Thermochemistry : 9.3 Born-Haber Cycle

• First Ionization Energy (IE₁)
  • Energy required for 1 mol of gaseous atom to lose 1 mol of electrons.
    
    
• Affinity Electron (EA) 
  • Energy change that occurs when 1 mol of gaseous atom gains 1 mol of electrons.
    
    
• Lattice Energy
  • Energy change when 1 mol of solid ionic compound formed from its gaseous ions
    
    
• Magnitude Lattice Energy
  • Indicates the strength of ionic bonding
  • The more negative lattice energy, the stronger ionic bonding
  • It influences : 
    • Melting point
    • Hardness
    • Solubility
      
      
• Determining Lattice Energy
  • Lattice energy cannot be measured directly.
    • Can be calculated by Born-Haber cycle
      
      
• Born-Haber Cycle
  • A series of chosen steps from elements to ionic compound for which all the enthalpies are known , except lattice energy.
    ΔH_f = sum of ΔH^o for multistep path
  • Calculation Step
  
  
  Example : LiF
  
  
  Overall : Formation of LiF compound
      Li(s) + ½ F₂(g)     LiF(s)        ΔH^o
  _overall = 617 kJ
          ΔH^o_overall = ΔH^o_f

    Step 1 :- atomization of lithium

        Li(s)     Li(g)                ΔH_f = 161 kJ

            ΔH₁^o = ∆H^o_atom or ∆H^o _sublim

    Step 2 :- atomization of fluorine

        ½ F₂(g)     F(g)             ∆H₂^o = 79.5 kJ

            ∆H₂^o = ∆H^o _atom

    Step 3 :- ionization of lithium atom

        Li(g)         Li⁺(g) + e^-         ∆H₃^o = 520 kJ

            ∆H₃^o = IE₁

    Step 4 :- Electron affinity of F atom

        F(g) + e^-     F^- (g)            ∆H₄^o = -328 kJ

            ∆H₄^o = EA

    Step 5 :- Formation of LiF(s) from its gaseous ions

        Li⁺(g) + F^-(g)         LiF(s)        ∆H₅^o = ?

            ∆H₅^o = ∆H^o_lattice of LiF

• Factors Affecting Lattice Energy
  • From Coulomb's Law

                             ΔE  α  (n⁺Q⁺)(n^-Q^-)

                                                    ---------------------------                                                          

                                                d

∆H : electrostatic energy

n⁺ : number
of positive charge

n^- : number of negative charge 

Q⁺ : electrostatic charge (+)

Q^- : electrostatic charge (-)

d : distance between the ions = r⁺ + r^- (radius of ions)

• Ionic bond strength increase when
  • Q, charge (Q) increase
  • Size of atoms (d) decrease

• Hydration Process of Ionic Crystal in Water
  • 2 main process 
    • Breaking lattice energy of ionic crystal
    • Solvation (hydration)
      
      

Thermochemistry : 9.2 Hess Law

• Hess's Law of Heat Summation
  

When reactants are converted to products, the change in enthalpy is the same whether the reaction take step in one step or in a series of step.

    ΔH₁ =ΔH₂ + ΔH₃

• Application Using Hess's Law
  
  • To find ΔH of any reaction for which we can write on equation, even if it is impossible to carry out.
    
  • Two methods of calculation
    
    • Algebraic method
      
    • Energy cycle method
      
• Algebraic Method
  
  • Important steps:
    
    • Identify the target equation whose ΔH unknown.
      
    • Rearrange the equations given mole of reactants and products are on the correct side.
      
    • Add the equation to obtain the target equation all other substances must cancel.
      
• Standard Enthalpy of Formation (ΔH_f)
  
  • Heat change when 1 mol of a compound is produced from its elements in their standard states.
    
• ΔH_f
  of Elements
  
  • In its standard states
    
• ΔH_f of Compounds
  
  • Most compound have negative ΔH_f
    
    • The compound is more stable than its components elements.
      
• Determining ΔH_rxn From ΔH_f
  
  aA + bB = cC + dD
  
  H_rxn = [cΔH_f (C) + dΔH_f (D) – aΔH_f (A) + bΔH_f (B)]
  
  H_rxn = ( sum of ΔH_f of all of the products ) – ( sum of ΔH_f of all of the reactant )

Thermochemistry : 9.1 Concept of Enthalpy

Heat

-The energy transferred between a system and surrounding.

System

-Part of universe whose change we are going to observe.

Surrounding

-The rest of the universe outside the system.

Exothermic

-Gives off heat.

-From the system to the surroundings.

-Ex : 2H₂(g) + O₂(g) → 2H₂O(l) + energy

Endothermic

-Absorbs heat.

-From the surrounding to the system.

-Ex : energy + 2HgO(s) → 2Hg(l) + O₂(g)

Enthalpy

-Used to quantify the heat flow into or out of system in a process that occurs at constant pressure.

Enthalpy Change, ΔH

-Heat given off or absorbed during a reaction at constant pressure.

-ΔH = H(Products) – H(Reactants)

-Exothermic : H(Products) < H(Reactants)

-Endothermic : H(Products) > H(Reactants)

Enthalpy/Energy Profile Diagram

-Energy profile diagram for an exothermic reaction.

-Energy profile diagram for an endothermic reaction.

Units of Energy

-S.I. unit : Joule(J) [1J = 1kgm²/s²]

-Older unit : Calorie(cal) [1cal = 4.184J]

Some Important Types of Enthalpy Change(ΔH)

-Ex : Heat of combustion(ΔH _comb)

            Heat of formation(ΔH _f)

            Heat of neutralization(ΔH _neut)

-Unit : kJ/mol

Enthalpy of Combustion(ΔH _comb)

-Heat released when 1 mole of a substance completely combusted in oxygen gas.

-Ex : C₄H₁₀(l) + 13/2O₂(g) → 4CO₂(g) + 5H₂O(l) ΔH = ΔH _comb

Enthalpy of Formation(ΔH _f)

-Heat change when 1 mole of a compound is produced from its elements.

-Ex : K(s) + 1/2Br₂(l) → KBr(s) ΔH = ΔH_f

Enthalpy of Atomization(ΔH_atom)

-Heat absorbed when 1 mole of gaseous atom is formed from its element.

-Ex : 1/2H₂(g) → H(g) ΔH = ΔH_atom

Na(s) → Na(g) ΔH = ΔH_atom

Enthalpy of Neutralization(ΔH _neut)

-Heat released when 1 mole of water formed when acid reacts with base.

-Ex : HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l) ΔH = ΔH_neut

HNO₃(aq) + 1/2Ba(OH)₂(aq) → 1/2Ba(NO₃)₂(aq) + H₂O(l) ΔH = ΔH_neut

Enthalpy of Solution(ΔH_soln)

-Heat change when 1 mole of solute dissolves in solvent/water to form infinite dilute solution.

-Ex : NaCl(s) → Na⁺(aq) + Cl^-(aq) ΔH = ΔH_soln

Enthalpy of Hydration(ΔH_hyd)

-Heat released when 1 mole of gaseous ion is hydrated in aqueous solution.

-Ex : Na⁺(g) → Na⁺(aq) ΔH = ΔH_hyd

Enthalpy of Sublimation(ΔH_sublim)

-Heat absorbed when 1 mole of substance in solid state sublimed.

-Ex : I₂(s) → I₂(g) ΔH = ΔH_sublim

CO₂(s) → CO₂(g) ΔH = ΔH_sublim

K(s) → K(g) ΔH = ΔH_{sublime =} ΔH_atom

ΔH°_rxn or ΔH°(kJ/mol)

-Standard enthalphy of reaction.

-the enthalpy change of a reaction carried out at standard state (1 atm)

-standard enthalpy of formation, ΔH°_f

-standard enthalpy of combustion, ΔH°_comb

Standard enthalpy of neutralization, ΔH°_neut

Standard states

-Gas: 1 atm & behave ideally

-Aqueous solution: 1 M

-Pure substance (element/compound): Most stable form of substance at 1 atm and temperature (usually 25°C)

Standard states of pure substance: oxygen,O₂, H₂, Na(s), Br₂, H₂O(l), NaCl(s)

Specific Heat Capacity (c)

-Amount of heat (q) required to raise temperature of 1 gram of a substance by 1 K (1°C)

c=q/mΔT

ΔT = T_final-T_initial

-unit: Jg^-1K^-1/Jg^-1°C^-1

Molar Heat Capacity

-Amount of heat required to raise temperature of 1 mol of a substance by 1 K/1°C

-unit: JK^-1/J°C^-1

C=mc    C=q/ΔT   q=CΔT

Calorimeter

-Device used to measure the heat released (or absorbed) by a physical or a chemical process.

Ø  Constant-pressure                                               

l  Coffee-cup calorimeter

Ø  Constant-volume

l  Bomb calorimeter

Bomb calorimeter

-To measure heat released in combustion reaction .

How bomb calorimeter works

-With continual stirring, the initial temperature of preweighed water bath is noted.

-The sample is ignited electrically.

-Heat released from the combustion reaction is transferred to the rest of the calorimeter.

-The maximum temperature is measured.

Calculation of ΔH_rxn

q_sys=q_water+q_cal+q_rxn

No heat enters/leaves the system

q_sys=0

q_rxn=-(q_cal+q_water)

q_water=mcΔT

q_cal=C_calΔT

Reaction at constant volume ΔH≈q_rxn

Coffee-cup calorimeter

-To measure heat released in non-combustion reaction such as heat of neutralization &heat of solution.

-constant pressure calorimeter

-the process is opened to the laboratory atmosphere.

-no heat enters or leaves.

How coffee-cup calorimeter works

-The calorimeter consists of a known mass of water (or solution) in an insulated container equipped with a thermometer and a stirrer.

-T_initial of water is measured

-The process takes place (addition of acid and base or soluble salt, etc)

-Contents are stirred.

-T_final of water is measured.

Calculation of ΔH_rxn

q_sys=q_soln+q_cal+q_rxn

No heat enters or leaves the system

q_sys=0

q_rxn=-(q_soln+q_cal)

q_soln=mcΔT

q_cal=C_calΔT

Reaction at constant P

ΔH=q_rxn

Assume specific heat capacities &density same like water.

(4.184Jg^-1°C^-1) (1.00gmL^-1)

Stoichiometry of thermochemical equation

CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l)

ΔH=-899.4kJ

-Sign=positive/negative

-Magnitude

Sign of ΔH

-Depends on reaction is exothermic or endothermic

 -ve: exothermic                      +ve: endothermic

-A forward reaction has a opposite sign of the reverse reaction

Magnitude of ΔH

-Proportional to amount of substance reacting or produced.

2H₂(g) + O₂(g) → 2H₂O(l) ΔH=-572kJ

H₂(g) + 1/2O₂(g) → H₂O(l) ΔH=-286kJ

 -286kJ if thermodynamically equivalent to 1 mole of H₂

 -286kJ is thermodynamically equivalent to 1/2 mole of O₂

 -286kJ is thermodynamically equivalent to 1 mole of H₂O

Formulae in chapter 9

• ΔH = H(Products) – H(Reactants)

• q = mcΔT

• q = CΔT

• q_(sys) = q_(water) + q_{(calorimeter)} + q_(rxn/soln)

• ΔH°_(rxn) = Sum of ΔH°_(f) of products – Sum ofΔH°_(f) of all reactants

• ΔH°_(overall)= ΔH°₁ + ΔH°₂ + ΔH°₃ + ΔH°₄ + ΔH°₅

• ΔH_(soln) = ΔH_(lattice) + ΔH_(hyd)

key terms in chapter 9

• Enthalpy Change: Heat given off or absorbed during a reaction at constant pressure.

• Exothermic: Gives off heat from system to surroundings.

• Endothermic: Absorbs heat from the surrounding to the system.

• Specific Heat Capacity: Amount of heat required to raise temperature of 1 gram of a substance by 1K/1℃.

• Heat Capacity: Amount of heat required to raise the temperature of a given quantity of substance by 1K/1℃.

• Calorimeter: Device used to measure the heat released (or absorbed) by a physical or chemical process.

• Lattice Energy: Energy change when 1 mole of solid ionic compound is formed from its’ gaseous ions.