Analytical Chem istry - DePauw University

Chapter 9 Titrimetric Methods433Before the equivalence point the concentrations of CH 3 COOH andCH 3 COO – areinitialmoles CH COOH − molesNaOH added3[ CH COOH]=3totalvolumeMV − MVa a b b=V + VabmolesNaOHadded[ CH COO− b b] = = MV3totalvolume V + VSubstituting these equations into the K a expression and rearranging leavesus withKa+[ HO ]( MV )3 b b=MV − MVa a b b+KMV − K MV = [ HO ]( MV )a a a a b b 3 b babKMVa a aMb− KV = [ HO+ ] × Va b 3 bFinally, recognizing that the equivalence point volume isleaves us with the following equation.VeqMVa=M[ HO+ ] × V = K V − K V3 b a eq a bFor volumes of titrant before the equivalence point, a plot of V b [H 3 O + ]versus V b is a straight-line with an x-intercept of V eq and a slope of –K a .Figure 9.14d shows a typical result. This method of data analysis, whichconverts a portion of a titration curve into a straight-line, is a Gran plot.baFi n d i n g t h e En d p o i n t b y Mo n i t o r i n g Te m p e ra t u r eThe reaction between an acid and a base is exothermic. Heat generated bythe reaction is absorbed by the titrand, increasing its temperature. Monitoringthe titrand’s temperature as we add the titrant provides us with anothermethod for recording a titration curve and identifying the titration’s endpoint (Figure 9.15).Before adding titrant, any change in the titrand’s temperature is the resultof warming or cooling as it equilibrates with the surroundings. Addingtitrant initiates the exothermic acid–base reaction, increasing the titrand’stemperature. This part of a thermometric titration curve is called the titra-