Bond Enthalpy Calculations (SL IB Chemistry)

• In 1840, the Russian chemist Germain Hess formulated a law which went on to be known as Hess’s Law
• This went on to form the basis of one of the laws of thermodynamics. The first law of thermodynamics relates to the Law of Conservation of Energy
• It is sometimes expressed in the following form:

Energy cannot be created or destroyed, it can only change form

• This means that in a closed system, the total amount of energy present is always constant
• Hess’s law can be used to calculate the standard enthalpy change of a reaction from known standard enthalpy changes
• Hess’s Law states that:

"The total enthalpy change in a chemical reaction is independent of the route by which the chemical reaction takes place as long as the initial and final conditions are the same."

• This means that whether the reaction takes place in one or two steps, the total enthalpy change of the reaction will still be the same

Diagram to show Hess's Law

The diagram above illustrates Hess’ Law: the enthalpy change of the direct route, going from reactants (A+B) to product (C) is equal to the enthalpy change of the indirect routes

• Hess’ Law is used to calculate enthalpy changes which can’t be found experimentally using calorimetry, eg:

3C (s) + 4H₂ (g) → C₃H₈(g)

• ΔH_f (propane) can’t be found experimentally as hydrogen and carbon don’t react under standard conditions

Calculating ΔH_r from ΔH_f using Hess’s Law energy cycles

• You can see the relationships on the following diagram:

Diagram to show Hess's Law 

The enthalpy change from elements to products (direct route) is equal to the enthalpy change of elements forming reactants and then products (indirect route)

 

• The products can be directly formed from the elements = ΔH₂

OR

• The products can be indirectly formed from the elements = ΔH₁ + ΔH_r

• Equation

ΔH₂ = ΔH₁ + ΔH_r

Therefore for energy to be conserved,

ΔH_r = ΔH₂ – ΔH₁

Average bond energy

• Bond energies are affected by other atoms in the molecule (the environment)
• Therefore, an average of a number of the same type of bond but in different environments is calculated
• This bond energy is known as the average bond energy and is defined as
  • 'The energy needed to break one mole of bonds in a gaseous molecule averaged over similar compounds

Average bond enthalpy of C-H in methane

• The average bond enthalpy of C-H is found by taking the bond dissociation enthalpy for the whole molecule and dividing it by the number of C-H bonds
• The first C-H bond is easier to break than the second as the remaining hydrogens are pulled more closely to the carbon
• However, since it is impossible to measure the energy of each C-H bond an average is taken
• This value is also compared with a range of similar compounds to obtain an accepted value for the average bond enthalpy

Bond enthalpy calculations

• Bond energies are used to find the ΔH^ꝋ_r of a reaction when this cannot be done experimentally
• The process is a step-by-step summation of the bond enthalpies of the all the molecules present finishing with this formula:

Formula for calculating the standard enthalpy change of reaction using bond energies

• These two worked examples show how to lay out your calculation