> restart;#'therm_eq9.mws'.22-6-00.

Chapter 9: Set of pre-written equations available.

Nomenclature for a chemical reaction: detailed and global forms

> eq9_1:=Sum(nu1[i]*Comp[i],i=1..C)=Sum(nu2[i]*Comp[i],i=1..C);eq9_2:=0=Sum(nu[i]*Comp[i],i=1..C);

Sum(`*`(nu1[i], `*`(Comp[i])), i = 1 .. C) = Sum(`*`(nu2[i], `*`(Comp[i])), i = 1 .. C)
0 = Sum(`*`(nu[i], `*`(Comp[i])), i = 1 .. C)

Definiton of advance of reaction

> eq9_3:=n[i]=n0[i]+nu[i]*xi;

n[i] = `+`(n0[i], `*`(nu[i], `*`(xi)))

Definiton of affinity

> eq9_6:=A=-Sum(nu[i]*mu[i],i=1..C);

A = `+`(`-`(Sum(`*`(nu[i], `*`(mu[i])), i = 1 .. C)))

Gibbs's function in terms of affinity

> eq9_7:=dG=-S*dT+V*dp-A*dxi;

dG = `+`(`-`(`*`(S, `*`(dT))), `*`(V, `*`(dp)), `-`(`*`(A, `*`(dxi))))

Chemical potential mu(T,p,xi)

> eq9_8:=mu[i]=mu[i0T]+R[u]*T*ln(x[i]*p/p0);

mu[i] = `+`(mu[i0T], `*`(R[u], `*`(T, `*`(ln(`/`(`*`(x[i], `*`(p)), `*`(p0)))))))

Enthalpy of reaction and similar functions

> eq9_9a:=grR=Sum(nu[i]*g[i],i=1..C);eq9_9b:=hrR=Sum(nu[i]*h[i],i=1..C);eq9_9c:=srR=Sum(nu[i]*s[i],i=1..C);eq9_9d:=vrR=Sum(nu[i]*v[i],i=1..C);

grR = Sum(`*`(nu[i], `*`(g[i])), i = 1 .. C)
hrR = Sum(`*`(nu[i], `*`(h[i])), i = 1 .. C)
srR = Sum(`*`(nu[i], `*`(s[i])), i = 1 .. C)
vrR = Sum(`*`(nu[i], `*`(v[i])), i = 1 .. C)

Relation between Gibbs function of reaction, enthalpy of reaction and entropy of reaction

> eq9_10:=gr=hr-T*sr;

gr = `+`(hr, `-`(`*`(T, `*`(sr))))

Definition of the equilibrium constant and its relation to equilibrium concentrations

> eq9_219:=K(T,p0)=A(T,p0,1);eq9_20:=Product(x[Comp[i]]^nu[i],i=1..C)=(p0/p)^Sum(nu[i],i=1..C)*K(T);

K(T, p0) = A(T, p0, 1)
Product(`^`(x[Comp[i]], nu[i]), i = 1 .. C) = `*`(`^`(`/`(`*`(p0), `*`(p)), Sum(nu[i], i = 1 .. C)), `*`(K(T)))

Temperature dependance of the equilibrium constant  

> eq9_25:=lnK=(-grR+hrR*(1-T25/T))/(R[u]*T25);

lnK = `/`(`*`(`+`(`-`(grR), `*`(hrR, `*`(`+`(1, `-`(`/`(`*`(T25), `*`(T)))))))), `*`(R[u], `*`(T25)))

WARNING. A list of all variables follows, to copy and paste to the save command (after Maple7 there is no saving all). CAUTION: After pasting all, I must MANUALLY delete system variables: like RealRange_...

> sort([anames()]);

[eq9_1, eq9_10, eq9_2, eq9_20, eq9_219, eq9_25, eq9_3, eq9_6, eq9_7, eq9_8, eq9_9a, eq9_9b, eq9_9c, eq9_9d, ln, `tools/membertype`, `type/SymbolicInfinity`]
[eq9_1, eq9_10, eq9_2, eq9_20, eq9_219, eq9_25, eq9_3, eq9_6, eq9_7, eq9_8, eq9_9a, eq9_9b, eq9_9c, eq9_9d, ln, `tools/membertype`, `type/SymbolicInfinity`]

> #save eq9_1, eq9_10, eq9_2, eq9_20, eq9_219, eq9_25, eq9_3, eq9_6, eq9_7, eq9_8, eq9_9a, eq9_9b ,eq9_9c, eq9_9d, "../therm_eq9.m":`

>