ChemicalChemical ThermodynamicsThermodynamics2013/20142013/2014

5th Lecture:ThermochemistryValentim M B Nunes, UD de Engenharia

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ThermochemistrThermochemistryyThe study oh heat required or produced by chemical transformations is called thermochemistrythermochemistry. Its an application of the first Law.

Remember: qp = ΔH and qV = ΔU

Thermochemistry is a branch of thermodynamics. We can measure (indirectly, for instance work or temperature) the energy a reaction produces as heat, and identify q, depending on the conditions, with a change in internal energy or enthalpy.

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Standard enthalpy Standard enthalpy changeschangesChanges in enthalpy when a system undergoes a physical or chemical change are normally reported to a set of standard conditions. We will consider the standard enthalpy changestandard enthalpy change, ΔH°, the change of enthalpy for a process in which the initial and final states are in their standard states.

Standard states: The standard state of a substance is its pure more stable form at the pressure of p° = 1 bar, and specified temperature

“°” means standard state!

Normally values are tabled at given temperatures, usually 298.15 K

Examples: phase Examples: phase transitionstransitions

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Standard enthalpy of vaporization, ΔH°vap

H2O(l) H2O(g): ΔH°vap(373.15 K) = 44.7 kJ.mol-1

Standard enthalpy of fusion, ΔH°fus

H2O(s) H2O(l): ΔH°fus(273.15 K) = 6.01 kJ.mol-1

Standard enthalpy of sublimation, ΔH°subl

C(s, graphite) C(g): ΔH°subl(298 K) = 716.7 kJ.mol-1

Standard enthalpy change in chemical Standard enthalpy change in chemical reactions reactions

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The standard reaction enthalpy, ΔH°r ,at a given temperature T, is the enthalpy of reaction when all reagents and products of reaction are in their standard states.

CH4(g) + 2 O2(g) CO2(g) + 2 H2O(l): ΔH°r = - 890 kJ.mol-1

The “-” signal means the process is EXOTHERMIC!

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Standard enthalpy of formation Standard enthalpy of formation

The standard enthalpy of formation, ΔH°f , of a substance is the standard enthalpy for the reaction of its formation from its constituent elements in their reference states.

6 C(s, graphite) + 2 H2(g) C6H6(l): ΔH°f (benzene, l) = 49 kJ.mol-1

As a consequence, by definition, the standard enthalpy of formation of any element in their reference state is zero at all temperatures

ΔH°f (C, graphite) = 0ΔH°f (O2, g) = 0

…...

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Standard enthalpy of formation Standard enthalpy of formation

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Hess's LawHess's Law

We can now combine standard enthalpies of individual reactions to obtain the enthalpy of another reaction. This is an application of the first Law, resulting from the fact that enthalpy is a state function, is called the Hess’s LawHess’s Law:

The enthalpy of an overall reaction is the sum of reaction The enthalpy of an overall reaction is the sum of reaction enthalpies of individual reactions into which a reaction may enthalpies of individual reactions into which a reaction may be divided.be divided.As a consequence, we may calculate the enthalpy of a chemical reaction, if we now the standard enthalpy of formation of all the substances (see for instance table of slide 7)

reagentsproducts º.

º,

ºif

iiif

iir HHH

νi are the stoichiometric coefficients

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Exothermic and Endothermic Exothermic and Endothermic processesprocesses

At constant pressure, if ΔHr < 0, qp < 0, and heat flows from the reaction to the surroundings and the process is exothermicexothermic.

If ΔHr > 0, qp > 0 , and heat flows into the reaction from the surroundings and the process is endothermicendothermic.

Combustion reactionsCombustion reactions

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Combustion reactions are of particular importance in thermodynamics and applications (thermoelectric power stations, motors,…). The standard enthalpy of combustionstandard enthalpy of combustion, ΔH°c is the standard reaction enthalpy for the complete oxidation of organic compounds to CO2(g) and H2O(l) and N2 if nitrogen is also present. Take for instance the combustion of natural gas (mainly methane):

CH4(g) + 2 O2(g) CO2(g) + 2 H2O(l)

2º

4º

2º

2ºº 22 OHCHHCOHOHHH ffffc

Zero!

kJ 890)87.74()5.393()8.285(2º cH

All combustions are extremely exothermic!If we obtain water vapor (instead of

liquid): kJ 802442890 cH

Vaporization of two moles of water!

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CalorimetryCalorimetry

Constant volume

qr = ΔU

ΔH = ΔU + Δ(pV)

Assume only contributions from gases

Adiabatic!qV = (qwater + qpump + qr) = 0 qr = -(qwater + qpump)

qwater = mwater 4.184 J.g-1.K-1 Tqpump = Cpump t

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CalorimetryCalorimetry

Constant pressure

qp = ΔH

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The variation of enthalpy with The variation of enthalpy with temperaturetemperatureThe majority of industrial or biological reaction with interest occurs at temperatures different from 298 K. Knowing the ΔHr at one temperature, how to calculate it at other temperatures?Consider the following thermodynamic thermodynamic cyclecycle:

Reagents(T)

Products(T)

Reagents(298 K)

Products(298 K)

ΔHR

ΔHT

ΔHp

ΔH298

0298 TPR HHHH

)(TH r

PRr HHHTH 298)(

Tables! ?

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The variation of enthalpy with The variation of enthalpy with temperaturetemperatureRecall

pp T

HC

or dTCdH p

Integrating over two temperatures, T1 and T2:

dTCTHTHT

Tp

2

1

12 )(

This equation is especially simple when Cp is independent of T:

1212 TTCpTHTH

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The variation of enthalpy with The variation of enthalpy with temperaturetemperatureSince the previous equation applies to each substance in the reaction, the standard reaction enthalpy at temperature T2 is:

dTCTHTHT

Tprr

2

1

1º

2º

This equation is known as Kirchhoff’s lawKirchhoff’s law. ΔCp is calculated by;

ReagentsProducts ,, ipi

iipi

ip CCC

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Temperature dependence of heat capacitiesTemperature dependence of heat capacities

If heat capacity is temperature independent previous equations are very simple. If not, the temperature dependence of heat capacity is taken into account by writing:

For organic compounds:

2cTbTaTC p

For inorganic gases:

2

´´´TcTbaTC p

Characteristic coefficients for each substance!

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Adiabatic flame temperatureAdiabatic flame temperature

For a combustion process that takes place adiabatically with no shaft work, temperature of the products is referred to as the adiabatic flame temperature. This is the maximum temperature that can be achieved for given reactants.

The maximum temperature for a given fuel and oxidizer combination occurs with a stoichiometric mixture.

if

T

Tp

p

T

Tp

c

a

TT

dTC

C

dTCH

HH

HHH

f

i

f

i

_

2

º1

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process isothermic

0

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Adiabatic flame temperatureAdiabatic flame temperature

Adiabatic Flame Temperature (K)Fuel Oxygen as oxidizer Air as oxidizer

Hydrogen, H2 3079 2384

Methane, CH4 3054 2227

Propane, C3H8 3095 2268

Octane, C8H18 3108 2277