Topic 2.1: Energetics I

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2.1a Enthalpy change
Enthalpy (H) is the heat content of a system.  In a reaction this may increase or decrease and produce an enthalpy change (/\H).
/\H = H₂ - H₁
where   H₁ = enthalpy of reactants and H₂ = enthalpy of products
The enthalpy change is affected by pressure and temperature so standard conditions are used for measurements.  These conditions are 1 atmosphere pressure and a temperature of 25^oC or 298K.
for 2H₂(g) + O₂(g) -----> 2H₂O(l) standard enthalpy of reaction /\H^o ₂₉₈ = -571.6 kJmol^-1
This enthalpy change is per mole of equation.

2.1b Exothermic and endothermic reactions
An exothermic reaction is one in which heat is given out.  It results in a temperature increase.  /\H is given a negative sign to indicate an exothermic reaction, e.g.
2H₂(g) + O₂(g) -----> 2H₂O(l) ; /\H^o ₂₉₈ = -571.6 kJmol^-1
An endothermic reaction is one in which heat is taken in.  It results in a temperature decrease.  /\H is given a positive sign to indicate an endothermic reaction, e.g.
2Ag₂O(s)  ---> 4Ag(s) + O₂(g) ; /\H^o ₂₉₈ = + 61 kJmol^-1

2.1c Enthalpies of formation, combustion and neutralisation
Enthalpy of formation (/\H^o_f)is the enthalpy change when 1 mole of a substance is formed from its constituent elements in their standard states with measurements made under standard conditions of  298K and 1 atm.
C(s) + 2S(s) -----> CS₂(l)   /\H^o_f = + 88kJmol^-1
The positive sign means that for each mole of CS₂ formed 88kJ  are absorbed.
NB. The enthalpy of formation of an element is O kJmol^-1
Enthalpy of combustion (/\H^o_c) is the enthalpy change when 1 mole of a substance  is burnt completely in oxygen with measurements made at 298K and at 1 atm.
C₃H_{6 (g)} + 4 1/2 O_2(g) ----> 3CO_{2 (g)} + 3H₂ O _(l)   /\H^o_c = -2219.7 kJ per mole
The negative sign means that each mole of propane burnt releases 2219.7 kJ.
Enthalpy of neutralisation (/\H^o_neut) is the enthalpy change when 1 mol of water is formed by the neutralisation of hydrogen ions by hydroxide ions with measurements made under standard conditions.
H⁺(aq) + OH^-(aq) ---> H₂O(l) (/\H^o_neut) = -57kJmol^-1
Task 2.1c.1:  State the names of the following energy changes and given the amounts of reactant or product that they involve.
HCl(aq) + NaOH(aq) ---> NaCl(aq) + H₂O(l)
C(s) + 2H₂(g) ---> CH₄(g)
C₂H₅OH(l) + 3O₂(g) ---> 2CO₂(g) + 3H₂O(l)
Task 2.1c.2:  Write balanced equations for reactions which would have the following enthalpy changes:  Enthalpy of combustion of methane, enthalpy of formation of water, enthalpy of combustion of hydrogen and twice the enthalpy of formation of hydrogen sulfide (H₂S).
2.1d Enthalpy level diagrams and reaction profiles
Exothermic reaction                                            Endothermic reaction
enthalpy level diagram                                         enthalpy level diagram

reactants                                                                products   
                   |                                                                                               /\
               |   negative enthalpy  change                                    |    positive enthalpy change
                  |                                                                             |
products \/                                                             reactants  |

A reaction profile shows how the enthalpy of a system changes during the reaction.  It shows that heat needs to be put into a system before molecules can react or break up. For example hydrogen and iodine react in a reversible reaction to form hydrogen iodide.
H₂(g) + I₂(g) ---> 2HI(g)  The reaction profile is shown below.


Task 2.1d: Draw enthalpy level diagrams and reaction profiles for the reactions shown in 2.1c above.

2.1e The direction of spontaneous change
Exothermic reactions with a -ve enthalpy change often proceed spontaneously.  This means they start as soon as the reactants meet like with magnesium and acid.  This is in the direction of greatest stability.  
Endothermic reactions with +ve enthalpy changes are often not spontaneous.  When reactants are mixed no change occurs.  
The sign of enthalpy change does not always indicate the direction of spontaneous change because other factors affect events e.g. the speed of the reaction.  Some endothermic processes are spontaneous e.g. glucose dissolving in water.  Some exothermic processes are not spontaneous although may start if heated e.g. sugar reacts with oxygen exothermically but sugar does not burst into flames in a sugar bowl.

2.1f Application of Hess's law
This states that the total enthalpy change for a chemical reaction is the same regardless of the route taken for the reaction. It is also a consequence of a more general physical law- the Law of Conservation of Energy which states that energy can not be created nor destroyed.

route A                   reactants     ----/\H1---->     products
                                             |                                      /\
                                 /\H2                                    |
                                             |                                      |
route B                        \/                                      |
                              intermediates  -----/\H3--------->
Enthalpy change along route A (/\H1) = Enthalpy change along route B (/\H2 + /\H3)
/\H1 = /\H2 + /\H3
Applying Hess's Law using enthalpy of formation data

DH[reaction] = sum DH_f^o[products] - sum DH_f^o[reactants]
Task 2.1f.1
Applying Hess's Law using enthalpy of combustion data

DH[reaction] = sum DH_com^o[reactants] - sum DH_com^o[products]

Task 2.1f.2
Applying Hess's Law using bond enthalpy term data see 2.1h

DH[reaction] = sum E[reactants] - sum E[products]

2.1g The experimental measurement of standard enthalpy changes
Enthalpy of combustion
Weigh a burner containing a flammable liquid.
Place burner under a copper calorimeter of known mass containing a know mass of water.
Record the initial temperature of the water.
Light the burner then  remove and it put it out when the temperature has gone up by about 20^oC.
Weigh the burner again.
Calculate the energy given out into the copper and the water using (specific heat capacity of copper = 385Jkg^-1K^-1, of water = 4180Jkg^-1K^-1  and
energy = mass of substance * specific heat capacity of substance * temperature rise
Calculate the energy given out by 1 mol of the flammable liquid substance
Task 2.1g Draw up a results table for this experiment.

2.1h Average bond enthalpies
Bond dissociation enthalpy is the enthalpy change when one mole of bonds of a particular type in a particular environment are broken.
The Bond Enthalpy Term or E is an average value of bond dissociation enthalpies for a particular bond.  The bond dissociation enthalpies for the O-H bonds in water differ slightly, the bond enthalpy term is the average.
so E(O-H) = Average bond dissociation enthalpy  = (494 + 430)/2 kJmol^-1
so E(O-H) = +462 kJmol^-1

The enthalpy of atomisation is often needed.  This is the enthalpy change when 1 mole of gaseous atoms are formed from an element in its standard state. e.g. The enthalpies of atomisation of carbon and hydrogen are the enthalpy changes for:
C(s) --> C(g)    and      1/2 H₂(g) --> H(g)

These quantities can be combined to calculate enthalpies of reaction when all of the reactants and products are in the gas state E.g. What is the enthalpy of reaction for the formation of gaseous water given E(O-H) = +462 kJmol^-1, E(H-H) =  +436  kJmol^-1    , E(O=O) = 498 kJmol^-1 .

DH_r + 2E[O-H] = E[H-H] +1/2E [O=O]
DH_r = E[H-H] +1/2E [O=O] - 2E[O-H] 
DH_r = 436kJmol^-1 +1/2*498kJmol^-1 -2*462kJmol^-1
DH_r = -239kJmol^-1

Task 2.1h