Titration method using a tracer to quantify the titrant

Abstract

A titration method uses a tracer in the titrant or titrand to quantify the amount of titrant added. The method does not require quantitative addition of titrant or sample. The tracer can be inert or can participate as an indicator of the titrant-analyte reaction. The tracer concentration is quantified by an appropriate method depending upon the type of tracer and analytical performance desired (e.g. precision, accuracy). The method simplifies titrations because it eliminates the need for a precision dispensing device and analytical balance.

1 . A titration method wherein a tracer of an initial concentration [trace] I  quantifies the relative proportions of titrant to titrand, the method comprising the steps of:
 a) placing an amount of the titrand in a mixing vessel;   b) adding an amount of titrant to the titrand;   c) mixing the titrant and titrand to obtain a homogeneous mixture;   d) measuring an extent of reaction of the titration with a recording means;   e) concurrently, measuring a concentration of the tracer [tracer] mix  with a tracer recording means;   f) determining a dilution factor wherein the dilution factor f is the ratio of total concentration of tracer in the titrant-titrand mixture [tracer] mix  to initial tracer concentration [tracer] I ,   
       
         
           
             
               
                 f 
                 = 
                 
                   
                     
                       [ 
                       tracer 
                       ] 
                     
                     mix 
                   
                   
                     
                       [ 
                       tracer 
                       ] 
                     
                     I 
                   
                 
               
               ; 
             
           
         
       
       and
 g) determining the concentration of the analyte in the titrand using the dilution factor, the measurement of the extent of reaction and a titration data analysis method. 
 
     
     
         2 . The method of  claim 1 , wherein the tracer is in the titrant and the dilution factor is the ratio of total concentration of tracer in the titrant-titrand mixture [tracer titrant ] mix  to tracer in the titrant [tracer titrant ] T , 
       
         
           
             
               
                 f 
                 T 
               
               = 
               
                 
                   
                     M 
                     T 
                   
                   
                     M 
                     mix 
                   
                 
                 = 
                 
                   
                     
                       
                         [ 
                         
                           tracer 
                           titrant 
                         
                         ] 
                       
                       mix 
                     
                     
                       
                         [ 
                         
                           tracer 
                           titrant 
                         
                         ] 
                       
                       T 
                     
                   
                   = 
                   
                     
                       
                         [ 
                         titrant 
                         ] 
                       
                       mix 
                     
                     
                       
                         [ 
                         titrant 
                         ] 
                       
                       T 
                     
                   
                 
               
             
           
         
       
       where M T  is the quantity of titrant added, M mix  is the quantity of the titrant-titrand mixture, [titrant] mix  is the total titrant added to the titrand, and [titrant] T  is the concentration of titrant. 
     
     
         3 . The method of  claim 1 , wherein the tracer is in the titrand and the dilution factor is the ratio of total concentration of tracer in the titrant-titrand mixture [tracer titrand ] mix  to tracer in the titrand [tracer titrand ] S , 
       
         
           
             
               
                 f 
                 S 
               
               = 
               
                 
                   
                     M 
                     S 
                   
                   
                     M 
                     mix 
                   
                 
                 = 
                 
                   
                     
                       
                         [ 
                         
                           tracer 
                           titrand 
                         
                         ] 
                       
                       mix 
                     
                     
                       
                         [ 
                         
                           tracer 
                           titrand 
                         
                         ] 
                       
                       S 
                     
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           [ 
                           titrant 
                           ] 
                         
                         mix 
                       
                       
                         
                           [ 
                           titrant 
                           ] 
                         
                         T 
                       
                     
                   
                 
               
             
           
         
       
       where M S  is the quantity of the sample (titrand) and M mix  is the quantity of the titrant-titrand mixture. 
     
     
         4 . The method of  claim 1 , wherein the titrant is a liquid. 
     
     
         5 . The method of  claim 1 , wherein the titrant is gas. 
     
     
         6 . The method of  claim 1 , wherein the titrant is a solid. 
     
     
         7 . The method of  claim 1 , wherein steps b, c, d, and e are repeated. 
     
     
         8 . The method of  claim 2 , wherein said tracer is of a known concentration and is in said titrant. 
     
     
         9 . The method of  claim 2 , wherein said tracer is of an unknown concentration and is in said titrant. 
     
     
         10 . The method of  claim 9 , wherein said method further comprises a chemical blank and a chemical blank value is recorded for said tracer when f T =1. 
     
     
         11 . The method of  claim 3 , wherein said tracer is of a known concentration and is in said titrand. 
     
     
         12 . The method of  claim 3 , wherein said tracer is of an unknown concentration and is in said titrand. 
     
     
         13 . The method of  claim 12 , wherein said method further comprises a chemical blank and a chemical blank value is recorded for said tracer when f S =1. 
     
     
         14 . The method of  claim 1 , wherein said tracer is selected from the group consisting of an optical species, a spectrochemical species, an electrochemical species and a physical species. 
     
     
         15 . The method of  claim 1 , wherein said tracer is selected from the group consisting of an inert species and a species that participates in the titration reaction. 
     
     
         16 . The method of  claim 1 , wherein said extent of reaction recording means is selected from the group consisting of optical, spectrochemical, electrochemical, and physical means. 
     
     
         17 . The method of  claim 1 , wherein said tracer recording means is selected from the group consisting of optical, spectrochemical, electrochemical, and physical means. 
     
     
         18 . The method of  claim 1 , wherein said extent of reaction recording means and said tracer recording means are spectrochemical means and concentrations are calculated using Beer's Law
     A=εb[C]     
       where A is absorbance at a specified wavelength, ε is molar absorptivity of species C over the bandpass, b is the optical pathlength in cm, and [ ] denotes concentration of species C. 
     
     
         19 . The method of  claim 18 , wherein A is calculated by reference to a chemical blank where f S =1 or f T =1 as a starting value 
       
         
           
             
               A 
               = 
               
                 
                   - 
                   
                     log 
                     10 
                   
                 
                  
                 
                   I 
                   
                     I 
                     o 
                   
                 
               
             
           
         
       
       where I o  is optical intensity at the specified wavelength with titrant or titrand only in the titration chamber and I is optical intensity at the specified wavelength in said mixture of titrant and titrand. 
     
     
         20 . A titration apparatus for a titration method wherein a tracer of an initial concentration [tracer] I  quantifies the relative proportions of titrant to titrand, the method comprising the steps of:
 g) placing an amount of the titrand in a mixing vessel;   h) adding an amount of titrant to the titrand;   i) mixing the titrant and titrand to obtain a homogeneous mixture;   j) measuring an extent of reaction of the titration with a recording means;   k) concurrently, measuring a concentration of the tracer [tracer] mix  with a tracer recording means;   l) determining a dilution factor wherein the dilution factor f is the ratio of total concentration of tracer in the titrant-titrand mixture [tracer] mix  to initial tracer concentration [tracer] I ,   
       
         
           
             
               
                 f 
                 = 
                 
                   
                     
                       [ 
                       tracer 
                       ] 
                     
                     mix 
                   
                   
                     
                       [ 
                       tracer 
                       ] 
                     
                     I 
                   
                 
               
               ; 
               and 
             
           
         
       
       g) determining the concentration of the analyte in the titrand using the dilution factor, the measurement of the extent of reaction and a titration data analysis method.