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Dynamic Buffer Capacity in Acid-Base Systems.

Michałowska-Kaczmarczyk AM, Michałowski T - J Solution Chem (2015)

Bottom Line: The generalized concept of 'dynamic' buffer capacity β V is related to electrolytic systems of different complexity where acid-base equilibria are involved.The resulting formulas are presented in a uniform and consistent form.The detailed calculations are related to two Britton-Robinson buffers, taken as examples.

View Article: PubMed Central - PubMed

Affiliation: Department of Oncology, The University Hospital in Cracow, Cracow, Poland.

ABSTRACT

The generalized concept of 'dynamic' buffer capacity β V is related to electrolytic systems of different complexity where acid-base equilibria are involved. The resulting formulas are presented in a uniform and consistent form. The detailed calculations are related to two Britton-Robinson buffers, taken as examples.

No MeSH data available.


The plots of aβV vs. V and bβV vs. pH relationships obtained for BRB-I and BRB-II. For detailssee the text
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Fig2: The plots of aβV vs. V and bβV vs. pH relationships obtained for BRB-I and BRB-II. For detailssee the text

Mentions: Two buffers proposed by Britton and Robinson [14], marked as BRB-I and BRB-II, are obtained bytitration to the desired pH value over the pH range 2–12 [15]. The D (V =10 mL) in BRB-I, consisting of H3BO3(C01) + H3PO4(C02) + CH3COOH (C03), is titrated to the desired pH with NaOH (C) as T; in this case, C01 = C02 = C03 = 0.04 mol·L−1, and C = 0.2 mol·L−1. The D inBRB-II, consisting of H3BO3 (C01) + KH2PO4(C02) + citric acidH3L(3) (C03) + veronal HL(4) + HCl (C0a), is titrated to the desired pH with NaOH (C) as T; inthis case C01 = C02 = C03 = C04 = C0a = 0.0286 mol·L−1, and C = 0.2 mol·L−1. For BRB-I wehave the equation for the titration curve:39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V = V_{0} \cdot \frac{{(3 - \bar{n}_{1} ) \cdot C_{01} + (3 - \bar{n}_{2} ) \cdot C_{02} + (1 - \bar{n}_{3} ) \cdot C_{03} - \alpha }}{C + \alpha } $$\end{document}V=V0·(3-n¯1)·C01+(3-n¯2)·C02+(1-n¯3)·C03-αC+α(see Fig. 1), where:40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{1} = \, ( 3\times 10^{{ 3 4. 2 4- 3 {\text{pH}}}} + 2\times 10^{{ 2 5. 7- 2 {\text{pH}}}} + 10^{{ 1 3. 3- {\text{pH}}}} )/( 10^{{ 3 4. 2 4- 3\cdot {\text{pH}}}} + 10^{{ 2 5. 7- 2 {\text{pH}}}} + 10^{{ 1 3. 3- {\text{pH}}}} + 1) $$\end{document}n¯1=(3×1034.24-3pH+2×1025.7-2pH+1013.3-pH)/(1034.24-3·pH+1025.7-2pH+1013.3-pH+1)41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{2} = \, ( 3\times 10^{{ 2 1- 7 1 {\text{pH}}}} + 2\times 10^{{ 1 9. 5 9- 2 {\text{pH}}}} + 10^{{ 1 2. 3 8- {\text{pH}}}} )/( 10^{{ 2 1. 7 1- 3 {\text{pH}}}} + 10^{{ 1 9. 5 9- 2 {\text{pH}}}} + 10^{{ 1 2. 3 8- {\text{pH}}}} + 1) $$\end{document}n¯2=(3×1021-71pH+2×1019.59-2pH+1012.38-pH)/(1021.71-3pH+1019.59-2pH+1012.38-pH+1)42\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{3} = { 1}0^{{ 4. 7 6- {\text{pH}}}} /( 10^{{ 4. 7 6- {\text{pH}}}} + 1) $$\end{document}n¯3=104.76-pH/(104.76-pH+1) For the BRB-II buffer we have the equation for titration curve43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V = V_{0} \cdot \frac{{(3 - \bar{n}_{1} ) \cdot C_{01} + (2 - \bar{n}_{2} ) \cdot C_{02} + (3 - \bar{n}_{3}^{ \bullet } ) \cdot C_{03} + (1 - \bar{n}_{4} ) \cdot C_{04} + C_{0a} - \alpha }}{C + \alpha } $$\end{document}V=V0·(3-n¯1)·C01+(2-n¯2)·C02+(3-n¯3∙)·C03+(1-n¯4)·C04+C0a-αC+α(see Figs. 1, 2), where (Eq. 40) and(Eq. 41) and:44\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{3}^{ \bullet } = \, ( 3\times 10^{{ 1 4. 2 8- 3 {\text{pH}}}} + 2\times 10^{{ 1 1. 1 5- 2 {\text{pH}}}} + 10^{{ 6. 3 9- {\text{pH}}}} )/( 10^{{ 1 4. 2 8- 3 {\text{pH}}}} + 10^{{ 1 1. 1 5- 2\cdot{\text{pH}}}} + 10^{{ 6. 3 9- {\text{pH}}}} + 1) $$\end{document}n¯3∙=(3×1014.28-3pH+2×1011.15-2pH+106.39-pH)/(1014.28-3pH+1011.15-2·pH+106.39-pH+1)45\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{4} = { 1}0^{{ 7. 4 3- {\text{pH}}}} /( 10^{{ 7. 4 3- {\text{pH}}}} + 1) $$\end{document}n¯4=107.43-pH/(107.43-pH+1)Fig. 1


Dynamic Buffer Capacity in Acid-Base Systems.

Michałowska-Kaczmarczyk AM, Michałowski T - J Solution Chem (2015)

The plots of aβV vs. V and bβV vs. pH relationships obtained for BRB-I and BRB-II. For detailssee the text
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4495796&req=5

Fig2: The plots of aβV vs. V and bβV vs. pH relationships obtained for BRB-I and BRB-II. For detailssee the text
Mentions: Two buffers proposed by Britton and Robinson [14], marked as BRB-I and BRB-II, are obtained bytitration to the desired pH value over the pH range 2–12 [15]. The D (V =10 mL) in BRB-I, consisting of H3BO3(C01) + H3PO4(C02) + CH3COOH (C03), is titrated to the desired pH with NaOH (C) as T; in this case, C01 = C02 = C03 = 0.04 mol·L−1, and C = 0.2 mol·L−1. The D inBRB-II, consisting of H3BO3 (C01) + KH2PO4(C02) + citric acidH3L(3) (C03) + veronal HL(4) + HCl (C0a), is titrated to the desired pH with NaOH (C) as T; inthis case C01 = C02 = C03 = C04 = C0a = 0.0286 mol·L−1, and C = 0.2 mol·L−1. For BRB-I wehave the equation for the titration curve:39\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V = V_{0} \cdot \frac{{(3 - \bar{n}_{1} ) \cdot C_{01} + (3 - \bar{n}_{2} ) \cdot C_{02} + (1 - \bar{n}_{3} ) \cdot C_{03} - \alpha }}{C + \alpha } $$\end{document}V=V0·(3-n¯1)·C01+(3-n¯2)·C02+(1-n¯3)·C03-αC+α(see Fig. 1), where:40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{1} = \, ( 3\times 10^{{ 3 4. 2 4- 3 {\text{pH}}}} + 2\times 10^{{ 2 5. 7- 2 {\text{pH}}}} + 10^{{ 1 3. 3- {\text{pH}}}} )/( 10^{{ 3 4. 2 4- 3\cdot {\text{pH}}}} + 10^{{ 2 5. 7- 2 {\text{pH}}}} + 10^{{ 1 3. 3- {\text{pH}}}} + 1) $$\end{document}n¯1=(3×1034.24-3pH+2×1025.7-2pH+1013.3-pH)/(1034.24-3·pH+1025.7-2pH+1013.3-pH+1)41\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{2} = \, ( 3\times 10^{{ 2 1- 7 1 {\text{pH}}}} + 2\times 10^{{ 1 9. 5 9- 2 {\text{pH}}}} + 10^{{ 1 2. 3 8- {\text{pH}}}} )/( 10^{{ 2 1. 7 1- 3 {\text{pH}}}} + 10^{{ 1 9. 5 9- 2 {\text{pH}}}} + 10^{{ 1 2. 3 8- {\text{pH}}}} + 1) $$\end{document}n¯2=(3×1021-71pH+2×1019.59-2pH+1012.38-pH)/(1021.71-3pH+1019.59-2pH+1012.38-pH+1)42\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{3} = { 1}0^{{ 4. 7 6- {\text{pH}}}} /( 10^{{ 4. 7 6- {\text{pH}}}} + 1) $$\end{document}n¯3=104.76-pH/(104.76-pH+1) For the BRB-II buffer we have the equation for titration curve43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ V = V_{0} \cdot \frac{{(3 - \bar{n}_{1} ) \cdot C_{01} + (2 - \bar{n}_{2} ) \cdot C_{02} + (3 - \bar{n}_{3}^{ \bullet } ) \cdot C_{03} + (1 - \bar{n}_{4} ) \cdot C_{04} + C_{0a} - \alpha }}{C + \alpha } $$\end{document}V=V0·(3-n¯1)·C01+(2-n¯2)·C02+(3-n¯3∙)·C03+(1-n¯4)·C04+C0a-αC+α(see Figs. 1, 2), where (Eq. 40) and(Eq. 41) and:44\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{3}^{ \bullet } = \, ( 3\times 10^{{ 1 4. 2 8- 3 {\text{pH}}}} + 2\times 10^{{ 1 1. 1 5- 2 {\text{pH}}}} + 10^{{ 6. 3 9- {\text{pH}}}} )/( 10^{{ 1 4. 2 8- 3 {\text{pH}}}} + 10^{{ 1 1. 1 5- 2\cdot{\text{pH}}}} + 10^{{ 6. 3 9- {\text{pH}}}} + 1) $$\end{document}n¯3∙=(3×1014.28-3pH+2×1011.15-2pH+106.39-pH)/(1014.28-3pH+1011.15-2·pH+106.39-pH+1)45\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \bar{n}_{4} = { 1}0^{{ 7. 4 3- {\text{pH}}}} /( 10^{{ 7. 4 3- {\text{pH}}}} + 1) $$\end{document}n¯4=107.43-pH/(107.43-pH+1)Fig. 1

Bottom Line: The generalized concept of 'dynamic' buffer capacity β V is related to electrolytic systems of different complexity where acid-base equilibria are involved.The resulting formulas are presented in a uniform and consistent form.The detailed calculations are related to two Britton-Robinson buffers, taken as examples.

View Article: PubMed Central - PubMed

Affiliation: Department of Oncology, The University Hospital in Cracow, Cracow, Poland.

ABSTRACT

The generalized concept of 'dynamic' buffer capacity β V is related to electrolytic systems of different complexity where acid-base equilibria are involved. The resulting formulas are presented in a uniform and consistent form. The detailed calculations are related to two Britton-Robinson buffers, taken as examples.

No MeSH data available.