# Energetics

Energetics IB Topics 5 & 15 PART 3: Energy Cycles STANDARD ENTHALPY CHANGE OF FORMATION, Hf Definition: the enthalpy change when one mole of the compound is formed from its elements in their standard states at 298 K and 1 atm of pressure. Note: it follows that the for an element in its standard state

will be zero. 0 0 H2(g) + O2(g) H2O(l) Hrxn=? Hrxn = Hf (H2O) = -285.8 kJ Recall that Hrxn

npHf (products) - sum of (sigma) nr Hf (reactants) moles STANDARD ENTHALPY CHANGE OF COMBUSION,Hc Definition: the enthalpy change when one mole

of a substance is completely combusted in oxygen under standard conditions. Example: An accurate value for the standard enthalpy change of formation of ethanol can be determined from the cycle below. Hf (C 2H5OH) 2C(s) + C2H5OH(l) 2O2(g) 3H2(g) + O2(g) 2 Hf (CO2 )

2CO2(g) + 3/2 (g) 3O2 H (H O) f 2 3O2(g) Hc (C 2H5OH) 3H2O(g) By Hess' Law : 2Hf (CO 2 ) 3Hf (H2O) Hf (C 2H5OH) Hc (C 2H5OH)

2(-393.5) 3( 285.8) Hf (C 2H5OH) ( 1371) Hf (C 2H5OH) 273.4 kJ mol -1 LATENT HEAT OF FUSION, Hfus Definition: the enthalpy change (energy absorbed) when one mole of the compound is converted from a solid to a liquid without a change in temperature. Latent means hidden; the heat absorbed/released during a phase change does not cause the temperature to change. Note:

for water is 334 kJ/kg = 334 J/g = 6.01 kJ mol-1 LATENT HEAT OF FUSION, Hfus A = solid B = melting (solid + liquid) C = liquid D = boiling (liquid + gas) E = gas LATENT HEAT OF VAPORIZATION, Hvap Definition: the enthalpy change (energy

absorbed) when one mole of the compound is converted from a liquid to a gas without a change in temperature. Note: for water is 2260 kJ/kg = 2260 J/g = 40.8 kJ mol-1 LATENT HEAT OF VAPORIZATION, Hvap A = solid B = melting (solid + liquid) C = liquid D = boiling (liquid + gas) E = gas

Example: How much heat is released by 250.0 g of H2O as it cools from 125.0C to -40.0C? (Recall that the specific heat of water = 4.18 J/gC) Five steps 1. Cool the steam mcsteamT 2. Condense m(-Hvap) 3. Cool the liquid water mcwaterT

4. Freeze 5. Cool the solid ice mciceT m(-Hfus) Example: How much heat is released by 250.0 g of H2O as it cools from 125.0C to -40.0C? (Recall that the specific heat of water = 4.18 J/gC) When substances change state, they often have different specific heats: cice = 2.09 J/goC cwater

= 4.18 J/goC csteam = 2.03 J/goC Example: How much heat is released by 250.0 g of H2O as it cools from 125.0C to -40.0C? (Recall that the specific heat of water = 4.18 J/gC) cooling = exothermic negative heat values qsteam = mcT = (250.0g)(2.03J/goC)(100.0125.0) = -12,700 J qvap = mHvap = (250.0g)(-2260J/g) = -565,000 J qwater = mcT = (250.0g)(4.18J/goC)(0-100) = -105,000 J qfus = mHfus = (250.0g)(-334J/g) = -83,500 J qice = mcT = (250.0g)(2.09J/goC)(-40.0-0) = -20,900 J qtotal = -787,000J

-787 kJ Example: What will be the final temperature of 50.0 mL of water, initially at 60C, after a 3.2 g ice-cube is dropped in and allowed to melt. Assume no heat transfer to/from the surroundings. qrxn = (334 J/g)(3.2 g) qrxn = 1068.8 J qcalorimeter = - qrxn = -1068.8 J qcalorimeter = mcT -1068.8 J = (50.0 g)(4.18 J/gC)(T) T = -5.11 C = Tf - Ti -5.11 C = Tf 60 C STANDARD ENTHALPY CHANGE OF ATOMIZATION, Hat Definition: enthalpy change when one mole of gaseous atoms is

formed from the element in its standard state under standard conditions. For diatomic molecules this is equal to half the bond dissociation enthalpy. Cl2(g) Cl(g) mol-1 Hat = +121 kJ EA H ELECTRON AFFINITY, Definition: the enthalpy change when an electron is added to an isolated atom in the gaseous state.

X(g) + e X (g) - - EA H ELECTRON AFFINITY, Atoms want an excess electron, so electron affinity values are negative for the first electron. However, when oxygen forms the O2- ion, the overall process is endothermic.

O(g) + e- O-(g) O-(g) + e- O2-(g) ll a r e O(g) ov H = -142 kJ mol-1 H = +844 kJ mol-1 + 2e- O2-(g)H = +702 kJ mol-1 Hlatt LATTICE ENTHALPY, relates either to the endothermic

process of turning a crystalline solid into its gaseous ions or to the exothermic process of turning gaseous ions into a crystalline solid. MX(s) M (g) + X (g) + - Hlatt LATTICE ENTHALPY, The sign of the lattice enthalpy indicates whether the lattice is

being formed (-) or broken (+). The size of the lattice enthalpy depends both on the size of the ions and on the charge carried by the ions. Hlatt LATTICE ENTHALPY, increasing Cation size ____________ Lattice Enthalpy (kJ mol-1)

LiC l NaCl KCl 84 6 77 1 70 1 Hlatt

LATTICE ENTHALPY, increasing anion size ____________ Lattice Enthalpy (kJ mol-1) NaCl NaB r NaI 77 1

73 3 68 4 Makes sense the larger the ion, the easier to separate Hlatt LATTICE ENTHALPY, Charge on cationincreasing ____________ Lattice Enthalpy

(kJ mol-1) NaCl MgCl2 77 1 2493 Hlatt LATTICE ENTHALPY, Charge on anion increasing ____________ Lattice

Enthalpy (kJ mol-1) MgCl2 MgO 2493 3889 Makes sense the greater the difference in charge, the stronger the attraction and the harder it is to separate ions

BORN-HABER CYCLES energy cycles for the formation of ionic compounds. Example: The enthalpy change for the formation of sodium chloride can be considered to occur through a series of separate steps. Na(s) + Hat (Na) Na+Cl-(s

Hat (Cl) Na(g) Cl(g) HIE (Na) Na+(g) Cl2(g) Hf (NaCl) H EA (Cl) +

Hlatt (NaCl) Cl-(g) Using Hess' Law : H f ( NaCl) H at ( Na ) H IE ( Na ) H at (Cl) H EA (Cl) H latt ( NaCl) Hf (NaCl) 108 494 121 - 364 - 771 Hf (NaCl) 412 kJ mol -1 Use of Born-Haber Cycles: Like any energy cycle, Born-Haber cycles can be used to find the value of an unknown.

They can also be used to assess how ionic a substance is. Use of Born-Haber Cycles: The lattice enthalpy can be calculated theoretically by considering the charge and size of the constituent ions. It can also be obtained indirectly from the Born-Haber cycle. If there is good agreement between the two values then it is reasonable to assume that there is a high degree of ionic character (e.g. NaCl). However, if there is a big difference between the two values then it is because the compounds possess a considerable degree of covalent character (eg. AgCl).

Use of Born-Haber Cycles: Compound Theoretical value (kJ mol-1) Experimental value (kJ mol-1) NaCl 76 6 77 1 Good agreement of #s high degree of

ionic character AgCl 77 0 90 5 poor agreement considerable covalent character

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