计算二聚体系平衡常数新方法研究

Study on the new algorithm for equilibrium constant of dimerization system

计算二聚体系平衡常数的三元方程组受实验数据的影响十分敏感,现有精确解法存在增根,且判定、消除增根困难。通过分析实验数据与三元方程组的关系发现:只要比例关系C_(t3)/C_(t1)=A_3/A_1、C_(t3)/C_(t2)=A_3/A_2、C_(t2)/C_(t1)=A_2/A_1和(A_3-A_2)/(A_2-A_1)=(C_(t3)-C_(t2))/(C_(t2)-C_(t1))中任何一个成立,则相应方程组无解,否则有解。经过一系列代数变换,导出了判定合法解的有效准则。并以拟合误差为判据提出了确定总常数的方法。用该方法算出二碳化和三磺化酞菁的平衡常数分别为47973.4和30271.8。

Trivariate algebraic equations of calculating equilibrium constant of dimerization system are sensitively affected by experiment data, there is exceptional root in the current exact solution and it is difficult to decide and delete the exceptional root. The authors, through analysingthe relationship between experiment data and trivariate algebraic equations, have found that if any one of the proportional relation Ct3/Ct1=A3/A1, is established, the equations are unsolvable, on the contrary, the equations are solvable. For thesolvable equations, through a series of algebraic transformation, the effective criterion of determining validation solution is obtained. The final e-quilibrium constant of dimerization system is determined according to the principle of error of fitting. The equilibrium constant of trisulfoph-thalocyanine and biosulfophthalocyanine obtained with the method is 47973 .4 and 30271.8.