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Citation: Lin Daoguang, Wang Haishui. A New and Easy Understanding Way to Derive Approximation Formulas for Estimating the Hydrogen Ion Concentration of a Monoprotic Weak Acid Solution[J]. Chemistry, ;2019, 82(6): 563-565, 533. shu

A New and Easy Understanding Way to Derive Approximation Formulas for Estimating the Hydrogen Ion Concentration of a Monoprotic Weak Acid Solution

Lin Daoguang ,
Wang Haishui ^,

School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640

Corresponding author: Wang Haishui, wanghsh@scut.edu.cn
Received Date: 30 November 2018
Accepted Date: 20 March 2019

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Among the mainstream analytical chemistry textbooks, the hydrogen ion concentration of a monoprotic weak acid solution can be estimated by approximation formulas \begin{document}${\left[ {{{\rm{H}}^ + }} \right]_{{\rm{AV}}1}} = \frac{1}{2}\left({ - {K_{\rm{a}}} + \sqrt {K_{\rm{a}}^2 + 4c{K_{\rm{a}}}} } \right)$\end{document} or \begin{document}${\left[ {{{\rm{H}}^ + }} \right]_{{\rm{AV}}2}} = \sqrt {c{K_{\rm{a}}}} $\end{document}. In this paper, the two above formulas are derived from a new and easy understanding way. (1) If [H⁺]>>[OH^-], [H⁺]_AV1 can be used to estimate the pH of the solution. If the relative error between [H⁺]_AV1 and the accurate hydrogen ion concentration [H⁺]_T is within ±5%, then both c>6×10^-6mol·L^-1 and cK_a≥10K_w are required. (2) When use [H⁺]_AV2 to estimate the pH of the solution, it needs two conditions: [H⁺]>>[OH^-] and c≈[HA]. If the relative error between [H⁺]_AV2 and [H⁺]_T is less than ±5%, both cK_a≥10K_w and c≥105K_a are required. The conclusions obtained in this study are more accurate and reliable, the physical meanings of the approximation formulas are clear. Therefore, it is easy for the students to understand and master the related approximate calculation correctly.
- Monoprotic weak acid,
- Hydrogen ion concentration,
- Approximation formula,
- Criterion
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