## On the Ringbom's Equation

Gan Feng,, Zhu Fang, Fang Pingping

Abstract

There is no unified equation for calculating titration error in the textbook of analytical chemistry. The Ringbom's equation is the most frequently used, but the equation has problems. This work made a theoretic analysis of the Ringbom's equation based on the definition of titration error. The results show that the calculated end point error using Ringbom's formula is different from that based on the definition. We believe this work can provide fundamental basis for the establishment of reasonable titration error calculation.

Keywords： End point error ; Ringbom's formula

Gan Feng. On the Ringbom's Equation. University Chemistry[J], 2020, 35(9): 164-167 doi:10.3866/PKU.DXHX201910027

## 1 结果与讨论

${({\rm{TE}}\% )_{主流}}{\rm{ = }}\frac{{终点时滴定剂过量{\rm{(}}或不足{\rm{)}}的摩尔数}}{{待测物质的摩尔数}}$

${({\rm{TE}}\% )_{主流}}{\rm{ = }}\frac{{c({\rm{L}}){V_{{\rm{ep}}}} - c({\rm{M}}){V_0}}}{{c({\rm{M}}){V_0}}}$

$c\left(\text{L}\right)\times {V}_{\text{sp}}=c\left(\text{M}\right)\times {V}_{0}$

$\frac{{{V_{{\rm{sp}}}}}}{{{V_0}}} = \frac{{c({\rm{M}})}}{{c({\rm{L}})}}$

${\eta _{{\rm{sp}}}} = \frac{{c({\rm{M}})}}{{c({\rm{L}})}}$

${\eta _{{\rm{ep}}}} = \frac{{{V_{{\rm{ep}}}}}}{{{V_0}}}$

${({\rm{TE}}\% )_{主流}}{\rm{ = }}\frac{{{\eta _{{\rm{ep}}}} - {\eta _{{\rm{sp}}}}}}{{{\eta _{{\rm{sp}}}}}}$

${({\rm{TE}}\% )_{林帮}}{\rm{ = }}\frac{{{{[{\rm{L}}]}_{{\rm{ep}}}} - {{{\rm{[M]}}}_{{\rm{ep}}}}}}{{{C_{\rm{M}}}}}$

$\frac{{c({\rm{L}}){V_{{\rm{ep}}}}}}{{{V_{{\rm{ep}}}} + {V_0}}} = {[{\rm{L}}]_{{\rm{ep}}}} + {[{\rm{ML}}]_{{\rm{ep}}}}$

$\frac{{c({\rm{M}}){V_{\rm{0}}}}}{{{V_{{\rm{ep}}}} + {V_0}}} = {[{\rm{M}}]_{{\rm{ep}}}} + {[{\rm{ML}}]_{{\rm{ep}}}}$

${[{\rm{L}}]_{{\rm{ep}}}} - {[{\rm{M}}]_{{\rm{ep}}}} = \frac{{c({\rm{L}}){V_{{\rm{ep}}}}}}{{{V_{{\rm{ep}}}} + {V_0}}} - \frac{{c({\rm{M}}){V_{\rm{0}}}}}{{{V_{{\rm{ep}}}} + {V_0}}} = \frac{{c({\rm{L}}){V_{{\rm{ep}}}} - c({\rm{M}}){V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}}$

${C_{\rm{M}}} = \frac{{c({\rm{M}}){V_0}}}{{{V_{{\rm{sp}}}} + {V_0}}}$

$\begin{array}{l}{\left( {{\rm{TE}}\% } \right)_{林帮}} = {\rm{}}\frac{{{{\left[ {\rm{L}} \right]}_{{\rm{ep}}}} - {{\left[ {\rm{M}} \right]}_{{\rm{ep}}}}}}{{{C_{\rm{M}}}}}\\ = \frac{{\frac{{c\left( {\rm{L}} \right){V_{{\rm{ep}}}} - c\left( {\rm{M}} \right){V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}}}}{{\frac{{c\left( {\rm{M}} \right){V_0}}}{{{V_{{\rm{sp}}}} + {V_0}}}}}\\ = \frac{{{V_{{\rm{sp}}}} + {V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}} \times \frac{{c\left( {\rm{L}} \right){V_{{\rm{ep}}}} - c\left( {\rm{M}} \right){V_0}}}{{c\left( {\rm{M}} \right){V_0}}}\\ = \frac{{{V_{{\rm{sp}}}} + {V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}} \times \frac{{\frac{{{V_{{\rm{ep}}}}}}{{{V_0}}} - \frac{{c\left( {\rm{M}} \right)}}{{c\left( {\rm{L}} \right)}}}}{{\frac{{c\left( {\rm{M}} \right)}}{{c\left( {\rm{L}} \right)}}}}\\ = \frac{{{V_{{\rm{sp}}}} + {V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}} \times \frac{{{\eta _{{\rm{ep}}}} - {\eta _{{\rm{sp}}}}}}{{{\eta _{{\rm{sp}}}}}}\\ = \frac{{{V_{{\rm{sp}}}} + {V_0}}}{{{V_{{\rm{ep}}}} + {V_0}}} \times {\left( {{\rm{TE}}\% } \right)_{主流}}\end{array}$

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Ringbom, A.分析化学中的络合作用.戴明,译.北京:高等教育出版社, 1987.

Skoog, D. A.; West, D. N.; Holler, F. J.; Crouch, F. J. Fundamentals of Analytical Chemistry, 4nd ed.; Cengage Learning: Belmont, CA, USA, 2014.

De Levie R. Anal. Chem. 1996, 68, 585.

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