P Chem Flashcards
Bohr Atom Energy
En = 13.6 eV / n^2
Nodes
Total: n - 1
Radial: n - l - 1
Angular: l
First Law of Thermodynamics
dU = q + w
Cp/Cv relationship
Cp - Cv = nR
PV work with Pext
w = -P(ext) (Vf - Vi)
Solving 1st Law for Q
q = dU - w = dU + P(ext)dV
Irreversible process work
w = - nRT ln(V2/V1)
Internal Energy with C
dU = qv = Cv(Tf - Ti)
Enthalpy/Interal Energy relationship
H = U + PV = U + nRT
Enthalpy with C
dH = qp = Cp(Tf-Ti)
Carnot efficiency
e = 1 - Tcold/Thot
Entropy, general
dS = nR ln(Vf/Vi) = -nR ln(Pf/Pi)
Entropy at constant V
dS = n Cv,m ln(Tf/Ti)
Entropy at constant P
dS = n Cp,m ln(Tf/Ti)
Entropy at phase change
dS = dHvap / dTvap (or fus)
Total entropy
dS(total) = dS + dS(surroundings)
Second Law of Thermodynamics
The entropy of an isolated system never decreases
Third Law of Thermodynamics
The entropy of a pure, perfectly crystalline substance is zero at zero kelvin
Absolute entropy
S = k ln (W)
DOF nonlinear gas molecule
3 Translational
3 Rotational
3n - 6 Vibrational
DOF linear gas molecule
3 Translational
2 Rotational
3n - 5 Vibrational
The entropy of all substances is a…
monotonically increasing function of temperature
Helmholtz Free Energy
A = U - TS
Gibbs Free Energy
G = H - TS G = U + PV - TS
dU
dU = TdS - PdV
dH
dH = TdS + VdP
dA
dA = -SdT - PdV
dG
dG = -SdT + VdP
Isobaric volumetric thermal expansion coefficient
a or b = (1/V) (dV/dT)_P
Isothermal compressibility
k = -(1/V)(dV/dP)_T
Gibbs-Helmholtz Equation
[d(G/T)/dT]_P = -H/T^2
dS(mixing)
dS(mixing) = -nR sum(xi ln(xi))
dG(R)
dG(R) = dG(R0) + RT ln Q
G/K relationship
dG = -RT ln K
K/T dependence
ln K@Tf = ln K@T0 - (dH/R)(1/Tf - 1/T0)
Error in IDG
z = Vm/Vm(ideal) = PVm/RT
Boyle temperature
Tb = a/Rb
An increase in P always leads to…
a boiling point elevation
Freezing point is elevated with increased P if…
V liq > V solid
Freezing point is depressed with increased P if…
V liq < V solid
dH(sublimation)
dH(sub) = dH(fus) + dH(vap)
Gibbs’s Phase Rule for pure system
DOF = 3 - p
Clapeyron Equation
dP/dT = dSm/dVm
Slope of coexistence curve!
Trouton’s Rule
dSm(vap) ~ 90 J/mol*K for liquids
Clausius-Clapeyron Equation
ln(Pf/Pi) = -(dHm(vap)/R) (1/Tf - 1/Ti)
Raoult’s Law
Pi = xi Pi*
DOF for system with C components
DOF = C - p + 2
Gibbs-Duhem equations
n1dmu1 + n2dmu2 = 0
x1dmu1 + x2dmu2 = 0
x1dV1 + x2dV2 = 0
Boiling Point Elevation
dT(boiling) = Kb*molality(solute)
Freezing Point Depression
dT(freezing) = - Kf*molality(solute)
van’t Hoff Equation
pi = n(solute)RT/V
Ideal Solution characterized by…
dGmix < 0
dSmix > 0
dV mix = 0
dH mix = 0
Henry’s Law for solute
Pi = xi kHi as xi –> 0
Positive Deviation from Raoult’s Law
A-B interactions are least attractive
Minimum boiling azeotrope formed
kH > Pi*
Negative Deviation from Raoult’s Law
A-B interactions are most attractive
Maximum boiling azeotrope formed
kH < Pi*
Standard Solvent State
as xi –> 1,
ai = Pi/Pi*
gi = ai/xi
Standard Solute State
as xi –> 0,
ai = Pi/kHi
gi = ai/xi
G/E relationship
dG = -nfE
E/K relationship
E = (RT/nF) ln K
pH/pKa relationship
pH = pKa + log([A-]/[HA])
Vibrational states…
are only significantly populated at high T
Rotational states…
are populated at room T
rate k/Ea relationship
ln(k) = -Ea/RT
3 amino acids that have an isoelectric point not the average of their two lowest pKa’s
Arg, His, Lys
+ charged side chains
U(translation)
UT = (3/2)nRT
U(rotation)
UR = nRT (linear polyatomic) UR = (3/2)nRT (nonlinear polyatomic)
U(vibration)
UV = nRT in high T limit
U(electronic)
UE = 0
Dulong & Petit Law
Limiting value of heat capacity of a solid is 3R at high T
Debye modification to Einstein solids
Low T heat capacity is proportional to T^3
