9a248212-5656-4a34-b1de-70cde5c20119 39 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Chemical equilibrium

Reference: Butler, Carbon Dioxide Equilibria. Prob 2-11, pg.41

http://www.edasolutions.com/old/MathCad/DrGriffin/ Butler/Chap2/IC_dist_in_an_open_system.PDF

Coefficients pertaining to the "Equilibrium solution" k1 10 6.3 -^: 1rst dissociation constant carbonic acid ≡ k2 10 10.3 -^: 2nd dissociation constant carbonic acid ≡ kw 1014 -^: kh 10 1.5 -^: PCO2 10 3.5 -^: 61 line

Something else C 1.5 103 -^* : inorganic carbon ≡ Na 2103 -^* : inorganic sodium ≡ 21 line

balance H OH * kw ≡ CO2 kh PCO2 * ≡ H HCO3 * k1 CO2 * ≡ H CO3 * k2 HCO3 * ≡ H HCO3 2 CO3 * + OH + ≡ 51 mat :

ionisation of water: equilibrium expression Henry's law: equilibrium gas/liquid 1rst dissociation carbonic gas: equilibrium expression 2nd dissociation carbonic gas: equilibrium expression charge balance 51 mat

α 0.1 :

initial H 107 -^≡ OH 107 -^≡ CO2 101 -^≡ CO3 109 -^≡ HCO3 107 -^≡ 51 mat :

b balance initial FindRoot (: 1.5764 105 -^* - 0.005 0.0155 0.0041 0.0014 51 mat

That it does not check with Mathcad is not indication of failure. Mathcad initials are not given as they came out of the blue. Our choice of common 'α' and low CO2=0.000001 ... !solves!

Sanity check within FindRoot ± 0.0001 kw b 1 el b 2 el * (- b 2 el kh PCO2 * (- b 1 el b 5 el * (k1 b 3 el * (- b 1 el b 4 el * (k2 b 5 el * (- b 1 el b 5 el 2 b 4 el * + b 2 el + (- 51 mat 8108 -^* 03108 -^* - 6108 -^* - 051 mat

Initials.... found... sanity ---------- Smath IC---------

Initials.... found... sanity ------- Mathcad 11 IC ------

1105 -^* 1.0054 106 -^* - 1106 -^* 4.0063 106 -^* 9.9557 107 -^* - 51 mat

11011 -^* 1105 -^* - 11011 -^* - 41011 -^* 4106 -^* 51 mat

H 107 -^≡ OH 107 -^≡ CO2 101 -^≡ CO3 109 -^≡ HCO3 107 -^≡ 51 mat

H α ≡ OH α ≡ CO2 0.000001 ≡ CO3 α ≡ HCO3 α ≡ 51 mat

8108 -^* 03108 -^* - 6108 -^* - 051 mat

1.5764 105 -^* - 0.005 0.0155 0.0041 0.0014 51 mat

Radovan 20161030

Analytical solution equations, closed system [no gas phase]

C 103 -^: Total carbon concentration ≡

h CO.2 C 102 h * -^* k1 k2 * k1 10 h -^* 102 h * -^+ (+ / :

h CO.3 C k1 * k2 * k1 k2 * k1 10 h -^* 102 h * -^+ (+ / :

h HCO.3 C k1 * 10 h -^* k1 k2 * k1 10 h -^* 102 h * -^+ (+ (/ :

h C C :

scale C 1017^(* 2.5 log10 * :

x species_1 x CO.3 C / : x species_2 x HCO.3 C / : x species_3 x CO.2 C / : 31 line

x species_1 x species_2 x species_3 3 1 sys

Hello Jean, Here is a bit better solution (I think) and might help in these situations.

The acidity of this solution is close to the acidity of natural rain (ph=5.65,[H]~2.2e-6 ... Radovan: 20161030