Thermodynamics- Chemical and Phase Equilibrium

Question 1

What is the positive direction of heat transfer for a reacting system?

Answer 1

Heat transfer to the system

Question 2

Which direction does a chemical reaction proceed in an adiabatique chamber?

Answer 2

The direction of increasing entropy

Question 3

When does a chemical reaction stop?

Answer 3

When the entropy reaches a maximum

Question 4

What can a system and its surroundings be treated as?

Answer 4

They form an adiabatic system

Question 5

Derive the formula showing that a chemical reaction at a specified temperature and pressure proceeds in the direction of a decreasing Gibbs function

Answer 5

Combine 1st and 2nd law relations, δQ-PdV=dU and dS>=δQ/T, to get dU+PdV-TdS<=0. Then differentiate the Gibbs function, G=H-TS, at constant temperature and pressure to get (dG)T,P=dH-TdS-SdT. You know dH=dU+PdV+VdP so sub into previous equation. dP and dT are 0 so (dG)T,P=dU+PdV-TdS which you have shown previously is less than or equal to 0.
All δ symbols are correct.

Question 6

Express the criterion for chemical equilibrium as an equation in terms of the Gibbs function and explain where it comes from

Answer 6

(dG)T,P=0

Reaction stops and chemical equilibrium established when Gibbs function is at a minimum

Question 7

How to find the proportionality constant (extent of reaction), ε, of a reaction

Answer 7

Equal to the change in moles of one component divided by the stoichiometric coefficient of that component if it is involved in the reaction.

Question 8

What is g bar of a component in a mixture?

Answer 8

The molar Gibbs function of that component at the specified temperature and pressure. Also known as chemical potentials.

Question 9

Deriving the criterion for chemical equilibrium

Answer 9

(dG)T,P=Σ(dGi)T,P=Σ(gidNi)T,P=0 (g is g bar, i means component). For a reaction A+B->C+D:
gCdNC+gDdND+gAdNA+gBdNB=0 when small change in number of moles. Differential changes in number of moles of reactants are negative (products positive). And dNi=+/-εvi (v i coefficient) So:
vCgC+vDgD-vAgA-vBgB=0
All component letters are subscript and g is g bar.

Question 10

Deriving the formula for variation of Gibbs function of an ideal gas with pressure at a fixed temperature.

Answer 10

Start with definition of Gibbs function, g=h-Ts (all bar), and the entropy change relation for isothermal processes, Δs=-Ruln(P2/P1) where Δs is bar. Turn the Gibbs function into one with Δs to get (Δg)T=Δh-T(Δs)T. Ts after brackets are subscript. Δh is 0. Sub in Δs equation to get (Δg)T=RuTln(P2/P1)
All g, h and s are bar.

Question 11

Formula for molar Gibbs energy of one component in an ideal gas mixture

Answer 11

gi(T,P)=gi*(T)+RuTlnPi
All i are subscript
* is superscript and means to 1atm
Pi is partial pressure of component in atm

Question 12

Deriving expression that relates partial pressures at equilibrium

Answer 12

Substitute the formula for Gibbs function of each component in ideal gas mixture into criterion for chemical equilibrium equation (values for g bar are substituted to get a very long equation). Standard state Gibbs function change defined as
ΔG(T)=vCgC(T)+vDgD(T)-vAgA(T)-vBgB(T)
Rearrange the previous equation made to get all vigi(T) on one side. Substitute all these in equation above to get
ΔG*(T)=-RuT(vClnPC+vDlnPD-vAlnPA-vBlnPB)
Rearrange to put in one ln function, with each partial pressure to the power of its coefficient, multiplied by -RuT
All component letter are subscript and g is bar

Question 13

Deriving equation to find Kp of ideal gas mixture at specified temperature using standard-state Gibbs energy change

Answer 13

Define Kp as Kp=(PC)(PD)/(PA)(PB) with each partial pressure to the power of its coefficient. Substitute into expression that relates partial pressures at equilibrium (-RuT times ln function). Rearrange to make Kp the subject and get
Kp=e^(-ΔG(T)/RuT)

Question 14

Derive equation for Kp in terms of mole numbers

Answer 14

Start with normal Kp expression in terms of partial pressures. Use fact that Pi=(Ni/Nt)P and Δv=vC+vD-vA-vB. Sub in partial pressures in terms of mole numbers. Expression is generalised to get
Kp=(NC)(ND)/(NA)(NB)^Δv
All to power of their coefficients
Nt is total number of moles

Question 15

Why does Kp only depend on temperature?

Answer 15

It depends on ΔG(T) which depends on temperature only. Isn’t dependent on the pressure of equilibrium mixture and not affected by the presence of inert gases as the ΔG(T) for them is 0.

Question 16

What is the Kp of the reverse reaction in terms of the Kp of the forward reaction?

Answer 16

Equal to 1/Kp of forward reaction

Question 17

What does a larger Kp tell you about the extent of a reaction?

Answer 17

That the reaction is more complete. The value for Kp approaches infinity in the limiting case of a complete reaction.

Question 18

What does the mixture pressure affect?

Answer 18

The equilibrium composition. Kp isn’t changed so if P changes, the mole numbers of reactants and products change to counteract the pressure change. How they change depends on the sign of Δv. If Δv is positive and P increases, moles of reactants increases and moles of products decreases. Opposite true for negative Δv.

Question 19

Does Nt include moles of inert gases in the ideal-gas mixture?

Answer 19

Yes

Question 20

How does the equilibrium composition change with varying amounts of inert gases added?

Answer 20

Depends on sign of Δv. If it’s positive, an increase in moles of inert gases (at specified temperature and pressure) means fewer moles of reactants and more moles of products. Opposite true for negative Δv.

Question 21

What happens to Kp when stoichiometric coefficients are doubled?

Answer 21

It is squared

Question 22

Deriving van’t Hoff equation (derivative of ln(Kp) with respect to temperature)

Answer 22

Start with ln(Kp)=-(ΔG(T))/RuT. Substitute ΔG(T) for ΔH(T)-TΔS(T) and differentiate with respect to temperature to get
d(lnKp)/dT=(ΔH(T))/(RuT^2)-d(ΔH(T))/(RuTdT)+d(ΔS(T))/(RudT)
At constant pressure, Tds=dh. Also Td(ΔS)=d(ΔH) so last 2 terms in above equation cancel leaving
d(lnKp)/dT=(ΔH(T))/(RuT^2)=hR(T)/(RuT^2)
R after h is subscript and h is bar. hR(T) is the enthalpy of reaction at temperature T.

Question 23

Integrate the van’t Hoff equation between two similar temperatures

Answer 23

ln(Kp2/Kp1)=(hR/Ru)(1/T1-1/T2)
h is bar and the R after it subscript
Only true for small temperature changes because that is when hR can be assumed to be constant
hR can be positive or negative

Question 24

Are exothermic reactions more or less complete at higher temperatures?

Answer 24

Less

Question 25

What do the conditions of phase equilibrium depend on?

Answer 25

Temperature and pressure

Question 26

What is phase equilibrium?

Answer 26

When there is no net transformation from either phase of two phases of a pure substance because each phase has the same value of specific Gibbs function

Question 27

Prove that the two phases of a pure substance have the same value of specific Gibbs function when they are in equilibrium

Answer 27

Total Gibbs function for mixture if G=mfgf+mggg (f, g subscript)
If a differential amount of liquid dmf evaporates at constant temperature and pressure, the change in total Gibbs function is
(dG)T,P=gfdmf+ggdmg
gf and gg remain constant at constant temperature and pressure and at equilibrium, (dG)T,P=0 and by conservation of mass dmg=-dmf
Substituting gives 0=gf-gg so gf and gg are equal.

Question 28

What energy is the driving force for phase change?

Answer 28

Gibbs function difference

Question 29

What is the Gibbs phase rule?

Answer 29

In general IV=C-PH+2
Where IV is the number of independent variables
C is the number of components
PH is the number of phases present in the equilibrium

Question 30

Do the two phases of a two component system have the same composition (mole fraction) in each phase?

Answer 30

In general, no

Question 31

Does phase equilibrium always exist at the interface of two phases of a species?

Answer 31

Yes

Question 32

Deriving Henry’s law

Answer 32

Start with the fact that the mole fractions of a species i in the gas and liquid phases at the interface are proportional to each other. Times both side by pressure to get partial pressure on gas side proportional to Pyi on liquid side. This is Henry’s law and is expressed as
yi,liquid side=(Pi, gas side)/H
H is Henry’s constant which is the product of total pressure of gas mixture and proportionality constant (law can be written in terms of concentrations as well). Only holds for dilute gas-liquid solutions.

Question 33

How does concentration of gas dissolved in liquid vary with Henry’s constant?

Answer 33

It is inversely proportional to Henry’s constant

Question 34

How does Henry’s constant depend on temperature?

Answer 34

It increases with increasing temperature (thus fraction of dissolved gas in the liquid decreases)

Question 35

What is Raoult’s law?

Answer 35

Pi,gas side=(yi,gas side)Ptotal=(yi,liquid side)(Pi,sat(T))
Where Pi,sat(T) is the saturation pressure of the species i at the interface temperature
Ptotal is the total pressure on the gas phase side
Applies when gas is highly soluble in the liquid