New method for increasing the accuracy of back titration

Titrimetric analysis is an important quantitative analysis method in which the amount of constituent to be determined is calculated from the volumes and concentrations of titrants used in titration procedure. In most literature about titrimetric analysis it has been emphasized that the volumes of titrants used in a titration procedure should be greater than 20 mL to obtain more accurate titration result by reducing the relative error of volume of titrants. By the theory of error propagation, therefore, this emphasis stated above is not valid for a back titration procedure. In back titration procedure the constituent to be determined, represented by A, reacts with the direct titrant, represented by B, according to reaction αA+bB-&gtyY+zZ when an excess of Be is added to the titration vessel that contains A. Then the amount of excess is determined by titration with back titrant, represented by D, according to reaction dD+fB-&gtgG+hH. The amount of A, represented by NA, can be calculated by equation NA = a÷b·(CB·VB-f÷d·CD·VD), where CB, CD, VB and VD represent the concentrations and volumes of B and D respectively. Introducing the concept of limit error and using the theory of error propagation here, the limit relative error of NA may be shown as qq where |ECB|, |ECD|, |EVB|, |EVD|, and |ENA| represent the absolute limit error of CB, CD, VB, VD and NA respectively; XA, XB and XD are the limit relative error of A, B and D; XA = |ENA|/NA, XB = |ECB|/CB, XD = |ECD|/CD, and q=(CB ·d)/(CD ·f). For a special back titration procedure, apparently, the value of each of |EVB| and EVD|, created by reading error of pipette and burette respectively, should be a constant. Similarly, the value of each of q, q·|EVB|+|EVD|, CB, CD, XB and XD should be a constant too. Considering NA = a·CB ·(q·VB - VD)/(b·q), the value of q·VB - VD will remain constant when the value of NA is unchanged, although the values of VB and VD may vary. Consequently, the conclusions for back titration can be drawn from equation (1) that the linear relationship between the values of XA and VD exists and that the bigger VD, the bigger XA. Also it can be seen from equation (1) that no relationship exists between the values of |EVD|/VD and XA. Thus, if there is a outside demand for XA to be smaller than a specified permissible error X, the suitable values of VB and VD that satisfy XA B gt; VBMIN =(q· |EVB|+|EVD|) / [q·(X-XB)] VD DMAX =[q·VB ·(X-XB) - (q· |EVB|+|EVD|)] / (X+XD) where VDMAX is the biggest permissible value of VD and VBMIN is the smallest permissible value of VB.