Steps
Before applying this formula, two preparatory steps are necessary. The chemical reaction must first be written as a balanced equation to ensure the correct number of moles of each reactant and product is considered. Second, the Lewis structures of all reactant and product molecules must be drawn. This identifies every single, double, or triple bond present, allowing for a precise count of the type and number of bonds broken and formed.
Step-by-Step Calculation Walkthrough
To illustrate the procedure, consider the combustion of methane: \(\text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O}\). The first step is to quantify the bonds broken in the reactants: four C-H single bonds in methane and two O=O double bonds in oxygen.
Using average bond enthalpy values (C-H \(\approx 413 \text{ kJ/mol}\), O=O \(\approx 495 \text{ kJ/mol}\)), the total energy absorbed is calculated by summing the products of bond count and energy:
\((4 \times 413 \text{ kJ/mol}) + (2 \times 495 \text{ kJ/mol}) = 1652 \text{ kJ/mol} + 990 \text{ kJ/mol} = 2642 \text{ kJ/mol}\). This is the total energy input.
Next, identify the bonds formed in the products: two C=O double bonds and four O-H single bonds. Using their respective average bond enthalpies (C=O \(\approx 799 \text{ kJ/mol}\), O-H \(\approx 485 \text{ kJ/mol}\)), the total energy released upon formation is calculated:
\((2 \times 799 \text{ kJ/mol}) + (4 \times 485 \text{ kJ/mol}) = 1598 \text{ kJ/mol} + 1940 \text{ kJ/mol} = 3538 \text{ kJ/mol}\).
The final step applies the formula: \(\Delta H_{rxn} = 2642 \text{ kJ/mol} – 3538 \text{ kJ/mol}\). The resulting enthalpy change is \(-896 \text{ kJ/mol}\). The negative sign indicates the reaction is exothermic, meaning more energy was released during bond formation than was absorbed during bond breaking.