《High-Speed Version》pH Calculation
Author: novchemistryExecutions: 12815
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Perform an acid-base titration of Solution A with Solution B.
To speed up the calculation, the horizontal axis represents pH and the vertical axis represents volume.
Additionally, if the volume of Solution B falls outside the specified range, the function returns the value at the edge of the range.
Acid valence refers to the valence of free acids (e.g., -COOH), while base valence refers to the valence of free bases (e.g., -NH2).
Acid salts (e.g., -ONa) should be included in the base valence.
Include salts of bases (such as -NH₃Cl) in the acid valence.
Express the dissociation constant in the form of the pKa of the conjugate acid.
pKa = 14 – pKb.
Select pKa values from the left in order until the sum of the acid valence and base valence is reached, and ignore any remaining values.
To speed up the calculation, the horizontal axis represents pH and the vertical axis represents volume.
Additionally, if the volume of Solution B falls outside the specified range, the function returns the value at the edge of the range.
Acid valence refers to the valence of free acids (e.g., -COOH), while base valence refers to the valence of free bases (e.g., -NH2).
Acid salts (e.g., -ONa) should be included in the base valence.
Include salts of bases (such as -NH₃Cl) in the acid valence.
Express the dissociation constant in the form of the pKa of the conjugate acid.
pKa = 14 – pKb.
Select pKa values from the left in order until the sum of the acid valence and base valence is reached, and ignore any remaining values.
Reference Values for pKa
Monoprotic Acids
Acetic acid 4.76
Monoprotic Bases
Ammonia 9.25
Diprotic Acids
Oxalic acid 1.27, 4.27
Carbonic acid 6.35, 10.25
Trivalent acids
Phosphoric acid 2.12, 7.21, 12.67
Citric acid 3.09, 4.75, 6.41
Divalent acids / Monovalent bases
Glutamic acid 2.10, 4.07, 9.47
Monoprotic acids and diprotic bases
Histidine 1.70, 6.04, 9.09
Tetraprotic acids
Ethylenediaminetetraacetic acid 0.0, 1.5, 2.00, 2.69
Strong acid (H₃O⁺) -1.7
Strong base (OH⁻) 15.7
Let the substance number be i = 1, 2, ..., and the dissociation number be j = 1, 2, ..., n.
Let AiHai denote a compound that is “electrically neutral including its counterion.”
Let the valence of the acid be ai and the valence of the base be bi.
Kij = [AiH(ai + bi - j)^(bi - j) +] [H+] / [AiH(ai + bi - j + 1)^(bi - j + 1) +]
Ki₁ = [AiH(ai + bi − 1)^(bi − 1) +] [H⁺] / [AiH(ai + bi)^(bi − 1) +]
[AiH(ai + bi − 1)^(bi − 1) +] = Ki₁ [AiH(ai + bi)^(bi − 1) +] /[H+]
Recursively,
[AiH(ai+bi-j)^(bi-j)+] = Ki1Ki2...Kij[AiH(ai+bi)^bi+]/[H+]^j
Let the concentration before ionization be ci0. From the mass balance, we have
ci0 = [AiH(ai+bi)^bi+] ∑[j=0, ai+bi] Ki1...Kij / [H+]^j
[AiH(ai+bi)^bi+] = ci0 / Σ[j=0, ai+bi] Ki1...Kij / [H+]^j
The total charge of the AiHai ions is
ci0 × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j) / Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
The charge balance equation is
0 = [H+] - Kw/[H+] + Σ[i=1,n]
ci0 × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j)/Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
.
Let the volumes of each solution be V1 and V2.
Let the concentration before mixing be ci.
When present in Solution 1, ci0 = ciV1/(V1 + V2)
When present in Solution 2, ci0 = ciV2/(V1 + V2)
Let x = V2/V1.
When the substance is present in Solution 1, ci0 = ci/(1+x).
When the substance is present in Solution 2, ci0 = cix/(1+x).
0 = (1+x)([H+] - Kw/[H+])
+ Σ[i=1,n1]
ci × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j)/Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
+ x Σ[i = n1 + 1, n]
ci × Σ[j = 0, ai + bi](bi - j)(Ki1...Kij/[H+]^j)/Σ[j = 0, ai + bi](Ki1...Kij/[H+]^j)
Monoprotic Acids
Acetic acid 4.76
Monoprotic Bases
Ammonia 9.25
Diprotic Acids
Oxalic acid 1.27, 4.27
Carbonic acid 6.35, 10.25
Trivalent acids
Phosphoric acid 2.12, 7.21, 12.67
Citric acid 3.09, 4.75, 6.41
Divalent acids / Monovalent bases
Glutamic acid 2.10, 4.07, 9.47
Monoprotic acids and diprotic bases
Histidine 1.70, 6.04, 9.09
Tetraprotic acids
Ethylenediaminetetraacetic acid 0.0, 1.5, 2.00, 2.69
Strong acid (H₃O⁺) -1.7
Strong base (OH⁻) 15.7
Let the substance number be i = 1, 2, ..., and the dissociation number be j = 1, 2, ..., n.
Let AiHai denote a compound that is “electrically neutral including its counterion.”
Let the valence of the acid be ai and the valence of the base be bi.
Kij = [AiH(ai + bi - j)^(bi - j) +] [H+] / [AiH(ai + bi - j + 1)^(bi - j + 1) +]
Ki₁ = [AiH(ai + bi − 1)^(bi − 1) +] [H⁺] / [AiH(ai + bi)^(bi − 1) +]
[AiH(ai + bi − 1)^(bi − 1) +] = Ki₁ [AiH(ai + bi)^(bi − 1) +] /[H+]
Recursively,
[AiH(ai+bi-j)^(bi-j)+] = Ki1Ki2...Kij[AiH(ai+bi)^bi+]/[H+]^j
Let the concentration before ionization be ci0. From the mass balance, we have
ci0 = [AiH(ai+bi)^bi+] ∑[j=0, ai+bi] Ki1...Kij / [H+]^j
[AiH(ai+bi)^bi+] = ci0 / Σ[j=0, ai+bi] Ki1...Kij / [H+]^j
The total charge of the AiHai ions is
ci0 × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j) / Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
The charge balance equation is
0 = [H+] - Kw/[H+] + Σ[i=1,n]
ci0 × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j)/Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
.
Let the volumes of each solution be V1 and V2.
Let the concentration before mixing be ci.
When present in Solution 1, ci0 = ciV1/(V1 + V2)
When present in Solution 2, ci0 = ciV2/(V1 + V2)
Let x = V2/V1.
When the substance is present in Solution 1, ci0 = ci/(1+x).
When the substance is present in Solution 2, ci0 = cix/(1+x).
0 = (1+x)([H+] - Kw/[H+])
+ Σ[i=1,n1]
ci × Σ[j=0, ai+bi](bi-j)(Ki1...Kij/[H+]^j)/Σ[j=0, ai+bi](Ki1...Kij/[H+]^j)
+ x Σ[i = n1 + 1, n]
ci × Σ[j = 0, ai + bi](bi - j)(Ki1...Kij/[H+]^j)/Σ[j = 0, ai + bi](Ki1...Kij/[H+]^j)
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Simulates acid-base titrations of polybasic acids, polybasic bases, and mixtures.
To improve speed, the horizontal axis represents pH and the vertical axis represents volume.