bb905714-efa2-4f8e-a70f-749d651202d6 5 4 5 decimal

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Smath solving Butler ... MCD11 failed

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 -^: 13 mat 31 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 CO2: equilibrium gas/liquid equilibrium expression for bicarbonate HCO3 equilibrium expression for carbonate CO3 charge balance 51 mat

Doctored ... courtesy Radovan init H OH * 1100000000000000 / ≡ CO2 1100000 / ≡ H HCO3 * CO2 1010 nthroot (63^/ ≡ H CO3 * HCO3 1010 nthroot (103^/ ≡ H HCO3 OH + 2 CO3 * + ≡ 51 mat :

pedal to initialise the system !

H CO2 OH HCO3 CO3 51 mat init H CO2 OH HCO3 CO3 51 mat roots (: 2.241 106 -^* 1105 -^* 4.4623 109 -^* 2.2364 106 -^* 5.0017 1011 -^* 51 mat

re-write the 'balance'wrt roots[H,CO2,OH,HCO3,CO3]

sanity H OH * kw - CO2 kh PCO2 * - H HCO3 * k1 CO2 * - H CO3 * k2 HCO3 * - H HCO3 2 CO3 * + OH + (- 51 mat : 61022 -^* 51021 -^* 11021 -^* 71022 -^* 11015 -^* - 51 mat

61022 -^* 51021 -^* 11021 -^* 71022 -^* 11015 -^* - 51 mat

H 2.241 106 -^*

alkalinity H log10 - 5.65

Reference: Butler,Carbon Dioxide Equilibria, Prob. 2-11, pg 41 A solution containing 10^-3 M sodium bicarbonate [NaHCO3] is treated with 5*10^4 M sodium carbonate [Na2CO2] What is the alkalinity of the final solution ?