Thermodynamics

Enthalpy change of formation The standard enthalpy change of formation of a compound is the energy transferred when 1 mole of the compound is formed from its elements under standard conditions (298K and 100kpa), all reactants and products being in their standard states Na (s) + ½Cl2 (g)  NaCl (s) [fH = – 411.2 kJ mol-1 ]Enthalpy of atomisation The enthalpy of atomisation of an element is the enthalpy change when 1 mole of gaseous atoms is formed from the element in its standard state Na (s)  Na(g) [atH = +148 kJ mol-1 ] ½ O2 (g)  O (g) [atH = +249 kJ mol-1 ] The enthalpy change for a solid metal turning to gaseous atoms can also be called the Enthalpy of sublimation and will numerically be the same as the enthalpy of atomisation Na (s)  Na(g) [Hsub = +148 kJ mol-1 ] Bond dissociation enthalpy (bond energy) The bond dissociation enthalpy is the standard molar enthalpy change when one mole of a covalent bond is broken into two gaseous atoms (or free radicals) Cl2 (g)  2Cl (g) dissH = +242 kJ mol-1 Or CH4 (g)  CH3 (g) + H(g) dissH = +435 kJ mol-1 For diatomic molecules the dissH of the molcule is the same as 2x atH of the element Cl2 (g)  2Cl (g) Hdiss = +242 kJ mol-1 ½ Cl2 (g)  Cl (g) atH = +121 kJ mol-1 First Ionisation enthalpy The first ionisation enthalpy is the enthalpy change required to remove 1 mole of electrons from 1 mole of gaseous atoms to form 1 mole of gaseous ions with a +1 charge Mg (g)  Mg+ (g) + e- [ IE 1H] Second Ionisation enthalpy The second ionisation enthalpy is the enthalpy change to remove 1 mole of electrons from one mole of gaseous 1+ ions to produces one mole of gaseous 2+ ions. Mg+ (g)  Mg 2+ (g) + e- [ IE 2H] First Electron affinity The first electron affinity is the enthalpy change that occurs when 1 mole of gaseous atoms gain 1 mole of electrons to form 1 mole of gaseous ions with a –1 charge O (g) + e-  O- (g) [eaH] = -141.1 kJ mol-1 ] The first electron affinity is exothermic for atoms that normally form negative ions because the ion is more stable than the atom and there is an attraction between the nucleus and the electron second electron affinity The second electron affinity is the enthalpy change when one mole of gaseous 1- ions gains one electron per ion to produce gaseous 2- ions. O – (g) + e-  O2- (g) [eaH = +798 kJ mol-1 ] The second electron affinity for oxygen is endothermic because it take energy to overcome the repulsive force between the negative ion and the electron Enthalpy of lattice formation The Enthalpy of lattice formation is the standard enthalpy change when 1 mole of an ionic crystal lattice is formed from its constituent ions in gaseous form. Na+ (g) + Cl- (g)  NaCl (s) [H Latt = -787 kJ mol-1 ] Enthalpy of lattice dissociation The Enthalpy of lattice dissociation is the standard enthalpy change when 1 mole of an ionic crystal lattice form is separated into its constituent ions in gaseous form. NaCl (s)  Na+ (g) + Cl- (g) [H Latt = +787 kJ mol-1 ] Note the conflicting definitions and the sign that always accompanies the definitions Enthalpy of Hydration Hhyd Enthalpy change when one mole of gaseous ions become aqueous ions . X+ (g) + aq  X+ (aq) For Li+ hydH = -519 kJ mol-1 or X- (g) + aq  X- (aq) For F- hydH= -506 kJ mol-1 This always gives out energy (exothermic, -ve) because bonds are made between the ions and the water molecules Enthalpy of solution The enthalpy of solution is the standard enthalpy change when one mole of an ionic solid dissolves in an large enough amount of water to ensure that the dissolved ions are well separated and do not interact with one another NaCl (s) + aq  Na+ (aq) + Cl-(aq)

The lattice enthalpy cannot be determined directly. We calculate it indirectly by making use of changes for which data are available and link them together in an enthalpy cycle the Born Haber cycle N Goalby chemrevise.org 2 MgCl2 (s) Mg (s) + Cl2 (g) Mg (g) + Cl2 (g) 2 xEaH(Cl) atH (Mg) 2x atH (Cl) LEH fH (MgCl2 ) + 2Cl- Mg (g) 2+ (g) Mg + 2Cl (g) 2+ (g) + 2e- Mg2+ (g) + 2e- + Cl2 (g) Mg+ (g) + e- + Cl2 (g) IE 1H(Mg) IE 2H (Mg) NaCl (s) Na (s) + ½ Cl2 (g) Na (g) + ½ Cl2 (g) EaH (Cl) atH (Na) atH (Cl)  LE H (NaCl) fH (NaCl) + Cl- Na (g) + (g) Na + Cl (g) + (g) + eNa+ (g) + e- + ½ Cl2 (g) IE 1H(Na) Born Haber cycle: sodium Chloride By applying Hess’s law the heat of formation equals to the sum of everything else fH =atH (Na) + IEH(Na)+ atH(Cl) + EaH(Cl) + LEH Rearrange to give LEH = fH – (atH (Na) + IEH(Na)+ atH (Cl) EaH(Cl) ) Pay attention to state symbols and direction of arrows. Usually all pieces of data are given except the one that needs to be calculated LEH =-411 – (+107 + 496 + 122 + -349) = -787 kJmol-1 Born Haber cycle: magnesium Chloride The data for the at H (Cl) could also be given as the bond energy for E(Cl-Cl ) bond. Remember : E(Cl-Cl ) = 2 x at H (Cl) Note in this example the first and second ionisation energies of magnesium are needed as Mg is a +2 ion Careful This Born Haber cycle has been constructed using a lattice enthalpy of formation. Sometimes questions will give the enthalpy of lattice dissociation which has the opposite sign and the arrow points in the opposite direction. This changes the calculation. Notice the second electron affinity for oxygen is endothermic because it take energy to overcome the repulsive force between the negative ion and the electron

Trends in Lattice Enthalpies The strength of a enthalpy of lattice formation depends on the following factors 1. The sizes of the ions: The larger the ions, the less negative the enthalpies of lattice formation (i.e. a weaker lattice). As the ions are larger the charges become further apart and so have a weaker attractive force between them. 2. The charges on the ion: The bigger the charge of the ion, the greater the attraction between the ions so the stronger the lattice enthalpy (more negative values). The lattice enthalpies become less negative down any group. e.g. LiCl, NaCl, KCl, RbCl e.g group 1 halides (eg NaF KI) have lattice enthalpies of around –700 to – 1000 group 2 halides (eg MgCl2 ) have lattice enthalpies of around –2000 to –3500 group 2 oxides eg MgO have lattice enthalpies of around –3000 to –4500 kJmol-1 Perfect Ionic Model Theoretical lattice enthalpies assumes a perfect ionic model where the ions are 100% ionic and spherical and the attractions are purely electrostatic. There is a tendency towards covalent character in ionic substances when •the positive ion is small •the positive ion has multiple charges •the negative ion is large •the negative ion has multiple negative charges. When the negative ion becomes distorted and more covalent we say it becomes polarised. The metal cation that causes the polarisation is called more polarising if it polarises the negative ion. + – Ionic with covalent 100% ionic character When 100 % ionic the ions are spherical. The theoretical and the born Haber lattice enthalpies will be the same The charge cloud is distorted .Differences between theoretical and Born Haber (experimental) lattice enthalpies The Born Haber lattice enthalpy is the real experimental value. When a compound shows covalent character, the theoretical and the born Haber lattice enthalpies differ. The more the covalent character the bigger the difference between the values. When a compound has some covalent character- it tends towards giant covalent so the lattice is stronger than if it was 100% ionic. Therefore the born haber value would be larger than the theoretical value.

Free-energy change (G) and entropy change (S) A problem with ∆H A reaction that is exothermic will result in products that are more thermodynamically stable than the reactants. This is a driving force behind many reactions and causes them to be spontaneous (occur without any external influence). Some spontaneous reactions, however, are endothermic. How can this be explained? We need to consider something called entropy A SPONTANEOUS PROCESS (e.g. diffusion) will proceed on its own without any external influence. Entropy, S˚ Entropy is a description of the number of ways atoms can share quanta of energy. If number of ways of arranging the energy (W) is high, then system is disordered and entropy (S) is high. Substances with more ways of arranging their atoms and energy (more disordered) have a higher entropy. Elements …tend to have lower entropies than… Compounds Simpler compounds Complex compounds Pure substances Mixtures solid Liquid gas Temperature Entropy Solids have lower entropies than liquids which are lower than gases. When a solid increases in Temperature its entropy increases as the particles vibrate more. There is a bigger jump in entropy with boiling than that with melting. Gases have large entropies as they are much more disordered Predicting Change in entropy ‘∆S’ Qualitatively Balanced chemical equations can often be used to predict if ∆S˚ is positive or negative. In general, a significant increase in the entropy will occur if: -there is a change of state from solid or liquid to gas – there is a significant increase in number of molecules between products and reactants. NH4Cl (s)  HCl (g) + NH3 (g) ∆S˚ = +ve •change from solid reactant to gaseous products •increase in number of molecules both will increase disorder Na s + ½ Cl2 g  NaCl s ∆S˚ = -ve •change from gaseous and solid reactant to solid •decrease in number of molecules both will decrease disorder An increase in disorder and entropy will lead to a positive entropy change ∆S˚ = +ve Calculating ∆S˚ quantitatively Data books lists standard entropies (S˚) per mole for a variety of substances. It is not possible for a substance to have a standard entropy of less than zero. Elements in their standard states do not have zero entropy. Only perfect crystals at absolute zero (T = 0 K) will have zero ∆S entropy. At 0K substances have zero entropy. There is no disorder as particles are stationary. Note: the entropy change is very positive as a large amount of gas is being created increasing disorder

Gibbs Free Energy Change, ∆G Gibbs free energy is a term that combines the effect of enthalpy and entropy into one number The balance between entropy and enthalpy determines the feasibility of a reaction. This is given by the relationship : ∆G = ∆H – T∆S For any spontaneous change, ∆G will be negative. A reaction that has increasing entropy (+ve ∆S) and is exothermic (-ve ∆H ) will make ∆G be negative and will always be feasible ∆G = ∆H – T∆S Units: KJ mol-1 Unit of S= J K-1 mol-1 Need to convert to KJ K-1 mol-1 ( ÷1000) Units: KJ mol-1 Convert from ˚C to K (+ 273) Example : Data for the following reaction, which represents the reduction of aluminium oxide by carbon, are shown in the table. Al2O3 (s) + 3C(s) → 2Al(s) + 3CO(g) Calculate the values of ∆H , ∆S and ∆G for the above reaction at 298 K Substance ∆fH / kJmol–1 ∆S / JK–1mol–1 Al2O3 (s) -1669 51 C(s) 0 6 Al(s) 0 28 CO(g) -111 198 1. Calculate ∆S ∆S˚ = Σ S˚products – Σ S˚reactants = (2 x 28 + 3×198) – (51 + 3 x 6) = +581J K-1 mol-1 (3 S.F.) 2. Calculate ∆H˚ ∆H˚ = Σ∆fH˚ [products] – Σ∆fH˚ [reactants] = (3 x -111) – -1669 = +1336 kJ mol-1 3. Calculate ∆G ∆G = ∆H – T∆S = +1336 – 298x 0.581 = +1163kJ mol-1 ∆G is positive. The reaction is not feasible Calculating the temperature a reaction will become feasible Calculate the temperature range that this reaction will be feasible N2 (g) + O2 (g)  2 NO(g) ∆ H = 180 kJ mol-1 ∆S = 25 J K-1 mol-1 The reaction will be feasible when ∆ G ≤0 Make ∆G = 0 in the following equation ∆G = ∆H – T∆S 0 = ∆H – T∆S So T= ∆H / ∆S T = 180/ (25/1000) = 7200K The T must be >7200K which is a high Temp! ∆G during phase changes As physical phase changes like melting and boiling are equilibria, the ∆G for such changes is zero. What temperature would methane melt at? CH4(s)  CH4 (l) ∆H = 0.94 kJmol-1 ∆S = 10.3 Jmol-1K-1 Make ∆G = 0 in the following equation ∆G = ∆H – T∆S 0 = ∆H – T∆S So T= ∆H / ∆S T= 0.94 / (10.3÷1000) T= 91K If ∆G is negative there is still a possibility, however, that the reaction will not occur or will occur so slowly that effectively it doesn’t happen. If the reaction has a high activation energy the reaction will not occur. 6

Effect of Temperature on feasibility Changing Temperature will change the value of – T∆S in the above equation ∆G = ∆H – T∆S If the reaction involves an increase in entropy (∆S is +ve) then increasing Temperature will make it more likely that ∆G is negative and more likely that the reaction occurs e.g. NaCl + aq  Na+ (aq) + Cl- (aq) If the reaction involves an decrease in entropy (∆S is – ve) then increasing Temperature will make it more less likely that ∆G is negative and less likely for the reaction to occur. E.g. HCl(g) + NH3 (g) ➝ NH4Cl(s) If the reaction has a ∆S close to zero then temperature will not have a large effect on the feasibility of the reaction as – T∆S will be small and ∆G won’t change much e.g. N2 (g) + O2 (g)  2NO (g) This graph shows how the free-energy change for formation of ammonia varies with temperature above 240 K. ½ N2 (g) + 3 /2 H2 (g)  NH3 (g) Applying the equation of a straight line y= mx+c to the ∆G = ∆H – T∆S equation. c = ∆H The gradient of this graph is equal to -∆S The positive gradient means ∆S is negative which corresponds to the equation above showing increasing order. When ∆G <0 then the reaction is spontaneous. In this case at Temperatures below around 460K The slope of the line would change below 240K because ammonia would be a liquid and the entropy change would be different

Enthalpies of solution Using Hess’s law to determine enthalpy changes of solution MgCl2 (s) H lattice dissociation (MgCl2 ) + 2Cl- Mg (g) 2+ (g) + 2Cl- Mg (aq) 2+ (aq)  hyd H Mg2+ + 2 x  hyd H Cl- ΔHsolution In general Hsolution =  HL dissociation +  hydH When an ionic substance dissolves the lattice must be broken up. The enthalpy of lattice dissociation is equal to the energy needed to break up the lattice (to gaseous ions). This step is endothermic. The size of the lattice enthalpy depends on the size and charge on the ion. The smaller the ion and the higher its charge the stronger the lattice Sometimes in questions  HLatt formation is given instead of  HLatt dissociation in order to catch you out. Remember the difference between the two. OR H solution = –  HL formation +  hyd Hhyd When an ionic lattice dissolves in water it involves breaking up the bonds in the lattice and forming new bonds between the metal ions and water molecules. For MgCl2 the ionic equation for the dissolving is MgCl2 (s) + aq  Mg2+ (aq) + 2Cl- (aq) N Goalby chemrevise.org 7 -30 -20 -10 0 10 20 30 40 0 200 400 600 800 1000 ΔG kJ/ mol Temperature/ K Example . Calculate the enthalpy of solution of NaCl given that the lattice enthalpy of formation of NaCl is -771 kJmol-1 and the enthalpies of hydration of sodium and chloride ions are -406 and -364 kJmol-1 respectively  sol H = –  HLatt formation +  hyd H = – (-771) + (-406-364) = + 1 kJmol-1 What does ΔHSolution tell us? Generally ΔH solution is not very exo or endothermic so the hydration enthalpy is about the same as lattice enthalpy. In general the substance is more likely to be soluble if the ΔH solution is exothermic. If a substance is insoluble it is often because the lattice enthalpy is much larger than the hydration enthalpy and it is not energetically favourable to break up the lattice, making ΔH solution endothermic. BaSO4 (s) H lattice dissociation (BaSO4 ) + SO4 2- Ba (g) 2+ (g) + SO4 2- Ba (aq) 2+ (aq)  hydH Ba2+ +  hydH SO4 2- ΔsolH INSOLUBLE ΔH solution endothermic. We must consider entropy, however, to give us the full picture about solubility. When a solid dissolves into ions the entropy increases as there is more disorder as solid changes to solution and number of particles increases. This positive S can make G negative even if H solution is endothermic, especially at higher temperatures. Hydration enthalpies are exothermic as energy is given out as water molecules bond to the metal ions. The negative ions are attracted to the δ+ hydrogens on the polar water molecules and the positive ions are attracted to the δ – oxygen on the polar water molecules. The higher the charge density the greater the hydration enthalpy (e.g. smaller ions or ions with larger charges) as the ions attract the water molecules more strongly. e.g. Fluoride ions have more negative hydration enthalpies than chloride ions Magnesium ions have a more negative hydration enthalpy than barium ions For salts where ΔH solution is exothermic the salt will always dissolve at all Temperatures S is positive due to the increased disorder as more particles so – T∆S always negative ∆G = ∆H – T∆S H is negative G is always negative For salts where ΔH solution is endothermic the salt may dissolve depending on whether the -T∆S value is more negative than ∆H is positive S is positive due to the increased disorder as more particles so – T∆S always negative ∆G = ∆H – T∆S H is positive Will dissolve if G is negative Increasing the Temperature will make it more likely that G will become negative, making the reaction feasible and the salt dissolve