152B
fugacity liquid
(fugacity coeff)_sat*Psat(exp((Vbar*(P-Psat))/RT)
Relative Volatility (alpha12)
(y1/x1)/(y2/x2) = (gam1*P1sat/(gam2*P2sat) = 1 for azeotropes
deltaS_mix (ideal)
-R*sum(yi*lnyi) (J/molK)
deltaH_mix, deltaV_mix (ideal)
0
Phase rule (all)
2+1+NC-NP-r
Definition of ideal mixture
A solution which does not have any excess properties. A mixture where the fugacity depends linearly on concentration. A mixture where activity is one for all components.
M1_bar
M+x2(dM/dx1)
M2_bar
M-x1(dM/dx1)
deltaG_mix (ideal)
RT*sum(yi*lnyi) (J/mol)
Gi_R (or _E for liquid?)
RTln(fugacity coeff)
entropy of mixing
Smix-sum(xi*Si)
G_bar
chemical potential (ui) (effective energy of a particle in a system)
ln(gam_i)
d(nG_E/RT)/dni
T^-1
dS/dE
Stability of single phase
deltaGmixing<0, mixed system is lowest G, d(deltaG)^2/dxi^2 >0
Heat/Enthalpy of solution
deltaH~ = deltaH/xi
BP elevation/ FP depression
deltaT = Tboil-Tboil_pure = ((MWsolv)*R*Tboil^2/(deltaHvap))*molality_solute (molality_solute = xsolute*MWsolvent) (DONT FORGET DISSOCIATION)
Partial molar M_bar
dnM/dni
k
exp(-deltaG0/RT)
fugacity coefficent
f/p (=1 for IG)
gam_i (for liquids)
f_bar_i/(xi*fi)
fugacity coeff_bar_i
f_bar_i/(yiP)
Definition of ideal solution
fi = fi_bar for all i
activity coefficient in infinite dilution
gam_i ~ 1 (if xj ->0)
ln(fugacity coeff)
int(zi-1)/P dP|0,P
Adsorption henrys constant
k = lim(p->0) n/p
S (related to states)
kB*lnw
Hi (henrys constant)
lim(xi->0)fi_bar/xi = lim(fi*gami)
Arrhenius (k dependence on T)
ln(k(T1)/k(T2)) = -(deltaH0/R)(1/T1 - 1/T2) (from d(lnk)/dT = deltaH0/RT^2)
relation x and molality
molality = x_solute/MWsolvent
relation fugacity and chemical potential
mui = mui_IG +RTln(f/P0)
General phase equilibrium
mui_I = mui_II, f_bar_i = f_bar_i
k (liquid)
multi(xi*gam_i)^vi = k
k (gas)
multi(yi*coeffi)^vi = k*(P/P0)^-v
n_i
n0+vi*e
Adsorption ideal lattice gas
n=((m-n)/m)*k*p
yi (in terms of extent of rxn)
ni/n = (ni0+vi*e)/(n0+ve)
Vtot
ntot*Vmix
Eutectic Point
phi_1+phi_2 = 1 = exp((deltaH1/RTm1)*((Te-Tm1)/Te)+exp((deltaH2/RTm2)*((Te-Tm2)/Te) (only point x1=phi_1, x2=phi_2)
Osmosis (vant hoff)
pi = (RT*x1)/V2 (V2 = molar volume [=] m^3/mol) (DONT FORGET DISSOCIATION)
deltaM_mix
sum(xi*(M_bar_i-M_i))
Vmix
sum(xiV_bar_i) (volume per mole mixture)
relation mole fraction, mass fraction
w = MWsol*xsol/(MWsolv*xsolv+MWsol*xsol)
SLE
xi = zi*phi_i
LLE
xi*gamma_i = xi*gamma_i
Henrys Law
yi*P=xi*Hi
Raoults Law
yi*P=xi*Pisat
k factor
yi/xi
overall concentration (2-phase flash)
zi = xi*L+yi*V
