Enthalpy changes and Enthalpy changes and calorimetrycalorimetry

Enthalpy changes in reactionsEnthalpy changes in reactionsCalorimetry and heat measurementCalorimetry and heat measurement

Hess’s LawHess’s LawHeats of formationHeats of formation

Learning objectivesLearning objectives

• Describe the standard state for thermodynamic Describe the standard state for thermodynamic functionsfunctions

• Explain sign of enthalpy change for changes of stateExplain sign of enthalpy change for changes of state• Calculate enthalpy changes for reactionsCalculate enthalpy changes for reactions• Use specific heat and heat capacity in calorimetric Use specific heat and heat capacity in calorimetric

problemsproblems• Apply Hess’ law to calculations of enthalpy changeApply Hess’ law to calculations of enthalpy change• Use standard heat of formation in calculations of Use standard heat of formation in calculations of

enthalpy of reactionenthalpy of reaction• Use bond energies to estimate heats of reactionUse bond energies to estimate heats of reaction

The importance of stateThe importance of state

• The heat change in a reaction will depend The heat change in a reaction will depend upon the states of the reactants and/or upon the states of the reactants and/or productsproducts

• States must be specifiedStates must be specified– ΔΔH(1) = - 2043 kJH(1) = - 2043 kJ

– ΔΔH(2) = - 2219 kJH(2) = - 2219 kJ

• Additional heat is released in (2) because Additional heat is released in (2) because condensation of Hcondensation of H22O releases 176 kJO releases 176 kJ

)(4)(3)(5)(.1 22283 gOHgCOgOgHC

)(4)(3)(5)(.2 22283 lOHgCOgOgHC

Thermodynamic standard stateThermodynamic standard state

• Heat changes will also depend upon P and THeat changes will also depend upon P and T• The Standard State:The Standard State:

Most stable form of a substance at 1 atm Most stable form of a substance at 1 atm pressure and 25pressure and 25ºC(usually); 1 M ºC(usually); 1 M

concentration for solutionsconcentration for solutions• Conventionally, enthalpy change under Conventionally, enthalpy change under

standard conditions is represented by:standard conditions is represented by:

ΔΔHHºº• Any thermodynamic function referring to Any thermodynamic function referring to

standard conditions is identified by standard conditions is identified by ºº

Calculating Calculating ΔΔU from U from ΔΔHºHº• Reaction between NReaction between N22 and H and H22 at P = 40 atm and at P = 40 atm and ΔΔVV – 1.12 L – 1.12 L

• What is What is ΔΔU?U?ΔΔU = U = ΔΔH – PH – PΔΔVV

ΔΔU > U > ΔΔH H • Internal energy change is Internal energy change is less negativeless negative by amount of work by amount of work

done done byby surroundings on compressing system surroundings on compressing system

J

kJ

Latm

JLatmxkJU

1000

110112.1402.92

kJkJkJU 7.8752.42.92

NN22(g) + 3H(g) + 3H22(g) = 2NH(g) = 2NH33(g) ΔHº = -92.2 kJ(g) ΔHº = -92.2 kJ

Enthalpies of change of stateEnthalpies of change of state

• Conversion of a substance from one state to another Conversion of a substance from one state to another involves heat input or outputinvolves heat input or output

• Heat is Heat is absorbedabsorbed when breaking bonds when breaking bonds – Solid Solid → liquid → gas→ liquid → gas

• Heat is Heat is releasedreleased when making bonds when making bonds – Gas Gas → liquid → solid→ liquid → solid

• Heat of fusion, vaporization etc. (formerly known as Heat of fusion, vaporization etc. (formerly known as “latent” heats – heat consumed with no change in T)“latent” heats – heat consumed with no change in T)

State functions ignore pathState functions ignore path

• Transition from solid to gas may lie through liquid Transition from solid to gas may lie through liquid phase...phase...

• Or transition may be direct – sublimationOr transition may be direct – sublimation• Enthalpy change is the same by either routeEnthalpy change is the same by either route

ΔΔHHsublsubl = = ΔΔHHfusionfusion + + ΔΔHHvapvap

Heat of reactionHeat of reaction

• Enthalpy change for a reaction is commonly Enthalpy change for a reaction is commonly known as heat of reactionknown as heat of reaction

• ExothermicExothermic refers to reaction where heat is refers to reaction where heat is given out by system (we warm our hands): given out by system (we warm our hands): ΔΔH < 0H < 0

• EndothermicEndothermic refers to reaction where heat is refers to reaction where heat is absorbed by system and surroundings get absorbed by system and surroundings get cool (hands get cold): cool (hands get cold): ΔΔH > 0H > 0

• NOTE SIGNS OF NOTE SIGNS OF ΔΔH!H!

Calculations with Calculations with ΔΔHºHº

• ΔΔHº may be quoted for a given equation Hº may be quoted for a given equation or for one mole of a reactant or productor for one mole of a reactant or product

• Either way, it can be used to calculate Either way, it can be used to calculate the heat change for a given amount of the heat change for a given amount of substancesubstance

ExampleExample

• What is the heat evolved from the What is the heat evolved from the combustion of 15.5 g of Ccombustion of 15.5 g of C33HH88??

– Combustion of one mole of CCombustion of one mole of C33HH88 yields - yields -

2219 kJ2219 kJ

– Molar mass of CMolar mass of C33HH88 = 44.0 g/mol = 44.0 g/mol

– No moles in 15.5 g = 15.5/44.0 = 0.352 molNo moles in 15.5 g = 15.5/44.0 = 0.352 mol– Heat produced = - 2219 x 0.352 = - 782 kJHeat produced = - 2219 x 0.352 = - 782 kJ

molkJHlOHgCOgOgHC /2219)...(4)(3)(5)( 22283

Calorimetry: the universe in the Calorimetry: the universe in the palm of your handpalm of your hand

• Heat given out or taken in by process is Heat given out or taken in by process is measured by temperature change of measured by temperature change of water in calorimeter (surroundings)water in calorimeter (surroundings)

• Insulation confines heat exchange to Insulation confines heat exchange to process and calorimeterprocess and calorimeter

Heat capacity and specific heatHeat capacity and specific heat

• Heat capacity, C: Heat capacity, C:

Heat required to raise temperature of Heat required to raise temperature of body by 1ºC (body by 1ºC (extensiveextensive))

• Specific heat (capacity), c (Specific heat (capacity), c (σσ))::

Heat required to raise Heat required to raise 1 gram1 gram of the of the substance by 1ºC (substance by 1ºC (intensiveintensive))

T

qC

mTcq

Constant pressure and constant Constant pressure and constant volumevolume

• Heat capacity can be defined at Heat capacity can be defined at constant pressure and constant volumeconstant pressure and constant volume

• For solids and liquids they are similarFor solids and liquids they are similar

• For gases the values differ by R (the For gases the values differ by R (the ideal gas constant):ideal gas constant):

CCPP = C = CVV + R + R

T

qCV

T

qCP

Molar heat capacityMolar heat capacity

• Related to specific heat (sometimes Related to specific heat (sometimes known as specific heat capacity) is the known as specific heat capacity) is the molar heat capacity, Cmolar heat capacity, Cmm: the heat : the heat

required to raise the temperature of 1 required to raise the temperature of 1 molemole of a substance by 1ºC of a substance by 1ºC

molesTCq m

Some examplesSome examples

• The heat capacity of water is much larger The heat capacity of water is much larger than many other substancesthan many other substances– Consequence of strong H-bondingConsequence of strong H-bonding

• Important consequences for climate, the Important consequences for climate, the quality of life, and life itselfquality of life, and life itself

Hess’s law and the many Hess’s law and the many pathwayspathways

• Enthalpy being a state function means Enthalpy being a state function means that enthalpy change for process is that enthalpy change for process is independent of pathwayindependent of pathway

• Hess’s law states that:Hess’s law states that:

Overall enthalpy change for reaction Overall enthalpy change for reaction equals sum of enthalpy changes for equals sum of enthalpy changes for

individual stepsindividual steps

Application: determining Application: determining ΔΔH for unknown H for unknown process in terms of process in terms of ΔΔH for known processH for known process

• Consider the reactionConsider the reaction

Proceeds in two stepsProceeds in two steps

ΔΔHH11 = = ΔΔHH22 + + ΔΔHH33

• Reaction 1 is sum of reactions 2 + 3Reaction 1 is sum of reactions 2 + 3

1322 )...(2)(3)( HgNHgHgN

24222 )...()(2)( HgHNgHgN

33242 )...(2)()( HgNHgHgHN

Obtain Obtain ΔΔHH22 from from ΔΔHH11 and and ΔΔHH33

• ΔΔHH22, which is hard to determine , which is hard to determine

experimentally, is obtained using experimentally, is obtained using ΔΔHH11

and and ΔΔHH33

• ΔΔHH22 is endothermic, the others are is endothermic, the others are

exothermicexothermic

Combustion of CHCombustion of CH44 by alternate by alternate

routesroutes• Route 1: complete Route 1: complete

combustion to COcombustion to CO22

• Route 2: Route 2: intermediate intermediate product is COproduct is CO

• Different pathways, Different pathways, same heatsame heat

Standard heats of formationStandard heats of formation

• Standard heat of formation, Standard heat of formation, ΔΔHHffºº::

The enthalpy change for the formation of The enthalpy change for the formation of 1 mole of a substance in its 1 mole of a substance in its standard standard state state from it constituent elements in from it constituent elements in

their their standard statesstandard states

• ΔΔHºHºff for elements in most stable state is for elements in most stable state is by definition 0by definition 0

• Reactions are often hypotheticalReactions are often hypothetical– ΔΔHºHºff (CH (CH44) is -74.8 kJ/mol although direct ) is -74.8 kJ/mol although direct

reaction between C and Hreaction between C and H22 does not occur does not occur

• Important to know which is the Important to know which is the standard state for any substancestandard state for any substance

• ΔΔHºHºff values are tabulated for many values are tabulated for many

substancessubstances

Heats of reaction, Heats of reaction, ΔΔHHffºº, and , and

Hess’s lawHess’s law• Application of Application of ΔΔHºHºff to calculation of to calculation of

heats of reaction (heats of reaction (ΔΔHºHºRXNRXN) )

• For reaction:For reaction:

aA + bB = cC + dDaA + bB = cC + dD

• Products – reactantsProducts – reactants

)()()()( BHbAHaDHdCHcH of

of

of

of

oreaction

Estimating Estimating ΔΔHºHºff using bond energies using bond energies

• What if What if ΔΔHºHºff value(s) for reaction is value(s) for reaction is

(are) unknown?(are) unknown?

• Estimate enthalpy change as difference Estimate enthalpy change as difference between bonds broken (energy between bonds broken (energy costcost) ) and bonds made (energy and bonds made (energy gaingain))– ΔΔHºHºRXNRXN = D(reactant bonds) – D(product = D(reactant bonds) – D(product

bonds) bonds) – (Bond energies are positive values)(Bond energies are positive values)

COST GAIN

• Consider reaction:Consider reaction:

• On reactant side:On reactant side:– 3 C-H bonds and 3 Cl-Cl bonds are broken3 C-H bonds and 3 Cl-Cl bonds are broken

• On product side:On product side:– 3 C-Cl bonds and 3 H-Cl bonds are made3 C-Cl bonds and 3 H-Cl bonds are made

• Reaction is exothermicReaction is exothermic– H-Cl bond is much stronger than Cl-ClH-Cl bond is much stronger than Cl-Cl

)(3)()(3)( 324 gHClgCHClgClgCH

ClCClHHCClCl DDDDH 3333

kJkJxxxxH 3273303432341032433

More than enthalpyMore than enthalpy

• Some reactions are exothermicSome reactions are exothermic• Some reactions are endothermicSome reactions are endothermic• Both kinds of reaction can occur Both kinds of reaction can occur

spontaneously. Or not. Why?spontaneously. Or not. Why?• The enthalpy is not the arbiter of spontaneityThe enthalpy is not the arbiter of spontaneity• There is more to energy than heatThere is more to energy than heat• We must also consider entropyWe must also consider entropy• Stay tuned for the Second Law…Stay tuned for the Second Law…