Topic 15 Energetics (HL) 15.1 Standard enthalpy changes of reaction 15.2 Born-Haber cycle 15.3 Entropy 15.4 Spontaneity

15.1 Standard Enthalpy Change of reaction Standard state: 101kPa, 298K

Standard enthalpy of formation DHfq DHfq : The energy absorbed or evolved when 1 mol of the substance is formed from its elements in their standard states. The enthalpy of formation of any element is zero. ½ H2(g) + O2(g)  H2O(l) DHfq = -285 kJ/mol DH = SDHf(products) - SDHf(reactants)

Decomposition of ammonium nitrate NH4NO3(s)  N2O(g) + 2 H2O(l) NH4NO3(s) DHfq= -366 kJ/mol N2O(g) DHfq= +82 kJ/mol H2O(l) DHfq= -285 kJ/mol DH = [DHf (N2O(g)) + DHf (H2O(l))] – [DHf(NH4NO3(g)] = =[82 + 2(-285)] - [-366] = -122 kJ/mol

Standard enthalpy of combustion,DHcq When a substance is fully combusted in oxygen  CH4 + 2O2  CO2 + 2H2O DHcq= ?

15.2 Born-Haber cycle To determine the lattice enthalpy and the degree of ionic character of a salt To find an unknown value (Hess’ law)

Lattice enthalpy, DHlattice Relates to the endothermic process MX(s) M+(g) + X-(g) in which the gaseous ions of a crystal are separated to an infinitive distance from each other. NaCl(s)  Na+(g) + Cl-(g) DHlattice= 769 kJ/mol Endothermic reactions

Factors affecting the lattice enthalpy The greater the charge of the ions, the stronger the electrostatic attraction http://www.chemhume.co.uk/A2CHEM/Unit%202b/9%20Lattice%20enthalpy/Ch9Latticec.htm

Factors affecting the lattice enthalpy (2) The smaller the ionic radius, the shorter the distance, the stronger the electrostatic attraction

Electron affinity (electron gain enthalpy) The enthalpy change when an atom gain one electron in gas phase e.g. Cl(g) + e-(g)  Cl-(g) DHe.a. = -349 kJ/mol. Electron affinity can be both exothermic and endothermic depending on element.

Born-Haber cycle for the formation of NaCl (s) Enthalpy of atomisation of Na Na (s) →Na (g) DHat= +108 kJ/mol Enthalpy of atomisation of Cl ½ Cl2 (s) →Cl (g) DHat = +121 kJ/mol (½ energy of Cl-Cl bond)

Born-Haber cycle for the formation of NaCl (s)(2) Electron affinity of Cl Cl (g) + e- → Cl- (g) DHea= -349 kJ/mol Ionisation energy of Na Na (g) → Na+ (g) + e- DHie= + 496 kJ/mol

Born-Haber cycle for the formation of NaCl (s)(3) Lattice enthalpy of NaCl Cl- (g) + Na+ (g) → NaCl (s) DHlatt = -769 kJ/mol

Theoretical value of Enthalpy of formation of NaCl = -411kJ/mol Using Hess Law: Enthalpy of formation of NaCl DHf (NaCl)= DHat (Na) + DHie(Na) + DHat (Cl) + DHea(Cl) + DHlatt(NaCl) 108+494+121+(-364) + (-771)= -393 kJ/mol

Use of Born-Haber cycles In the Chemistry Data Booklet the lattice enthalpies is given booth as: Experimental values (obtained by Born-Haber cycle) Theoretical values (calculated from electrostatic principles) If the value differ in a significant way => indicate more covalent character of the salt

15.3 Entropy- disorder Entropy, S Unit: J/K*mol DS = change in disorder DS = Sproducts - Sreactants It’s possible to measure absolute values of S

Increasing entropy- DS positive Solid  Liquid  Gas increase in S Ice  Water  Steam 48.0 69.9 188.7 JK-1mol-1 Mixing different types of particles- dissolving NaCl in water Increasing no of particles- N2O4 (g) →2 NO2 (g)

Decreasing entropy- DS negative System becomes more ordered Formation of solid ammonium chloride from hydrogen chloride and ammonia gas NH3(g) + HCl(g)  NH4Cl(s) DS = - 285 J/K*mol

In any conversion there is both a change in DH and DS. DS is probably positive if number of mol of gas increases and number of mol of solid/liquid decrease. NH4Cl(s)  NH3(g) + HCl(g) DS = + 285J/K*mol Pb2+(aq) + 2 I-  PbI2(s) DS = - 70 J/K*mol

15.4 Spontaneity of a reaction- DG Nature likes low internal energy (DH to decrease) and high disorder (DS to increase) Spontaneity: is a reaction going to occur A reaction will occur if the final state is more probable than the initial state. => Decrease in DH => Increase in DS

DGq = DHq - TDSq Standard free energy, DGq (or Gibbs free energy) Temperature is important for spontaneity A reaction will be spontaneous if DG has a negative value (DGq < 0) A positive DGq is a non-spontaneous reaction. If DGq = 0 then its a equilibrium

DGq = DHq - TDSq DH DS DG Spontaneity Negative (Exothermic) Positive (More random) DG < 0 Always negative Always spontaneous Positive (Endothermic) (More order) DG > 0 Always positive Never Depends on T Spontaneous at low Temperature Spontaneous at high Temperature

Just the fact that a reaction is spontaneous doesn’t mean that it will occur at once- it might need activation energy (topic 6)