Energetics & Equilibria 6: Main recall Flashcards
Expression for weight, W
W = N! / n0! x n1! x n2! x … x nn!
formula for Boltzmann distribution
ni = n0e−εi /kT
- ni is the number of molecules in energy level i
- εi is the energy of i
- n0 is the population of the ground level, which has energy 0
- k is Boltzmann’s constant (k = R/NA, where NA is Avogadro’s constant)
Verbally, as the energy of a level increases, its population decreases. Levels with energies less than or similar to kT have significant populations. So ground level is most populated
Entropy is related to the number of ways of achieving a configuration. Give its formula in terms of this.
S = k lnW
An object at temperature T reversibly absorbs a small amount of heat. Give the formula for the entropy change.
dS = δqrev/T
Give the formula for the entropy change of the universe
∆Suniv = ∆Ssys + ∆Ssurr
= ∆Ssys - qsys/Tsys
equation for the first law of thermodynamics
∆U = q + w
q, heat absorbed by system
w, work done on system
ideal gas equation and units used?
pV = nRT
- P in Pa (Nm-1)
- V in m3
- n in mol
- T in K
- R in J K-1 mol-1
A gas is confined inside a cylinder by a piston. Give the expression for the work done by the gas when the piston moves.
δw’ = pextdV
work done by gas = external pressure x change in volume of gas
Integrated relationship for work done by a gas, when the gas expands from volume vi to vf, against constant external pressure.
w’ = pext(Vf - Vi)
Integrated relationship for work done by an ideal gas, when the gas expands isothermally from volume vi to vi.
w’ = nRTln(Vf/Vi)
What expression gives the heat absorbed in a reversible, isothermal expansion of an ideal gas, from volume Vi to Vf?
qrev = nRTln(Vf/Vi)
isothermal and ideal so w’ = q
What expression gives the entropy change of the gas in a reversible, isothermal expansion of an ideal gas, from volume Vi to Vf?
∆S = nRln(Vf/Vi)
What is the heat equal to under:
- constant volume conditions?
- constant pressure conditions?
- volume: ∆U, change in internal energy
- pressure: ∆H, enthalpy change
Give the definition of the
- constant volume molar heat capacity
- constant pressure molar heat capacity
CV,m = (∂Um/∂T)V
Cp,m = (∂Hm/∂T)p
State the definition of enthalpy (eq)
H = U + pV
The molar enthalpy of a substance is known at temperature T1. Give the expression for the molar enthalpy at temperature T2.
Hm(T2) = Hm(T1) + Cp,m(T2 - T1)
How are the molar entropy and enthalpy associated with a phase change related?
ΔSm,pc = ΔHm,pc/Tpc
Give the relationship for converting molar entropies from one temperature to another.
Sm(T2) = Sm(T1) + Cp,mln(T2/T1)
Definition of Gibbs energy, G (eq)
G = H - TS
ΔG = ΔH - TΔS
Give the first, second and third master equations
dU = TdS - pdV
dH = TdS + Vdp
dG = VdP - SdT
Give the expression for how molar Gibbs energy varies with pressure, at constant temp, for an ideal gas.
Gm(p) = Gom + RT ln(p/po) (const. temp, ideal gas)
Give the expression for how Gibbs energy varies with volume, at constant temp, for an ideal gas.
G(V2) = G(V1) + nRTln(V1/V2) (const. temp, ideal gas)
Give the expression for how molar Gibbs energy varies with temperature, at constant pressure, for an ideal gas.
Gibbs-Helmholtz equation:
d/dT(G/T) = -H/T2 (const. pressure)
Give the expressions for partial pressure and mole fraction.
Partial pressure: pi = xiptot
Mole fraction: xi = ni/ntot
Give the expression for how molar Gibbs energy varies with pressure, at constant temp, for an ideal gas in a mixture.
Gm,i(pi) = Gom,i + RT ln(pi/po) (const. temp, ideal gas)
Ideal gases don’t interact, so there is no distinction between a pure gas at pressure p, and that same gas at partial pressure pi in a mixture
Give the formula for the Gibbs energy of
- a mixture of ideal gases
- a mixture of solids/liquids/solutions
Ideal gases don’t interact, so just add the molar Gibbs energy of each species, each multiplied by its mole fraction, each at its own partial pressure:
- G = nAGm,A(pA) + nBGm,B(pB) + …
- G = nAμA + nBμB + …
Give the expression for how chemical potential of
- gaseous species i varies with pressure, at constant temp, in a mixture
- ideal, dissolved species i varies with pressure, at constant temp, in a mixture
- μ(pi) = μoi + RT ln(pi/po)
- μ(ci) = μoi + RT ln(ci/co)
- Both analagous to:*
- Gm,i(pi) = Gom,i + RT ln(pi/po) (const. temp, ideal gas)*
Give the expression for the standard Gibbs energy of a reaction.
ΔrGo = ΔrHo - TΔrSo
- ΔrHo varies with temperature. Give the relationship giving ΔrHo at temperature 2, given knowledge of ΔrHo at temperature 1.
- ΔrSo varies with temperature. State the relationship giving ΔrSo at temperature 2, given knowledge of ΔrSo at temperature 1.
ΔrHo(T2) = ΔrHo(T1) + ΔrCpo[T2 - T1]
ΔrSo(T2) = ΔrSo(T1) + ΔrCpoln(T2/T1)
What is true of Gibbs energy at equilibrium?
∆rG = 0
Give the expression linking the standard Gibbs energy of reaction and the equilibrium constant.
∆rGo = -RTlnK
Give the van’t Hoff equation.
dlnK/dT = ΔrHo/RT2
Write the equation showing the temperature-dependence of the equilibrium constant
lnK = -(ΔrHo/R)(1/T) + (ΔrSo/R)
How is the cell potential calculated from the half-cells?
Ecell = E = E1/2(RHS) - E1/2(LHS)
Eo = Eo1/2(RHS) - Eo1/2(LHS)
Give the equation relating cell potential (of the conventional cell reaction) to Gibbs energy.
ΔrGcell = -nFE (constant temp and pressure)
Give the expression for:
- the entropy change of a cell reaction
- the enthalpy change of a cell reaction
ΔrS = nF(∂E)/∂T)p
ΔrHcell = TnF(∂E)/∂T)p - nFE
Write the expression linking activity to chemical potential.
µi(ai) = µio + RTln(ai)
Give the general form of the Nernst equation.
E = Eo - (RT/nF) ln(products/reactants)
For solids/liquids, chemical potential = standard chemical potential, so E = Eo
