近似计算的普适性:一元弱酸的滴定突跃范围

The Universal Approximation Calculation:Range of Abrupt Change in Titration of a Monoprotic Weak Acid

突跃范围是选择指示剂的主要依据,也是决定能否准确滴定的重要条件。滴定一元弱酸HB溶液时,计量点前(滴定分数a=0.999),许多溶液中cHB与[OH-]或cHB与[H+]具有相同数量级,因此通用教科书介绍的近似式pH=pKa+lgcB^-/cHR存在较大局限性。本文新推导出了满足误差要求(在±0.02pH以内)的适用滴定各种浓度一元弱酸HB的pH的近似公式。计量点前,溶液酸性情形(pKa≤4.0),溶液[H+]=10-3cKa/c+2Ka;溶液碱性情形(pKa>4.0),溶液[H+]=cKa+√cKa(cKa+8×10^-8)/2000c。计量点后(a=1.001),考虑弱碱B-对溶液pH影响,则有溶液[H+]=-cKa+√cKa(cKa+8×10^-8)/2000c。

The range of abrupt change in the titration curve plays a key role in selecting an indicator,and also is the important factor to determine whether or not the titration proceeds accurately.Before the stoichiometric point of the chemical reaction,the approximate formula pH=pKa+lgcB^-/cHR can be normally used to obtain the solution pH.However,if[OH-]is close to cHB or[H+]approaches cHB,the above approximation should be a serious problem.In this paper,pH approximation formulas for monoprotic weak acid with different concentrations are derived,which satisfy the error requirement(within±0.02 pH).Before the stoichiometric point(a=0.999),if the solution is acidic (pKa≤4.0 case);[H+]=10-3cKa/c+2Ka;if the solution is alkaline (pka>4.0 case)[H+]=cKa+√cKa(cKa+8×10^-8)/2000c.After the stoichiometric point(a=1.001) ,[H+]=-cKa+√cKa(cKa+8×10^-8)/2000c.The three equations works more properly than the formula pH=pKa+lg cR-/CHR.