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) DHf

q = -285 kJ/mol DH = SDHf(products) - SDHf(reactants)

Decomposition of ammonium nitrateNH4NO3(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 NaNa (g) → Na+ (g) + e- DHie= + 496 kJ/mol

Born-Haber cycle for the formation of NaCl (s)(3)

• Lattice enthalpy of NaClCl- (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 Gasincrease 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 gasNH3(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

DH DS DG Spontaneity

Negative(Exothermic)

Positive(More random)

DG < 0 Always negative

Always spontaneous

Positive (Endothermic)

Negative(More order)

DG > 0Always positive

Never spontaneous

Negative(Exothermic)

Negative(More order)

Depends on T Spontaneous at low Temperature

Positive (Endothermic)

Positive(More random)

Depends on T Spontaneous at high Temperature

DGq = DHq - TDSq

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