APSC 132 Equation Sheet
Thermodynamics
R = 8.3145 kPa.L/mol K for monoatomic ideal gases = 8.3145 N m/mol K Cp = 5/2 R, Cv = 3/2 R = =
8.3145 J/mol K 1 Faraday = 96485 C/mol e- = 8.3145 kg m2 /s2 mol K = 0.08206 atm L/mol K
Summary Table (No Reaction)
Condition Work (w) Internal Energy (ΔU) Heat (q) Enthalpy (ΔH)
Isobaric w = -PextΔV ΔU = nCvΔT Q = nCpΔT ΔH = nCpΔT
ΔU= q+w ΔH = q
ΔH = ΔU + PΔV
Isochoric w=0 ΔU = nCvΔT q = ΔU ΔH = nCpΔT
ΔU = q q = nCvΔT ΔH = ΔU + Δ(PV)
Isothermal w = -PextΔV
Reversible:
V2 ∆U = 0 q = -w ∆H = 0
w = -nRT ln ( )
V1
P1
w = -nRT ln ( )
P2
Adiabatic w = -Pext∆V ∆U = nCv∆T q=0 ∆H = nCp∆T
(insulated) ∆U = w ∆H = ∆U + ∆(PV)
γ −1 γ−1 γ γ
Cp
Adiabatic Reversible processes: T 1 V 1 =T 2 V 2 and P1 V 1=P2 V 2, γ=
Cv
Other Special Conditions Equations
Ideal Gas Cp – C v = R
Ideal Monatomic Gas Cv = (3/2) R Cp = (5/2) R
Specific heat capacity Molar heat capacity Heat capacity
q=mcΔT q=nCΔT q=C∆T
∆H°f: enthalpy change for formation of one mole of a compound from elements in standard states
(∆H°f = 0 for elements in their standard state) – reversing a process reverses sign
∆H°rxn = ∑s.c. ∆H°f (products) - ∑s.c. ∆H°f (reactants)
∆S° = ∑s.c. ∆S°(products) - ∑s.c. ∆S°(reactants) ∆G or ∆S < 0: Spontaneous
∆G or ∆S > 0: Non-spontaneous
∆G° = ∑s.c. ∆S°(products) - ∑s.c. ∆S°(reactants) ∆G or ∆S = 0: Equilibrium
Gibb’s Free Energy: ∆G = ∆H - T∆S
∆H° ∆S° ∆G° (high T) ∆G° (low T) Spontaneity
- + - - All T
+ - + + No T
, + + - + High T
- - + - Low T
Entropy
qrev H fus J
S= ∫ Sfus = Svap =88 (Trouton’s Rule)
T T fus mol ∙ K
Stot =S sys +S sur
Condition Equations
Isobaric S = ncpln(T2/T1)
Isochoric S = ncvln(T2/T1)
Isothermal S = nRln(V2/V1)
S = nRln(P1/P2)
Adiabatic (reversible) S = 0
Spontaneous Process
Able to proceed in a given direction without needing to be driven by an outside source of energy
Entropy (ΔS)
Measure of degree of randomness or disorder
Measure of probability that a certain state will exist
Note that
In all irreversible processes Suniv > 0 (spontaneous)
In all reversible processes Suniv = 0 and q = 0 (equilibrium)
A process for which Suniv < 0 is impossible (nonspontaneous)
Kinetics & Mechanisms
At equilibrium, the concentrations of reactants and products can be predicted using the equilibrium
constant, Kc, which is a mathematical expression based on the chemical equation. For example, in the
reaction
aA +bB ⇌ cC+ dDa
where a, b, c, and d are the stoichiometric coefficients, the equilibrium constant is
[C ]c [ D ]d
Kc= a b
[ A] [ B ]
where [A], [B], [C], and [D] are the equilibrium concentrations. If the reaction is not at equilibrium, the
quantity can still be calculated, but it is called the reaction quotient, Qc, instead of the equilibrium
constant, Kc
[ C ]tc [ D ] dt
Qc= a b
[ A ] t [ B ]t
Thermodynamics
R = 8.3145 kPa.L/mol K for monoatomic ideal gases = 8.3145 N m/mol K Cp = 5/2 R, Cv = 3/2 R = =
8.3145 J/mol K 1 Faraday = 96485 C/mol e- = 8.3145 kg m2 /s2 mol K = 0.08206 atm L/mol K
Summary Table (No Reaction)
Condition Work (w) Internal Energy (ΔU) Heat (q) Enthalpy (ΔH)
Isobaric w = -PextΔV ΔU = nCvΔT Q = nCpΔT ΔH = nCpΔT
ΔU= q+w ΔH = q
ΔH = ΔU + PΔV
Isochoric w=0 ΔU = nCvΔT q = ΔU ΔH = nCpΔT
ΔU = q q = nCvΔT ΔH = ΔU + Δ(PV)
Isothermal w = -PextΔV
Reversible:
V2 ∆U = 0 q = -w ∆H = 0
w = -nRT ln ( )
V1
P1
w = -nRT ln ( )
P2
Adiabatic w = -Pext∆V ∆U = nCv∆T q=0 ∆H = nCp∆T
(insulated) ∆U = w ∆H = ∆U + ∆(PV)
γ −1 γ−1 γ γ
Cp
Adiabatic Reversible processes: T 1 V 1 =T 2 V 2 and P1 V 1=P2 V 2, γ=
Cv
Other Special Conditions Equations
Ideal Gas Cp – C v = R
Ideal Monatomic Gas Cv = (3/2) R Cp = (5/2) R
Specific heat capacity Molar heat capacity Heat capacity
q=mcΔT q=nCΔT q=C∆T
∆H°f: enthalpy change for formation of one mole of a compound from elements in standard states
(∆H°f = 0 for elements in their standard state) – reversing a process reverses sign
∆H°rxn = ∑s.c. ∆H°f (products) - ∑s.c. ∆H°f (reactants)
∆S° = ∑s.c. ∆S°(products) - ∑s.c. ∆S°(reactants) ∆G or ∆S < 0: Spontaneous
∆G or ∆S > 0: Non-spontaneous
∆G° = ∑s.c. ∆S°(products) - ∑s.c. ∆S°(reactants) ∆G or ∆S = 0: Equilibrium
Gibb’s Free Energy: ∆G = ∆H - T∆S
∆H° ∆S° ∆G° (high T) ∆G° (low T) Spontaneity
- + - - All T
+ - + + No T
, + + - + High T
- - + - Low T
Entropy
qrev H fus J
S= ∫ Sfus = Svap =88 (Trouton’s Rule)
T T fus mol ∙ K
Stot =S sys +S sur
Condition Equations
Isobaric S = ncpln(T2/T1)
Isochoric S = ncvln(T2/T1)
Isothermal S = nRln(V2/V1)
S = nRln(P1/P2)
Adiabatic (reversible) S = 0
Spontaneous Process
Able to proceed in a given direction without needing to be driven by an outside source of energy
Entropy (ΔS)
Measure of degree of randomness or disorder
Measure of probability that a certain state will exist
Note that
In all irreversible processes Suniv > 0 (spontaneous)
In all reversible processes Suniv = 0 and q = 0 (equilibrium)
A process for which Suniv < 0 is impossible (nonspontaneous)
Kinetics & Mechanisms
At equilibrium, the concentrations of reactants and products can be predicted using the equilibrium
constant, Kc, which is a mathematical expression based on the chemical equation. For example, in the
reaction
aA +bB ⇌ cC+ dDa
where a, b, c, and d are the stoichiometric coefficients, the equilibrium constant is
[C ]c [ D ]d
Kc= a b
[ A] [ B ]
where [A], [B], [C], and [D] are the equilibrium concentrations. If the reaction is not at equilibrium, the
quantity can still be calculated, but it is called the reaction quotient, Qc, instead of the equilibrium
constant, Kc
[ C ]tc [ D ] dt
Qc= a b
[ A ] t [ B ]t
