Energetics & Equilibria 6: Main recall
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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