Bond Energy Calculations

Bond energy calculations allow you to estimate the overall energy change for a reaction by comparing the energy needed to break bonds in the reactants with the energy released when new bonds form in the products. This is an Extended tier topic that links chemical bonding to energetics.

The method

1. Draw out the structural formulae of all reactants and products, showing every bond.
2. List all bonds broken in the reactants. Multiply each bond energy by the number of that bond broken.
3. Add up the total energy to break all bonds (this is energy input, always positive).
4. List all bonds made in the products. Multiply each bond energy by the number of that bond formed.
5. Add up the total energy to make all bonds (this is energy output, always positive when stated as energy released).
6. Calculate the overall energy change: energy change = energy to break bonds - energy to make bonds.

The formula

Energy change = sum of bond energies broken - sum of bond energies made

Where:

• A negative result means the reaction is exothermic (more energy released than absorbed)
• A positive result means the reaction is endothermic (more energy absorbed than released)

Worked examples

Example 1: Combustion of hydrogen

Question: Calculate the energy change for H2 + Cl2 -> 2HCl. Bond energies: H-H = 436 kJ/mol, Cl-Cl = 242 kJ/mol, H-Cl = 431 kJ/mol.

Working:

• Bonds broken: 1 x H-H = 436, 1 x Cl-Cl = 242. Total = 678 kJ
• Bonds made: 2 x H-Cl = 2 x 431 = 862 kJ
• Energy change = 678 - 862 = -184 kJ/mol

Answer: -184 kJ/mol (exothermic)

Examiner note: The negative sign indicates an exothermic reaction. More energy is released making H-Cl bonds than is needed to break H-H and Cl-Cl bonds.

Example 2: Combustion of methane

Question: Calculate the energy change for CH4 + 2O2 -> CO2 + 2H2O. Bond energies: C-H = 412 kJ/mol, O=O = 496 kJ/mol, C=O = 743 kJ/mol, O-H = 463 kJ/mol.

Working:

• Bonds broken: 4 x C-H = 4 x 412 = 1648, 2 x O=O = 2 x 496 = 992. Total = 2640 kJ
• Bonds made: 2 x C=O = 2 x 743 = 1486, 4 x O-H = 4 x 463 = 1852. Total = 3338 kJ
• Energy change = 2640 - 3338 = -698 kJ/mol

Answer: -698 kJ/mol (exothermic)

Examiner note: Methane has 4 C-H bonds. Water has 2 O-H bonds, and there are 2 water molecules, giving 4 O-H bonds total. Count every bond carefully.

Example 3: Formation of ammonia

Question: Calculate the energy change for N2 + 3H2 -> 2NH3. Bond energies: N-N triple bond = 944 kJ/mol, H-H = 436 kJ/mol, N-H = 388 kJ/mol.

Working:

• Bonds broken: 1 x N-N triple bond = 944, 3 x H-H = 3 x 436 = 1308. Total = 2252 kJ
• Bonds made: 6 x N-H = 6 x 388 = 2328 kJ (2 molecules of NH3, each with 3 N-H bonds)
• Energy change = 2252 - 2328 = -76 kJ/mol

Answer: -76 kJ/mol (exothermic)

Examiner note: There are 2 molecules of NH3, each with 3 N-H bonds, giving 6 N-H bonds total. This is a common counting error.

Example 4: An endothermic reaction

Question: Calculate the energy change for the decomposition of HBr: 2HBr -> H2 + Br2. Bond energies: H-Br = 366 kJ/mol, H-H = 436 kJ/mol, Br-Br = 193 kJ/mol.

Working:

• Bonds broken: 2 x H-Br = 2 x 366 = 732 kJ
• Bonds made: 1 x H-H = 436, 1 x Br-Br = 193. Total = 629 kJ
• Energy change = 732 - 629 = +103 kJ/mol

Answer: +103 kJ/mol (endothermic)

Examiner note: The positive value tells you this reaction is endothermic. More energy is needed to break the H-Br bonds than is released forming H-H and Br-Br bonds.

Example 5: Combustion of ethanol

Question: Calculate the energy change for C2H5OH + 3O2 -> 2CO2 + 3H2O. Bond energies: C-H = 412, C-C = 348, C-O = 360, O-H = 463, O=O = 496, C=O = 743 kJ/mol.

Working:

• Bonds broken in C2H5OH: 1 x C-C = 348, 5 x C-H = 2060, 1 x C-O = 360, 1 x O-H = 463. Subtotal = 3231
• Bonds broken in 3O2: 3 x O=O = 1488. Total broken = 3231 + 1488 = 4719 kJ
• Bonds made in 2CO2: 4 x C=O = 2972
• Bonds made in 3H2O: 6 x O-H = 2778. Total made = 2972 + 2778 = 5750 kJ
• Energy change = 4719 - 5750 = -1031 kJ/mol

Answer: -1031 kJ/mol (exothermic)

Examiner note: Drawing out the structural formula of ethanol (CH3CH2OH) helps you count the bonds correctly. There are 5 C-H bonds, not 6.

Common mistakes

1. Miscounting bonds. Draw structural formulae to count bonds accurately. Remember to multiply by the number of molecules (e.g., 2CO2 has 4 C=O bonds).
2. Subtracting in the wrong order. The formula is bonds broken minus bonds made. Reversing this gives the wrong sign.
3. Forgetting the sign. A negative answer means exothermic; a positive answer means endothermic. State which it is.
4. Using bond energies for ionic compounds. Bond energies apply only to covalent bonds. Do not use them for reactions involving ionic substances.
5. Not using the correct bond type. Distinguish between single (C-O), double (C=O) and triple (N-N triple) bonds. They have very different energies.

When this appears

Bond energy calculations are Extended tier content and appear on Paper 4. They connect to the chemical energetics topic and are often paired with energy profile diagram questions.