Introduction to BOND ENTHALPY (Bond Energy) CALCULATIONS

Doc Brown's Chemistry KS4 GCSE, IGCSE, O level & A level Revision Notes

PART C Exothermic and Endothermic Energy Changes – Chemical Energetics – Introduction to the calculation of energy transfers using bond enthalpy (bond energy) values

 Sub-index for this page

6(a) Introduction to bond energies

6(b) Analysing a reaction in terms of bonds broken and forming

6(c) The progress of a chemical reaction expressed as an energy profile

6(d) A STARTER bond energy CALCULATION

6(e) Further examples of bond energy calculations

Index of GCSE level energetics notes

GCSE Chemistry Revision notes

5. (a) Calculation of heat transfer using bond energies (bond enthalpies)

• PLEASE NOTE that section 5. is for higher GCSE students and an introduction for advanced level students of how to do bond enthalpy (bond dissociation energy) calculations.

• Atoms in molecules are held together by chemical bonds which are the electrical attractive forces between the atoms.
• The bond energy is the energy involved in making or breaking bonds and is usually quoted in kJ per mole of the particular bond involved.
• To break a chemical bond requires the molecule to take in energy to pull atoms apart, which is an endothermic change.
  • Bond breaking absorbs energy – endothermic, you need energy to prize the atoms apart.
  • For example, on heating molecules to a sufficiently high temperature, the atoms of the bond vibrate more energetically until they spring apart, this takes place when the highest kinetic energy particles collide.
• To make a chemical bond, the atoms must give out energy to become combined and electronically more stable in the molecule, this is an exothermic change.
  • Bond formation releases energy – exothermic, the atoms become electronically more stable, lowering their energy.
• The difference between the energy absorbed in breaking bonds and the energy released on forming the bonds gives the overall energy change for the reaction.
• So in chemical reactions, bonds must be broken in the reactants (energy absorbed, endothermic) and new bonds are made (energy released, exothermic) in product formation.

6(b) Analysing a reaction in terms of bonds broken and forming

• These ideas are illustrated with the diagram below displaying the reaction between methane and chlorine to make chloromethane and hydrogen chloride.
• 
• The diagram shows the bonds being broken (C–H and Cl–Cl) and then the atoms or molecular fragments joining together by forming new bonds (C–Cl and H–Cl).
• The energy change for the reaction is the difference between the energy absorbed in bond breaking and the energy given out in bond formation.
  • This forms idea the basis for doing theoretical calculations of the overall energy released (exothermic) or absorbed (endothermic) in a reaction.

• The energy to make or break a chemical bond is called the bond enthalpy (bond energy) and is quoted in kJ/mol of bonds.
  • Bond energies refer to breaking (endothermic) or making (exothermic) one mole of bonds.
    • One mole here means 6.023 x 10²³ bonds, but I wouldn't worry about it!
  • Each bond has a typical value e.g. to break 1 mole of C–H bonds is on average about 413kJ,
  • the C=O takes an average 743 kJ/mol in organic compounds and 803 kJ/mol in carbon dioxide, and note the stronger double bond, so more energy is needed,
  • and not surprisingly, a typical double bond needs more energy to break than a typical single bond.

6(c) The progress of a chemical reaction expressed as an energy profiles

• During a chemical reaction, energy must be supplied to break chemical bonds in the molecules, this the endothermic 'upward' slope on the reaction profile (shown in detail below).
• When the new molecules are formed, new bonds must be made in the process, this is the exothermic 'downward' slope on the reaction profile (shown in detail below).
• If we know all the bond energies (enthalpies) f the molecules involved in a reaction, we can theoretically calculate what the net energy change is for that reaction and determine whether the reaction is exothermic or endothermic.
  • These arguments can then be used to explain why reactions can be exothermic or endothermic.
• We do this by calculating the energy taken in to break the bonds in the reactant molecules.
  • We then calculate the energy given out when the new bonds are formed.
  • The difference between these two gives us the net energy change i.e. the energy absorbed from the surroundings (endothermic) or given out to the surroundings (exothermic).
  • In a reaction energy must be supplied to break bonds (energy absorbed, taken in, endothermic).
  • Energy is released when new bonds are formed (energy given out, releases, exothermic).
  • If more energy is needed to break the original existing bonds of the reactant molecules, than is given out when the new bonds are formed in the product molecules, the reaction is endothermic i.e. less energy is released to the surroundings than is taken in to break the reactant molecule bonds.
  • If less energy is needed to break the original existing bonds of the reactant molecules, than is given out when the new bonds are formed in the product molecules, the reaction is exothermic i.e. more energy released to surroundings than is taken in to break bonds of reactants.
  • So the overall energy change for a reaction (ΔH) is the overall energy net change from the bond making and bond forming processes. This idea is illustrated by the energy level diagrams and energy profile diagrams shown below.
  • overall energy change for an exothermic reaction
  • the energy profile for an exothermic reaction, now showing the activation energy and the idea of heat energy being absorbed to break bonds. The endothermic bond breaking process absorbs energy, the exothermic bond forming process gives out energy. More energy is released in bond formation in the products than the energy absorbed in breaking the bonds of the reactants. Therefore overall energy is transferred to the surroundings, an exothermic reaction (exothermic heat transfer).
  • overall energy change for an endothermic reaction
  • the energy profile for an endothermic reaction, now showing the activation energy and the idea of heat energy being absorbed to break bonds. The endothermic bond breaking process absorbs energy, the exothermic bond forming process gives out energy. Less energy is released in bond formation in the products than the energy absorbed in breaking the bonds of the reactants. Therefore overall energy is absorbed from the surroundings, an endothermic reaction (endothermic heat transfer).
  • These ideas are illustrated in the theoretical calculations below,
  • starting the reaction between methane and chlorine, an important sort of industrial reaction to make chlorinated hydrocarbons.

• methane + chlorine ==> chloromethane + hydrogen chloride
  • 
  • So, how can we theoretically calculate the energy change for this reaction?
  • The picture above shows how it is done
    • It looks complicated, but in this case you are only breaking two bonds (a C-H and a Cl-Cl) and only making two new bonds (a C-Cl and a H-Cl).
  • CH₄ + Cl₂ ==> CH₃Cl + HCl  is how we normally write the equation, BUT, using full displayed formula is often a much better approach because you can see all the bonds involved clearly.
  • To appreciate all the bonds in the molecules its better to set out as follows ...
  • + Cl–Cl ===> + H–Cl
  • Then by using the displayed formula equation above you can now do the calculation and what its all about in terms of the introductory discussion at the start of the page.
  • Bond energies: The energy required to break or make 1 mole of a particular bond in kJ/mol
  • C–H = 412, Cl–Cl = 242 kJ/mol, C–Cl = 331 kJ/mol, H–Cl = 432
  • First, imagine which bonds must be broken to enable the reaction to proceed.
  • The energy absorbed equals that to break one C–H bond (in methane molecule) plus energy to break one Cl–Cl bond (in chlorine molecule), both endothermic changes – 'bond breaking'.
    • Therefore energy required to break the C-H and Cl-Cl bonds = 412 + 242 = 654 kJ per mole
  • Theoretically imagine you've got these atomic or molecular fragments, put them together to form the products, in doing so, work out which bonds must be formed to give the products.
  • The energy released is that given out when C–Cl bond (in chloromethane molecule) is formed plus the energy released when one H–Cl bond (in hydrogen chloride molecule) is formed, both exothermic changes – 'bond making'.
    • Therefore energy released on making the C-Cl and H-Cl bonds = 331 + 432 = 763 kJ per mole
  • Calculating the difference in the two sums gives the numerical energy change and since more heat energy is given out to the surroundings in forming the bonds than that absorbed in breaking bonds, the reaction must be exothermic.
    • energy change = energy released on bond formation - energy absorbed in bond breaking
    • energy change = 763 - 654 = 109 kJ per mole equation
    • Since more heat is released than heat absorbed the reaction is exothermic
    • and the energy change is written as -109 kJ/mol per mole equation.
    • Remember exothermic reaction energy values are written with a negative sign - energy lost to the surroundings and endothermic reaction energy values are written with a positive sign.
    • -

6(e) Further examples of bond energy calculations (some easier than above, and some a bit harder!)

• Just work through the examples line by line.

Example 5.1 Hydrogen + Chlorine ==> Hydrogen Chloride

• The usual symbol equation is: H_2(g) + Cl_2(g) ==> 2HCl_(g)

• but think of it as: H–H + Cl–Cl ==> H–Cl + H–Cl   (displayed formula style)

• (where – represents the chemical bonds to be broken or formed)

• the bond energies in kJ/mol are: H–H 436; Cl–Cl 242; H–Cl 431

• Energy needed to break bonds = 436 + 242 = 678 kJ taken in

• Energy released on bond formation = 431 + 431 = 862 kJ given out

• The net difference between them = 862–678 = 184 kJ given out

• More energy is given out than taken in, so the reaction is exothermic.

• So the energy change is written as -184 kJ/mol

• (actually -92 kJ per mole of HCl formed)

• -

Example 5.2 Hydrogen Bromide ==> Hydrogen + Bromine

• The usual symbol equation is: 2HBr_(g) ==> H_2(g) + Br_2(g)

• but think of it as: H–Br + H–Br ==> H–H + Br–Br

• (where – represents the chemical bonds to be broken or formed)

• the bond energies in kJ/mol are: H–Br 366; H–H 436; Br–Br 193

• Energy needed to break bonds = 366 + 366 = 732 kJ taken in

• Energy released on bond formation = 436 + 193 = 629 kJ given out

• The net difference between them = 732–629 = 103 kJ taken in

• More energy is taken in than given out, so the reaction is endothermic

• So the energy change is written as +103 kJ/mol

• (actually +51.5kJ per mole of HBr decomposed)

Example 5.3 hydrogen + oxygen ==> water

• 

• 2H_2(g) + O_2(g) ==> 2H₂O_(g)

• or think of it as in the diagram above

  • 2 H–H  +  O=O ==> 2 H–O–H

    • (where – or = represent the single or double covalent bonds)

• bond energies in kJ/mol: H–H is 436, O=O is 496 and O–H is 463

• bonds broken and energy absorbed (taken in):

• (2 x H–H) + (1 x O=O) = (2 x 436) + (1 x 496) = 1368 kJ

• bonds made and energy released (given out):

• (4 x O–H) = (4 x 463) = 1852 kJ

• overall energy change is:

• 1852 – 1368 = 484 kJ given out - exothermic

• since more energy is given out than taken in, the reaction is exothermic.

  • Therefore the energy change is written as -484 kJ/mol equation

    • (actually -242 kJ per mole hydrogen burned or per mole of water formed)

• NOTE: Hydrogen gas can be used as fuel and a long–term possible alternative to fossil fuels (see methane combustion below in example 5..

  • It burns with a pale blue flame in air reacting with oxygen to be oxidised to form water.

  • hydrogen + oxygen ==> water

  • 2H_2(g) + O_2(g) ==> 2H₂O_(l) 

  • It is a non–polluting clean fuel since the only combustion product is water and so its use would not lead to all environmental problems associated with burning fossil fuels.

  • It would be ideal if it could be manufactured cheaply by electrolysis of water e.g. using solar cells, otherwise electrolysis is very expensive due to high cost of electricity.

  • Hydrogen can be used to power fuel cells.

Example 5.4 nitrogen + hydrogen ==> ammonia

• N_2(g) + 3H_2(g) ==> 2NH_3(g)

• or NN + 3 H–H ==> 2

• bond energies in kJ/mol: NN is 944, H–H is 436 and N–H is 388

• bonds broken and energy absorbed (taken in):

  • (1 x NN) + (3 x H–H) = (1 x 944) + (3 x 436) = 2252 kJ

• bonds made and energy released (given out):

  • 2 x (3 x N–H) = 2 x 3 x 388 = 6 x 388 = 2328 kJ

• overall energy change is: 

  • 2328 – 2252 = 76 kJ given out - exothermic

  • Therefore energy change = -76 kJ/mol equation

  • (actually -38 kJ per mole of ammonia formed)

• since more energy is given out than taken in, the reaction is exothermic.

Example 5.5 methane + oxygen ==> carbon dioxide + water

• CH_4(g) + 2O_2(g) ==> CO_2(g) + 2H₂O_(g)

• or

• or using displayed formulae

• bond energies in kJ/mol:

  • C–H single bond is 412, O=O double bond is 496, C=O double bond is 803 (in carbon dioxide), H–O single bond is 463

• bonds broken and heat energy absorbed from surroundings, endothermic change

  • (4 x C–H) + 2 x (1 x O=O) = (4 x 412) + 2 x (1 x 496) = 1648 + 992 = 2640 kJ taken in

• bonds formed and heat energy released and given out to surroundings, exothermic change

  • (2 x C=O) + 2 x (2 x O–H) = (2 x 803) + 2 x (2 x 463) = 1606 + 1852 = 3458 given out

• overall energy change is:

  • 3338 – 2640 = 818 kJ/mol given out per mole methane burned,

  • since more energy is given out than taken in, the reaction is exothermic.

  • Energy change = –818 kJ/mol

• At Advanced Level this will be expressed as enthalpy of combustion = ΔH_comb = –818 kJ/mol

• This shows that heats of combustion can be theoretically calculated.

• NOTE: This is the typical very exothermic combustion chemistry of burning fossil fuels but has many associated environmental problems. (see Oil Notes)

• -

• ethyl ethanoate

  • 2 x C–C single covalent bonds

  • 8 x C–H single covalent bonds

  • 2 x C–O single covalent bonds

  • 1 x C=O double covalent bond

• ethanol

  • 1 x C–C single covalent bond

  • 5 x C–H single covalent bonds

  • 1 x C–O single covalent bond

  • 1 x O–H single covalent bond

• If you wanted to work out the theoretical enthalpy/heat of combustion of propane, you could base your calculation on the displayed formula equation

• 

• Endothermic bond breaking: 8 C–H bonds broken, 2 C–C bonds broken, 5 O=O bonds broken.

• Exothermic bond formation: 6 x C=O bonds made, 8 x O–H bonds made.

• See also A Level Chemistry Notes on Bond Enthalpy Calculations

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Sub–index for ENERGY CHANGES:

1. Heat changes in chemical/physical changes – exothermic and endothermic

2. Reversible reactions and energy changes

3. Activation energy and reaction profiles

4. Catalysts and activation energy 

5. Introduction to bond energy/enthalpy calculations

6. Calorimeter methods of determining energy changes

7. Energy transfer calculations from calorimeter results

See also Advanced A Level Energetics–Thermochemistry – Enthalpies of Reaction, Formation & Combustion

and enthalpy calculations from calorimetry data for Advanced A Level chemistry students

Advanced A Level Energetics INDEX of revision notes on thermochemistry, enthalpy, entropy etc.

• LINKS to other associated webpages

  • Foundation tier–easier multiple choice GCSE QUIZ on exothermic/endothermic reactions etc.

  • Higher tier–harder multiple choice GCSE QUIZ on exothermic/endothermic reactions etc.

  • GCSE/IGCSE/O level notes on Oil–Fuel burning

  • GCSE/IGCSE/O level Types of Chemical Reaction Notes

  • GCSE/IGCSE/O Level Rates of Reaction Revision Notes