计算滴定分析法的理论及应用
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摘要
计算滴定分析法是滴定方法与数学方法及计算技术结合的产物。相对于传统滴定分析法,计算滴定分析法有其特殊的内在规律,也有更广的应用范围。对计算滴定分析法的研究,无论是在理论上还是在实际应用中,均有重要的意义。本文的主要研究内容和成果有:
首先,提出了将计算滴定分析法分为控制体积滴定法和控制电位滴定法两个大类的观点。其中,控制体积滴定法包括线性滴定法、单点滴定法及双点滴定法;控制电位滴定法包括控制单电位滴定法和控制多电位滴定法。同时还介绍了两类计算滴定分析法的基本原理、方法特点及相互之间的区别和联系。
其次,根据误差传递理论,研究了电动势的测定误差对控制体积滴定法及电动势的控制误差对控制电位滴定法的影响规律,并揭示了这些规律的本质。电动势的测定误差对控制体积滴定法测定结果准确度的影响与滴定分数有关,滴定分数越接近化学计量点,影响越小;电动势的控制误差对控制电位滴定法测定结果准确度的影响与计算模型中的比例系数及滴定曲线的形状有关,比例系数越大,滴定曲线的变化率越大,影响越小。此外,讨论了控制电位滴定法选择合适的滴定反应和滴定形式需要考虑的因素及这些因素之间的内在联系,并将其用于氨基酸的测定。
第三,利用氟离子选择性电极性能稳定,重现性好的特点,将氟-金属离子配位反应用于计算滴定分析法,对铝、铁及镓的测定进行了研究。其中,利用乙醇-水溶液中氟与铝只形成AlF~(2+)、AlF_2~+及AlF_3三种配合物,从而抑制了氟-铝高配位化合物形成的现象,用线性滴定法先测出这3个氟铝累积稳定常数,再测出待测溶液中铝的浓度,由此提高了测定结果的准确度。利用水溶液中氟可以与铝、铁及镓形成配合物的现象,用控制电位滴定法对铝、铁及镓单种离子或铝和铁及铝和镓混合离子进行了测定,并提出了在非平衡状态的条件下进行控制电位滴定法测定的观点。此外,在低pH条件下,对氟-铝动力学电位法测定铝进行了初步探索。
第四,对沉淀、酸碱及氧化还原计算滴定法进行了研究。对沉淀计算滴定银量法而言,当pK_(sp)＜9时,若已知滴定剂浓度,可以同时求出待测物质浓度和K_(sp);当pK_(sp)＞9时,化学计量点后,在未知K_(sp)的条件下,可以同时求出待测物质和滴定剂浓度;沉淀单点滴定法和双点滴定法只适用于pK_(sp)＞9,且化学计量点后的滴定体系。对酸碱计算滴定法而言,可以分别用单纯形最优化法、非线性最小二乘法或线性最小二乘法同时求出待测酸和滴定剂浓度;单元酸的单点滴定法简化式或双点滴定法计算式适用于K_(HA)＜10~7的酸及化学计量点后的滴定点,多元酸的单点滴定法简化式或双点滴定法计算式适用于m个K_(HAj)均＜10~7的酸及第m个化学计量点后的滴定点。影响酸碱单点滴定法测定结果准确度的因素有:电动势的测定误差、酸的条件质子化常数的误差及水的条件质子自递常数的误差,但在化学计量点附近,这些因素的综合影响可以达到最小。对氧化还原计算滴定铈量法而言,在存在Fe(Ⅲ)的条件下,可以同时测定Fe(Ⅱ)和Ce~(4+);在已知Ce~(4+)浓度的条件下,可以同时测定Fe(Ⅲ)和Fe(Ⅱ);当Fe(Ⅲ)浓度大于Fe(Ⅱ)浓度的20倍以上时,可以用单点滴定法或双点滴定法测定Fe(Ⅱ)。
最后,对计算滴定分析法在氨基酸及药物含量测定中的应用进行了研究。各类单种氨基酸及由酸性氨基酸和碱性氨基酸、碱性氨基酸和碱性氨基酸、酸性氨基酸和中性氨基酸及碱性氨基酸和中性氨基酸构成的混合氨基酸可以用控制电位滴定法测定,但不同的测定对象应该采用不同的滴定剂或不同的滴定形式。盐酸盐类药物可以用沉淀双点滴定法测定;弱酸或弱碱类药物可以用酸碱控制电位滴定法测定。
Calculational Titrimetric Analysis(simplified as CTA)is the resultant of titrimetry combined with mathematical methodology and computative technology.Compared with the traditional titrimetry CTA has its own inherent regularity and thus has more applications.The research into the CTA is of significance both in the academic approaches and practical applications.The following focuses mainly on CTA study and its applications.
First,the viewpoint is proposed here that CTA is to be divided into two categories, that is,Controlled Volume Titration(CVT)and Controlled Potential Titration(CPT).Of the two the former includes Linear Titration,Single Point Titration and Double Point Titration while the latter deals mainly with Controlled Single Potential Titration and Controlled Multiple Potential Titration.And further introduction to CTA is made such as the basic principles,specificities of CVT and CPT as well as their differences and interrelationship.
Second,according to the error transfer theory the regularities are studied affecting the determination error of the potential on CVT and the controlled error of the potential on CPT and thereby the nature of the regularities is found.The determination error of potential on the accuracy of CVT is related to the titration percentage.The closer the titration percentage is to stoichiometdc point(SP),the less its influence is.And the controlled error of the potential on the accuracy of CPT is connected to the proportional coefficient in the computational model and the shape of titration curve.The bigger the coefficient in the computational model and the change rate of titration curve are,the less their influence are.Besides the factors and their influences are considered that how to select suitable titration reaction and titration modality and under the guidance of the above theory amino acids were successfully determined.
Thirdly,the stable performance and the good reproducibility of fluoride ion selective electrode make it possible to determine Al~(3+),Fe~(3+)and Ga~(3+)using fluorin-metal complexometric titrations of CTA.The high accuracy is achieved taking advantage of only three kinds complexes forming in water-alcohol solution for F~- and Al~(3+),that is,AlF~(2+), AlF_2~+ and AlF_3.Thus the high ligancy complexes of F-Al are prevented from forming.The three order accumulative formation constants of F-Al complexs are determined first and then the concentration of Al~(3+)in test solution is detected in water-alcohol solution using Linear Titration.The determination of single ion such as Fe~(3+),Al~(3+)or Ga~(3+)and the mixtures of ions such as Al~(3+)and Fe~(3+)or Al~(3+)and Ga~(3+)were carried out in water solution using CPT.A brand-new viewpoint is proposed that under non-equilibrium state the determination could be carried out with CPT.In addition the preliminary exploration is probed into the determination of Al~(3+)with Kinetic Potentiometry in low pH condition.
Fourthly,The CTA was used in acid-base,precipitation and redox titrations.In the case of the argentimetry in precipitation titration of CTA when pK_(sp)＜9 the concentration of test solution and K_(sp)can be got simultaneously provided the concentration of the titrant is known.When pK_(sp)＞9 and after SP the concentrations of both test solution and titrant could be known at the same time even though K_(sp)is unknown.In precipitation titration both Single Point Titration and Double Point Titration only can be used in the system where the SP is passed and pK_(sp)＞9.As to the acid-base titration of CTA the concentration of the tested acid and the titrant could be acquired at once using any of the three means,Simplified Optimization Method,Non-Linear Least Squares Method or Linear Least Squares Method.The simplified Single Point Titration or Double Point Titration can be used to the monoacids whose protonation constant K_(HA)＜10~(-7)and to the points whereα＞1 while both titrations can be used to the polyprotic acids whose m multiple protonation constants K_(HAj)are less than 10~(-7)and to the points whereα＞m.The factors affecting the accuracy of determination in the case of Single Point Titration are the determination error of potential,the error of conditional protonation constants of acids as well as the error of proton transfer constant of water,fortunately the combined effect of the above factors reaches its minimum in the vicinity of SP.As to the cerimetry in redox titration of CTA Fe(Ⅱ)and Ce~(4+)can be analyzed simultaneously if Fe(Ⅲ)exists. And Fe(Ⅲ)and Fe(Ⅱ)also can be done if the concentration of Ce~(4+)is known.If the concentration of Fe(Ⅲ)is 20 times more than that of Fe(Ⅱ)the concentration of Fe(Ⅱ) can be got using Single Point Titration or Double Point Titration.
At last,as a practical application the analyses of amino acids and medicines were studied.Single amino acid or mixtures of amino acids can be determined by CPT such as acidic and alkaline,alkaline and alkaline,acidic and neutral,and alkaline and neutral amino acids,but the different object should be dealt with different titrant or different titrating modality.The muriate medicines can be done with Double Point Titration in the precipitation titration and the weak acid or base medicines with CPT in the acid-base titration.
首先,提出了将计算滴定分析法分为控制体积滴定法和控制电位滴定法两个大类的观点。其中,控制体积滴定法包括线性滴定法、单点滴定法及双点滴定法;控制电位滴定法包括控制单电位滴定法和控制多电位滴定法。同时还介绍了两类计算滴定分析法的基本原理、方法特点及相互之间的区别和联系。
其次,根据误差传递理论,研究了电动势的测定误差对控制体积滴定法及电动势的控制误差对控制电位滴定法的影响规律,并揭示了这些规律的本质。电动势的测定误差对控制体积滴定法测定结果准确度的影响与滴定分数有关,滴定分数越接近化学计量点,影响越小;电动势的控制误差对控制电位滴定法测定结果准确度的影响与计算模型中的比例系数及滴定曲线的形状有关,比例系数越大,滴定曲线的变化率越大,影响越小。此外,讨论了控制电位滴定法选择合适的滴定反应和滴定形式需要考虑的因素及这些因素之间的内在联系,并将其用于氨基酸的测定。
第三,利用氟离子选择性电极性能稳定,重现性好的特点,将氟-金属离子配位反应用于计算滴定分析法,对铝、铁及镓的测定进行了研究。其中,利用乙醇-水溶液中氟与铝只形成AlF~(2+)、AlF_2~+及AlF_3三种配合物,从而抑制了氟-铝高配位化合物形成的现象,用线性滴定法先测出这3个氟铝累积稳定常数,再测出待测溶液中铝的浓度,由此提高了测定结果的准确度。利用水溶液中氟可以与铝、铁及镓形成配合物的现象,用控制电位滴定法对铝、铁及镓单种离子或铝和铁及铝和镓混合离子进行了测定,并提出了在非平衡状态的条件下进行控制电位滴定法测定的观点。此外,在低pH条件下,对氟-铝动力学电位法测定铝进行了初步探索。
第四,对沉淀、酸碱及氧化还原计算滴定法进行了研究。对沉淀计算滴定银量法而言,当pK_(sp)＜9时,若已知滴定剂浓度,可以同时求出待测物质浓度和K_(sp);当pK_(sp)＞9时,化学计量点后,在未知K_(sp)的条件下,可以同时求出待测物质和滴定剂浓度;沉淀单点滴定法和双点滴定法只适用于pK_(sp)＞9,且化学计量点后的滴定体系。对酸碱计算滴定法而言,可以分别用单纯形最优化法、非线性最小二乘法或线性最小二乘法同时求出待测酸和滴定剂浓度;单元酸的单点滴定法简化式或双点滴定法计算式适用于K_(HA)＜10~7的酸及化学计量点后的滴定点,多元酸的单点滴定法简化式或双点滴定法计算式适用于m个K_(HAj)均＜10~7的酸及第m个化学计量点后的滴定点。影响酸碱单点滴定法测定结果准确度的因素有:电动势的测定误差、酸的条件质子化常数的误差及水的条件质子自递常数的误差,但在化学计量点附近,这些因素的综合影响可以达到最小。对氧化还原计算滴定铈量法而言,在存在Fe(Ⅲ)的条件下,可以同时测定Fe(Ⅱ)和Ce~(4+);在已知Ce~(4+)浓度的条件下,可以同时测定Fe(Ⅲ)和Fe(Ⅱ);当Fe(Ⅲ)浓度大于Fe(Ⅱ)浓度的20倍以上时,可以用单点滴定法或双点滴定法测定Fe(Ⅱ)。
最后,对计算滴定分析法在氨基酸及药物含量测定中的应用进行了研究。各类单种氨基酸及由酸性氨基酸和碱性氨基酸、碱性氨基酸和碱性氨基酸、酸性氨基酸和中性氨基酸及碱性氨基酸和中性氨基酸构成的混合氨基酸可以用控制电位滴定法测定,但不同的测定对象应该采用不同的滴定剂或不同的滴定形式。盐酸盐类药物可以用沉淀双点滴定法测定;弱酸或弱碱类药物可以用酸碱控制电位滴定法测定。
Calculational Titrimetric Analysis(simplified as CTA)is the resultant of titrimetry combined with mathematical methodology and computative technology.Compared with the traditional titrimetry CTA has its own inherent regularity and thus has more applications.The research into the CTA is of significance both in the academic approaches and practical applications.The following focuses mainly on CTA study and its applications.
First,the viewpoint is proposed here that CTA is to be divided into two categories, that is,Controlled Volume Titration(CVT)and Controlled Potential Titration(CPT).Of the two the former includes Linear Titration,Single Point Titration and Double Point Titration while the latter deals mainly with Controlled Single Potential Titration and Controlled Multiple Potential Titration.And further introduction to CTA is made such as the basic principles,specificities of CVT and CPT as well as their differences and interrelationship.
Second,according to the error transfer theory the regularities are studied affecting the determination error of the potential on CVT and the controlled error of the potential on CPT and thereby the nature of the regularities is found.The determination error of potential on the accuracy of CVT is related to the titration percentage.The closer the titration percentage is to stoichiometdc point(SP),the less its influence is.And the controlled error of the potential on the accuracy of CPT is connected to the proportional coefficient in the computational model and the shape of titration curve.The bigger the coefficient in the computational model and the change rate of titration curve are,the less their influence are.Besides the factors and their influences are considered that how to select suitable titration reaction and titration modality and under the guidance of the above theory amino acids were successfully determined.
Thirdly,the stable performance and the good reproducibility of fluoride ion selective electrode make it possible to determine Al~(3+),Fe~(3+)and Ga~(3+)using fluorin-metal complexometric titrations of CTA.The high accuracy is achieved taking advantage of only three kinds complexes forming in water-alcohol solution for F~- and Al~(3+),that is,AlF~(2+), AlF_2~+ and AlF_3.Thus the high ligancy complexes of F-Al are prevented from forming.The three order accumulative formation constants of F-Al complexs are determined first and then the concentration of Al~(3+)in test solution is detected in water-alcohol solution using Linear Titration.The determination of single ion such as Fe~(3+),Al~(3+)or Ga~(3+)and the mixtures of ions such as Al~(3+)and Fe~(3+)or Al~(3+)and Ga~(3+)were carried out in water solution using CPT.A brand-new viewpoint is proposed that under non-equilibrium state the determination could be carried out with CPT.In addition the preliminary exploration is probed into the determination of Al~(3+)with Kinetic Potentiometry in low pH condition.
Fourthly,The CTA was used in acid-base,precipitation and redox titrations.In the case of the argentimetry in precipitation titration of CTA when pK_(sp)＜9 the concentration of test solution and K_(sp)can be got simultaneously provided the concentration of the titrant is known.When pK_(sp)＞9 and after SP the concentrations of both test solution and titrant could be known at the same time even though K_(sp)is unknown.In precipitation titration both Single Point Titration and Double Point Titration only can be used in the system where the SP is passed and pK_(sp)＞9.As to the acid-base titration of CTA the concentration of the tested acid and the titrant could be acquired at once using any of the three means,Simplified Optimization Method,Non-Linear Least Squares Method or Linear Least Squares Method.The simplified Single Point Titration or Double Point Titration can be used to the monoacids whose protonation constant K_(HA)＜10~(-7)and to the points whereα＞1 while both titrations can be used to the polyprotic acids whose m multiple protonation constants K_(HAj)are less than 10~(-7)and to the points whereα＞m.The factors affecting the accuracy of determination in the case of Single Point Titration are the determination error of potential,the error of conditional protonation constants of acids as well as the error of proton transfer constant of water,fortunately the combined effect of the above factors reaches its minimum in the vicinity of SP.As to the cerimetry in redox titration of CTA Fe(Ⅱ)and Ce~(4+)can be analyzed simultaneously if Fe(Ⅲ)exists. And Fe(Ⅲ)and Fe(Ⅱ)also can be done if the concentration of Ce~(4+)is known.If the concentration of Fe(Ⅲ)is 20 times more than that of Fe(Ⅱ)the concentration of Fe(Ⅱ) can be got using Single Point Titration or Double Point Titration.
At last,as a practical application the analyses of amino acids and medicines were studied.Single amino acid or mixtures of amino acids can be determined by CPT such as acidic and alkaline,alkaline and alkaline,acidic and neutral,and alkaline and neutral amino acids,but the different object should be dealt with different titrant or different titrating modality.The muriate medicines can be done with Double Point Titration in the precipitation titration and the weak acid or base medicines with CPT in the acid-base titration.
引文
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