Lecture 6 Flashcards
How does Wln support entropy?
Imagine 2 systems Wa and Wb.
The multiplicity of the whole system is Wtotal = WaWb
Total entropy = Sa + Sb
Sa = ln k W
S total = lnkWtotal
S total = lnkWaWb
S total = lnkWa + lnkWb = Sa = Sb.
What is the residual entropy of solid mono-deuterated methane? (CH3D)
The D can occupy any of 4 spaces.
These are all equal in energy so
Sm(0) = k ln W = k ln 4^Na = kNaln4 = Rln4 = 11.52 J mol-1 K-1
Which is very close to the experimental value
What is the residual entropy of CO2?
CO2 has a low dipole, and both arrangements basically equal in energy.
However, below the freezing point some of the orientations from CO too OC(due to the activation energy making the re-orientation process slow) so some orientations are frozen into the crystal.
If the lattice is completly disorderd then the RE would be
Sm(0) = k ln W = k ln 2^Na = kNaln2 = Rln2 = 5.8 J mol -1 K-1
Very far from the experimental value, the value is more positive due to the fact that the small dipole causes some degree of order.
What is the Boltzmann equation for entropy?
S = -k Sum(i)ni(ln(ni/N))
What is the entropy for independent, distinguishable molecules?
S(T) = (U(T) - U(0)/T) + Nklnq
What is the entropy for independent, indistinguishable molecules? (Use Q = q^n/N!)
S(T) = (U(T) - U(0)/T) + Nklnq/N
What is the entropy for interacting molecules? (Q = q^n)
S(T) = (U(T) - U(0)/T) + NklnQ
What is the molar entropy of a 2-state system?
Using the MPF and the mean energy, and the mean energy for a molar system.
Sm = R (Be/1 + e^(Be) + ln(1 + e^(-Be))
How does temperature effect the entropy of a 2 state system?
As T->0, S-> 0 as there is only 1 available state, the GS (W=1)
As T -> infinity, the levels become equally populated and S -> Rln2
How do we find the entropy for the different energy contributions?
Using the entropy for independent, distinguishable molecules?
S(T) = (U(T) - U(0)/T) + Nklnq^M
Where M is the letter for each contribution (T, V ,R or E)
To get the entropy, we sub in the appropriate mean energy, partition function and the mean energy for molar.
What is the entropy for translational contribution? (used for monoatomic gases?
Known as the Sackur-Tetrode equation for a perfect monoatomic gas.
Sm = Rln(Vme^5/2)/NaTW^3)
Where TW is thermal wavelength, equal to h/((2pimkT)^1/2)
How can the standard molar entropy be found?
Using real gas law and pressure correction.
S^om = Rln(kTe^5/2)/p(c)TW^3)
What is the vibrational contribution to entropy?
S^vM = R ((Bhcv/e^(bhcv)-1) - ln(1-e^(Bhcv))
