topic 4: thermodynamics
TRANSCRIPT
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
TOPIC 4: Thermodynamics
Key concepts Heat and work First law of thermodynamics Enthalpy Heat capacity Second law of thermodynamics: Entropy Third law of thermodynamics Free energy
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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AIMS: 1. To learn how to calculate the absorbed or released heat of a chemical reaction at a reference temperature. 2. To learn how to calculate the absorbed or released heat of a chemical reaction at any temperature. 3. To learn how to predict if a given reaction takes place as it is written or in the opposite way. 4. To learn quantitative criteria to handle equilibrium reactions
Key concepts: 1. Thermodynamic state 2. Thermodynamic function 3. Reversible and irreversible processes 4. Chemical equilibrium
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Energy: the ability to do work Heat : is the form energy uses to be transferred from a system to other at lower temperature. Dynamics: time evolution of a physical system
System: A system is the specific portion of the universe that is being studied Environment: Everything outside the system
Universe = System + Surroundings (environment)
Thermochemistry is a part of thermodynamics: Thermochemistry is the scientific study of heat that is released or absorbed during chemical changes .
Thermodynamics is the part of physics that studies heat and its transformations
Hint: heat is not a form of energy, is an energy transference method
Key concepts
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Systems
Open systems
Closed systems
Isolated systems
Mass and energy (generally in the form of heat) can be exchanged with environment.
Energy can be transferred but not mass
Neither mass nor energy can be transferred
Isolated system
Closed system heat heat
Closed system heat heat
matter http://es.wikipedia.org/wiki/Agua_embotellada
http://creepypasta.wikia.com/wiki/File:Glass-‐of-‐water.jpg
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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State variables
♣ These macroscopic properties are called thermodynamic variables, for example P, T, V, ...
Is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state. When you fix a small number of these, the rest becomes automatically fixed.
State Function:
♣ A system is in thermodynamic equilibrium when a set of macroscopic properties are fixed. Equilibrium State
♣ Thermodynamic variables can be classified as: • intensive: independent of amount of matter: pressure, temperature • extensive: depend on the amount of matter: mass, volume (dividing the system→ divides the variable)
♣ Some thermodynamic variables are called state functions (functions of state, state quantities or state variables)
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Thermodynamics distinguishes between two modes energy uses to be transferred:
• heat (q) • work (w)
The term work includes all the forms of energy except heat (mechanic, electric, magnetic, etc.).
Work is the way energy is transferred due to a mechanical link between system and surroundings. Heat is the way energy is transferred due to a temperature difference between the system and the surroundings
A system can do two kinds of work: expansion work (associated to a change of volume of the system) and nonexpansion (does not involve change in volume, i.e. a battery)
Heat and work
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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r2
r1
fex
Assume a gas contained in a piston that expands against an external force fex DEFINITIONS w: work DONE BY THE ENVIRONMENT OVER THE SYSTEM
Expansion: the SYSTEM (GAS) MAKES WORK OVER THE SURROUNDINGS
VPVVAfrrA
Afrrfw ex
exexex Δ−=−−=−×−=−−= )()()( 121212
A
Let us consider the transformation from (P1,V1) to (P2,V2). There are several ways: a, b…
P1
P2
V1 V2
P1
P2
V1 V2
a) b)
VPwa Δ−= 1 VPwb Δ−= 2
wa ≠ wb so work is NOT a state function
For a general process where pressure P is not constant dVPw 21
VV ex∫−=
isobaric
isoc
horic
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Reversible process: TD functions differ infinitesimally in two successive instants Consider a gas inside a piston experiencing an expansion or a compression. The pressure inside will be Pint and the pressure exerted by surroundings Pext.
Reversible Expansion
dPPPdPPP
ex
ex
+=
−=
int
int
Reversible Compression
Irreversible Expansion
ex
ex
PPPP
<
>
int
int
Irreversible Compression
revintexirrev
intintexrev
wdVPdVPw
dVPdV)dPP(dVPw
=∫−<∫−=
∫∫ −≅±∫ −=−=
irrevrev ww >
The product between two infinitesimals is insignificant and can be disregarded
Reversible and irreversible processes
Let us calculate the expansion work done OVER the system for the two situations
More work is done in a reversible process
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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In mechanics, total energy is the sum of kinetic and potential energy. These two forms of energy can be exchanged in such a way that total energy
remains constant: law of conservation energy This definition can be extended including an additional term that depends on the
nature of the system. Therefore, total energy depends on three contributions:
a) Rest or motion state of the system b) Position state of the system c) Nature of the system
Internal Energy, E, of a system is that energy that only depends on the nature of the system and is independent on its position in any force field or its rest or motion state.
Internal Energy is the sum of the kinetic energy of the molecules or atoms of the
system (associated to translations, rotations and vibrations) and the potential energy associated to intermolecular forces.
First Law of thermodynamics
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Energy can neither be created nor destroyed: it can only be transformed from one state to another
To increase internal energy of a system, the environment must transfer heat and make work on it.
wqE +=Δ q= heat transferred TO THE SYSTEM (+)
w= work DONE OVER THE SYSTEM (+)
¿Is E a state function?
State 1
State 2 ΔEb
ΔEa Assume two states 1 and 2 with different internal energy. We can imagine at least two trajectories and let us assume that the energy change depends on trajectory. If ΔEb≠ΔEa then, for example, ΔEb>ΔEa. This means that the system returns more energy than we communicate on going from 1 to 2. → law of conservation energy is violated → YES, E is a state function .
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Sign criteria:
How is measured ΔE?
dVPqwqEV
V∫−=+=Δ2
1
If the process happens in a closed container at constant volume
VqqE =+=Δ 0
+w -w
+q -q
Surroundings
System
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Is the absorbed or released heat in a constant pressure process. (H)
pVEH += H is a state function
Its absolute value can not be
determined, only its change during a process. (ΔH)
PqVPVPqVPwqpVEH =Δ+Δ−+=Δ++=Δ+Δ=Δ )()(
Enthalpy
Heat Heat
System System
Surroundings Surroundings
ΔH > 0 Endothermic process
ΔH < 0 Exothermic process
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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In processes where liquids or solids take part, change of volume is very small due to its inherent incompressibility
pVEH +=
EpVEH Δ≈Δ+Δ=Δ )(
In processes in which (ideal) gases take part and at constant temperature, ΔE and ΔH are very different if gases are produced or consumed.
nRTEnRTEpVEH Δ+Δ=Δ+Δ=Δ+Δ=Δ )()(
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Physical quantity that characterizes the amount of heat, q, required to change a body's temperature by a given amount, ΔT, : q = C· ΔT
Molar Heat Capacity Heat capacity per mol of substance (Units J/mol·K), intensive property.
q = m·C·ΔT
q = n·C·ΔT
It can be used for identification of substances.
Specific Heat Capacity Heat capacity per unit mass (units J/Kg·K)
Substance c (J/gºC) Water (l) 4,18 Cu(s) 0.382 Cl2(g) 0.478 Benzene 1,72 NaCl 0.866
Heat capacity
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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dTdH
dT
dqC pp == ∫ Δ==∫==Δ 2
121
TT PP
TT pp TnCdTnCdTCnqH
V
vv
q0q)VP(qwqE
dTdE
dTdq
C
=+=
=Δ−+=+=Δ
==TnCdTnCdTCnqE v
TTv
TT vv
21
21
Δ=∫=∫==Δ
V = const. TnCE vΔ=Δ
P = const. TnCH pΔ=Δ
Heat capacity at constant pressure CP or constant volume CV
Assuming that CP and CV are independent of T
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Relation between Cv and CP
pVEH += dTpVd
dTdE
dTdH )(
+= dTpVdCC VP)(
+=
Gases pV= nRT
Cp – Cv = nR
Solids and liquids
ΔV ≅ 0 Cp ≅ Cv
nRCdTpVdCC VVP +=+=)(
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Enthalpy and chemical reactions
Standard state: (refer to transparency 14 Topic 0) the most stable state at P = 1 atm and an specific temperature (usually 298,15 K)
Standard Molar Enthalpy of reaction, ΔH0 : change of enthalpy for a chemical reaction when reactants and products are in standard state, per mole of reaction as it is written.
Standard Molar Enthalpy of formation, ΔH0 f: change of enthalpy when one mole of a pure compound is formed from its elementary antecedents.
Chemical reaction: a process in which reactants are transformed in products.
C(graphite) + 1/2O2(g) → CO2(g) ΔH0f = -393,51 kJ/mol
H2(g) + 1/2O2(g) → H2O(l) ΔH0f = -285,83 kJ/mol
By definition, the standard molar enthalpy of formation of a pure element is cero.
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Some rules of thermochemistry:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
ΔH = -890.4 kJ/mol
CO2(g) + 2H2O(g) → CH4(g) + 2O2(g) ΔH = +890.4 kJ/mol
1- Enthalpy of reaction ΔH is proportional to the amount of reactants or products:
2- The value of ΔH in a reaction is equal and opposite to the value of ΔH for the reverse reaction:
2CH4(g) + 4O2(g) → 2CO2(g) + 4H2O(g)
ΔH = -2x890.4 = 1780.8 kJ
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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)(2)()(2)( 2224 lOHgCOgOgCH +→+ ΔH = -890.4 kJ/mol
)()( 22 gOHlOH → ΔH = 40.7 kJ
)(2)()(2)( 2224 gOHgCOgOgCH +→+ ΔH = ? kJ
)(2)()(2)( 2224 lOHgCOgOgCH +→+ ΔH = -890.4 kJ/mol )(2)(2 22 gOHlOH → ΔH = 2x40.7 kJ
)(2)()(2)( 2224 gOHgCOgOgCH +→+ ΔH = -890.4 + 81.4 = -809 kJ/mol
3- The value of ΔH for a reaction is the same whether it occurs in one stage or in a series of stages ⇒ Hess law
Consider the following reactions
What is the enthalpy of reaction for the following?
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
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∑∑ Δ−Δ=Δi
ifii
ifireaction RHnPHnH )()( 000
4- For a given reaction, the reaction enthalpy ΔHºreaction can be calculated from
the enthalpy of formation of both the reactants ΔHºf(Ri) and the products ΔHº
f(Pi) according to
Example
)(2)(2)(2
)(2)()(2)(2)(
)()(2)(
)()(2)(2)(
)(2)()(
21
21
lgg
lgggs
ggs
lggs
lgl
OHOH
OHCOHOC
COOC
HCOOHHOC
OHCOHCOOH
→+
+→++
→+
→++
+→ Enthalpy of combustion of formic acid
Enthalpy of formation of formic acid, carbon monoxide and water
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Example (cont.)
)(2)(2)( ggs HOC ++
)(2)( lg OHCO +)(lHCOOH
ΔH1 = ΔHºf (CO) + ΔHº
f (H2O ) - ΔHºf (HCOOH) = ΔH2
ΔH3
According to Hess law, ΔH3 = ΔH2 + ΔH1 ΔH3 = - ΔHº
f (HCOOH) + ΔHºf (CO) + ΔHº
f (H2O ) ΔH3 = ΔHº
f (CO) + ΔHºf (H2O ) - ΔHº
f (HCOOH) ΔH3 = Σ ΔHº
f (P) - Σ ΔHºf (R)
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Temperature dependence of enthalpy
dDcCbBaA +→+
( ) ( ) ( ) ( )][][)( 0,
0,
0,
0,1
01111BHbAHaDHdCHcTH TfTfTfTf Δ+Δ−Δ+Δ=Δ
Assume the following reaction Its reaction enthalpy at T = T1 es ΔH0(T1)
We want to calculate the reaction enthalpy at T = T2.
(aA + bB) at T1
(aA + bB) at T2
(cC + dD) at T1
(cC + dD) at T2
ΔH0 (T1)
ΔH0 (T2)
ΔH’(T1→T2 ) ΔH’’(T2→T1 )
To go from 1 to 2 we have two paths:
a) Direct reaction at T1 b) Heating the reagents at T2,
reacting at T2, cooling the products at T1. 1 2
ΔH0 (T1) = ΔH’(T1→T2 ) + ΔH0 (T2) + ΔH’’(T2→T1 )
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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ΔH’ is the heating enthalpy of reagents
)(' 2
1
RCHT
T p∫=Δ
ΔH’’ is the cooling enthalpy of products
)(' 1
2
PCHT
T p∫=Δ
)()()( BbCAaCRC PPP +=
)()()()( 00000 BbCAaCDdCCcCC PPPPP −−+=Δ
)(''')( 20
10 THHHTH Δ+Δ+Δ=ΔTherefore
∫∫∫∫∫
Δ+Δ=−+Δ=
=−−Δ=Δ−Δ−Δ=Δ
2
1
2
1
2
1
1
2
2
1
01
01
0
10
10
20
)()()()(
)()()(''')()(T
T P
T
T P
T
T P
T
T P
T
T P
dTCTHdTRCdTPCTH
dTPCdTRCTHHHTHTH
Where
If CP of reagents and products do not differ too much, reaction enthalpy does not change appreciably with temperature
)()()( DdCCcCPC PPP +=
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Is a measure of the microscopic disorder within the system
It is a state function. In a process, the entropy change is: initialfinal SSS −=Δ
0>−=Δ initialfinal SSSIn all cases
Second Law of thermodynamics. Entropy
Liquid Solid Gas Liquid
Solid+liquid Solution T1 T2 (T2>T1)
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Reversible process: TD functions differ infinitesimally in two successive instants
irrevirrev
revrev
wqEwqE+=Δ
+=Δ
irrevrev qq >
irrevrev ww >
As state function internal energy does no depend on the path. So for two processes: reversible and irreversible
For an expansion, the work done reversibly is more negative (the system decreases its internal energy doing work) than irreversibly.
The more negative the work is, the more positive the heat must be to keep constant the internal energy variation
The heat absorbed by a system as it does reversible expansion work is higher than the heat absorbed irreversibly
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Wording
In an irreversible or spontaneous process, the entropy of Universe increases but remains constant in a reversible process or in equilibrium
0>Δ+Δ=Δ gssurroundinsystemuniverse SSSSpontaneous process
0=Δ+Δ=Δ gssurroundinsystemuniverse SSS Equilibrium process
0<Δ universeS Impossible process
http://en.wikipedia.org/wiki/File:Skier-‐carving-‐a-‐turn.jpg
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Let us assume: dDcCbBaA +→+
Standard reaction entropy ][][ 00000BADCreactionsystem bSaSdScSSS +−+=Δ=Δ
∑∑ −=Δ 000reactivesproductsreaction mSnSS
∫=Δ2
1 TdqS revDefinition
Temperature dependence of entropy
• Constant P process dqrev = dqP = dH = nCPdT
• Constant V process dqrev = dqV = dE = nCVdT
2
12
1
2
12
1
ln
ln
2
1
2
1
TTnCdT
TnC
TdqS
TTnCdT
TnC
TdqS
V
T
TVrev
P
T
TPrev
≈==Δ
≈==Δ
∫∫
∫∫ (constant P)
(constant V)
Reaction entropy
Absolute entropy can not be calculated (unless third law TD), only entropy changes.
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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As a system approaches absolute zero, all processes cease and the entropy of the system approaches a minimum value. This minimum value, the residual entropy, is not necessarily zero, although it is almost always zero in a perfect, pure crystal
This allows defining absolute entropies
dTTCSSS
T PTT ∫==−
0
000
00
dTTGC
SdTTLC
SdTTSCS
T
TP
v
T
TP
f
T PT
b
b
f
f
∫
∫
∫
+
+Δ++
+Δ+=
)(
)(
)(
0
0
0
00
Third Law of Thermodynamics
Temperature
Ent
ropy
(S)
Entropy of vaporization
Entropy of fusion
Boiling point Melting point
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Absolute entropies , S0 (J·mol-1·K-1) at 298.15 K GASES LIQUIDS SOLIDS
C 158 C(g) 5.74 C2 199 C(d) 2.38 S 238 Srhombic 31.8
Smonoclinic 32.3 H2O 189 H2O 69.9 SO3 257 SO3 114 CO 198 CO2 214
Fe 27 Fe2O3 87
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Gibbs energy is the capacity of a system to do non-mechanical work and ΔG measures the non-mechanical work done on it. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process. Therefore, ΔG is the available energy for doing work.
TSHG −=
TERMOQUÍMICA
rev
rev
dqdqdG
qTdSdqdH
dT
SdTTdSdHdG
−=
=
=
=
−−=
PconstantatTconstantat0 If the process is reversible
dq =dqrev → dG = 0 Equilibrium If the process is irreversible q<qrev → dG < 0 (Spontaneous)
Mahan, page 360
Free Energy
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
Spontaneity in chemical reactions
STHG Δ−Δ=Δ
0<ΔG Spontaneous reaction
0>ΔG Non spontaneous reaction
0=ΔG Equilibrium reaction
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Standard free energy of formation ΔGf0
dDcCbBaA +→+For a general reaction :
000reactivesproductsreaction GGG Δ−Δ=Δ
[ ] [ ])()()()( 00000 BGbAGaDGdCGcG ffffreaction Δ+Δ−Δ+Δ=Δ
( ) ( )[ ] ( ) ( )[ ]000000000 )()()()( BfAfDfCfreaction STBHbSTAHaSTDHdSTCHcG Δ−Δ+Δ−Δ−Δ−Δ+Δ−Δ=Δ
Change of free energy when a mol of a compound in standard state is formed from its antecedent elements in standard state
000fff STHG Δ−Δ=Δ
By definition, the free energy of formation of elements in standard state is zero
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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Relation between Free Energy and equilibrium
VdPdG
dTSdTVdPdG
qTdSdqdq
PdVdqdE
SdTTdSVdPPdVdEdGTSPVETSHG
rev
rev
=
=
−=
=
=
−=
−−++=
−+=−=
Tconstantat0
For a reversible process
For a change of pressure at constant T
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
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PnRTGnGn
PRTPPRTGG
PdPRTdG
PdPRTGd
VdPdG
P
P
G
G
ln~~lnln~~
~
0
00
1
~
~ 00
=−
==−
=
=
=
∫∫=
For 1 mole of ideal gas
Integrating between a standard state and a non standard state
For n moles of ideal gas
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
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QRTGPPPPRTGG
PbRTPaRTPdRTPcRTBGbAGaDGdCGcG
BGbAGaDGdCGcG
PdDPcCPbBPaA
bB
aA
dD
cC
BADC
DCBA
ln~ln~~
]lnlnlnln[)](~)(~)(~)(~[~
)(~)(~)(~)(~~)()()()(
00
0000
+Δ=+Δ=Δ
−−++
+−−+=Δ
−−+=Δ
+→+
Let us assume a general reaction between ideal gases each with a partial pressure Pi
We apply the equation found previously
Important equation since allows to calculate the free energy change for any arbitrary set of partial pressures
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
Autors: Juan Baselga & María González
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QRTGG ln~~ 0 +Δ=Δ
Let us assume that our general reaction is at equilibrium. Partial pressures correspond to the equilibrium ones. Since initial and final states are equal the free energy change will be 0 and
The functional relation between equilibrium partial pressures is called Equilibrium Constant
P
mequilibriu
KRTG
QRTG
ln~ln~0
0
0
−=Δ
+Δ=
RTH~
RS~
RTG~
P
000
eeeKΔ
−Δ
+Δ
−==
- No units - Only depends on T - Reaction entropy and reaction enthalpy
Chemistry for Biomedical Engineering. TOPIC 4: Thermodynamics Open Course Ware Universidad Carlos III de Madrid 2012/2013
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Temperature dependence of Equilibrium Constant
If the reaction takes place between gases, we can assume that the difference in heat capacities between reagents and products will be very small, so entropy change can be disregarded
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ−=
Δ−≈
Δ+
Δ−=
=Δ
−Δ
+
12
0
2
1
000
~~
11~
)()(ln
~~~ln
00
TTRH
TKTK
RTH
RTS
RTHK
eeK
P
P
P
RTH
RTS
P
This equation allows to calculate the equilibrium constant at any T if reaction enthalpy is known and if K is also known at a given temperature. These equations for KP can be extended to reactions in which reactants and products are in liquid phase. We will not demonstrate it. No units, same temperature dependence.