Ka2+4cKa+4c）出发，推导出了计算氢离子浓度的其他2个近似公式：（1）c越小，[H+]AV1越趋向c。计算表明，当满足c≤1/19Ka和c≥5.0×10-7 mol/L时，弱酸HA就可作强酸处理，此时得到近似式[H+]AV4=c，这极大简化了弱酸溶液氢离子浓度的计算。（2）c越大，[H+]AV1越接近√cKa。当满足c≥105Ka和cKa≥10Kw时，弱酸溶液氢离子浓度可按最简式[H+]AV2=√cKa计算。还解释了c≥105Ka和c≤1/19Ka时所包含的物理意义。需要强调的是，本文首次给出了各近似式的浓度适用范围，比如忽略水的解离时，除了满足cKa≥10Kw，还必须要求c≥6.0×10-6 mol/L。"/>
Ka2+4cKa), other two equations can be derived directly:(1) when c approaches 0,[H+]AV1 approaches c. In fact, when c ≤ 1/19Ka and c ≥ 5.0×10-7 mol/L, HA can be treated as a strong acid, namely[H+]=c. (2) when c approaches very large,[H+]AV1 approaches √cKa. In fact, when c ≥ 105Ka and cKa ≥ 10Kw, the hydrogen ionic concentration of the HA solution can be obtained by[H+]AV2=√cKa. Another purpose of this article is to discuss the working conditions of various approximations in detail. For example, if approximate equation[H+]AV1=1/2(-Ka+√Ka2+4cKa) works properly, both c ≥ 6×10-6 mol/L and cKa ≥ 10Kw should be fulfilled."/>
Estimating Hydrogen Ionic Concentration for a Dilute and Weak Monoprotic Acid Solution by Mathematical Method
Abstract Based on the concentration (c) and dissociation constant (Ka), pH value of HA (a weak monoprotic acid) solution can approximately be estimated by a simpler equation (the relative error should be within (5%). It is very important for the undergraduate students to master the approximation method. In this paper, various simplified equations were derived for the first time by using mathematical methods. From the approximate equation[H+]AV1=1/2(-Ka+√Ka2+4cKa), other two equations can be derived directly:(1) when c approaches 0,[H+]AV1 approaches c. In fact, when c ≤ 1/19Ka and c ≥ 5.0×10-7 mol/L, HA can be treated as a strong acid, namely[H+]=c. (2) when c approaches very large,[H+]AV1 approaches √cKa. In fact, when c ≥ 105Ka and cKa ≥ 10Kw, the hydrogen ionic concentration of the HA solution can be obtained by[H+]AV2=√cKa. Another purpose of this article is to discuss the working conditions of various approximations in detail. For example, if approximate equation[H+]AV1=1/2(-Ka+√Ka2+4cKa) works properly, both c ≥ 6×10-6 mol/L and cKa ≥ 10Kw should be fulfilled.
SONG Hui-Yu, WANG Hai-Shui. Estimating Hydrogen Ionic Concentration for a Dilute and Weak Monoprotic Acid Solution by Mathematical Method[J]. Chinese Journal of Chemical Education, 2019, 40(6): 25-29.
