Constants
R = 8.314 J/mol.K = 8.314 kPa.l/mol.K = 0.0821 atm.L/mol.K
STP = standard temperature and pressure = 273.2 K and 101.3 kPa
SATP = standard ambient temp. and press. = 298 K and 100.0 kPa
For monatomic gasses : Cv= 3/2R ; Cp=5/2R
cp - cv = R
Equations for finding ΔU, ΔH, q and w
• ΔU = q + w (special case ΔU = qv); ΔH = ΔU + ΔPV (special case ΔH =qp)
For isothermal processes
• w = -nRTln(V2/V1) = -nRTln(P1/P2) (reversible); w = -PextΔV (irreversible)
For adiabatic processes
T1V1γ-1 = T2V2γ-1 ; P1V1γ = P2V2γ where γ = cp/cv (reversible)
Thermodynamics
Δq=CΔT or Δq=CΔTm - per mole C=heat capacity – per gram
C= specific heat
ΔU=q+w
U is the total internal energy of the system
W=-Pext
ΔV =nRT/Pext
H=U+PV
ΔHrxn = ∑ 𝐻𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − ∑ 𝐻𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛
ΔU=qv constant V
ΔH=qp Constant P
ΔH=ΔU+PΔV (at constant P) = qp=(nCpΔT)
Solutions
Partial pressures: Pressure of mixture = sum of partial pressures
of each compound
-- X=mole fraction, all X’s add up to 1. – P*=partial pressure
Pa=XaPa*
Ptotal=XaPa*+XbPb* = (Pb*-Pa*)Xb+Pa*
𝑃2
ΔHvap
𝑃1
R
ln ( ) = − (
)(
1
T2
−
1
𝑇1
)
Somehow useful shit
U = ncvΔT = w ; cp - cv = R
ΔH = ΔU + ΔPV = ΔU + (P2V2 – P1V1); ΔH = ncpΔT
Equations for finding ΔS
ΔS =∫ qrev/T; ΔSvap = ΔHvap/Tb;Svap = 88 J/mol.K (Trouton’s rule)
Entropy, Enthalpy and Free Energy Changes for Individual Substances
ΔS = ncpln(T2/T1); ΔS = ncvln(T2/T1); ΔS = nRln(V2/V1)
and ΔS = nRln(P1/P2) constant T
ΔStot = ΔSsys + ΔSsur; ΔG = nRTln(P2/P1)
Changes Occurring During Reactions
ΔXreaction = Σ(s.c.)ΔXf(products) – Σ(s.c.)ΔXf(reactants) where X =H or G
ΔSreaction = Σ(s.c.)S(products) – Σ(s.c.)S(reactants)
ΔGosys = ΔHosys − ΤΔSosys
ΔGsys = ΔGosys + RTlnQ
ΔGosys = -RTlnK (at equilibrium)
ln(K2/K1) = -(ΔHo/R)[1/T2 – 1/T1] (van’t Hoff equation)
Equilibrium Review
An+BnCn+Dn
K=[C] n[D] n/[A] n[B] n
Kp=Kc (RT) ∆ngas
Isothermal = constant T
Adiabatic = q=o (no heat enters or leaves the system)
Isobaric = thermodynamic process with constant pressure
Isochoric = constant volume