Solution to Mohr’s method challenge

Analytical and Bioanalytical Chemistry, Jun 2016

Juris Meija, Anna Maria Michałowska-Kaczmarczyk, Tadeusz Michałowski

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Solution to Mohr’s method challenge

Anal Bioanal Chem Solution to Mohr's method challenge Juris Meija 0 1 2 Anna Maria Michałowska-Kaczmarczyk 0 1 2 Tadeusz Michałowski 0 1 2 0 Faculty of Engineering and Chemical Technology, Technical University of Cracow , 31-155 Cracow , Poland 1 Department of Oncology, The University Hospital in Cracow , 31-501 Cracow , Poland 2 National Research Council Canada , 1200 Montreal Road, Ottawa, ON , Canada K1A 0R6 3 Tadeusz Michałowski This challenge explores the precise endpoint location in Mohr's titration of sodium chloride with silver nitrate, in the presence of potassium chromate as indicator. First, we evaluate the pH of the titrand, i.e., NaCl (C0) + K2CrO4 (Cind) solution, and denote it as pH0. This system is characterized by charge balance - ½Hþ − ½OH− þ ½Kþ − ½HCrO4− − 2 CrO42− − ½HCr2O7− − 2 Cr2O72− þ ½Naþ − ½Cl− ¼ 0 and concentration balances can be written as follows: C0 ¼ ½Naþ C0 ¼ ½Cl− 2Cind ¼ ½Kþ Cind ¼ ½H2CrO4 þ ½HCrO4− þ CrO42− þ 2½HCr2O7− þ 2 Cr2O72− ð1Þ ð2aÞ ð2bÞ ð2cÞ ð2dÞ Addition of the sum of Eqs. 1, 2a, 2b, and 2c to Eq. 2d multiplied by 2 gives the proton balance 2½H2CrO4 þ ½HCrO4− þ 3½HCr2O7− þ 2 Cr2O72− þ a ¼ 0 where a ¼ ½Hþ − ½OH− ¼ 10−pH − 10pH − 14:0 From Eqs. 3 and 4 we see that the starting solution of NaCl and K2CrO4 is alkaline because a has to be negative, i.e., [H+] < [OH−]. Hence, we can now simplify the titration problem by omitting two species that are present only in very acidic conditions, namely H2CrO4 and HCr2O7−. Equations 2d and 3 become Cind ¼ ½HCrO4− þ þ 2 Cr2O72− ½HCrO4− þ 2 Cr2O72− þ a ¼ 0 Combination of these equations gives Cind − CrO42− ¼ −a This means [CrO42−] = Cind + a = Cind + 10−pH − 10(pH − 14.0). The concentration of other chromium species can be obtained from the expressions [H+][CrO42−] = K21[HCrO4−] and [Cr2O72−] = K1[HCrO4−]2. We still do not know the pH and it can be obtained by calculating the values of [CrO42−], [HCrO4−], and [Cr2O72−] at any given pH (>7). Equation 5 will hold true only at the value of pH corresponding to the pH of titrand. For values of Cind = 0.002, 0.005, and 0.010 mol/L, we obtain pH = 8.89, 9.09, and 9.24, respectively. We also can observe that [CrO42−] is the predominant chromium species (Fig. 1). The related ð3Þ ð4Þ ð5Þ ð6Þ ð7Þ -10 4 1 3 5 2 1 - H2CrO4 2 - HCrO4 3 - CrO4 4 - HCr2O7 5 - Cr2O7 2 3 4 5 6 7 8 9 10 11 12 pH Fig. 1 Logarithmic diagram for chromium species at Cind = 0.002 mol/L curves are plotted there on the basis of data presented in Table 1 of this Challenge [1] for different Cr species and without making simplifying assumptions as we did in the preceding paragraphs. Now let us turn to the titration of V0 = 100 mL of NaCl (C0 = 0.01 mol/L) + K2CrO4 (Cind). The addition of AgNO3 solution results in the total volume of the mixture becoming V0 + V, and the balances for Cl and Ag are as follows: 3 ½pr þ ½Cl− þ X i⋅ AgCli1−i i¼1 3 3 ½pr þ ½Agþ þ X hAgðOHÞi1−iiþX i¼1 i¼1 C0V 0 ¼ V 0 þ V AgCli1−i CV ¼ V 0 þ V where [pr] is the concentration of AgCl in the system. Subtraction of Eq. 9 from Eq. 8 gives 3 3 ½Cl− þ X ði−1Þ⋅ AgCli1−i −½Agþ −X hAgðOHÞi1−ii ¼ i¼2 i¼1 C0V 0−CV V 0 þ V Applying the relations [AgCli1−i] = KiClIKsp1[Cl−]i−1 and [Ag(OH)i1−i] = KiOHI[Ag+][OH−]i , Eq. 10 becomes z1½Cl− −z2½Agþ ¼ where C0V 0−CV V 0 þ V z1 ¼ 1 þ K2ClKsp1 þ 2K3ClKsp1½Cl− z2 ¼ 1 þ K1OH½OH− þ K2OH½OH− 2 þ K3OH½OH− 3 Further, by assuming that the pH remains unchanged during titration, i.e., pH ≈ pH0, we can evaluate the numerical values of z1 and z2, both of which are close to 1. Hence, Eq. 11 can be written as follows: ½Cl− −½Agþ ¼ At the equivalence point (eq) we have the relation C0V0 = CVeq. Hence, V eq ¼ C0V 0 C ¼ 10 mL At the titration endpoint, V = Vend, the solubility product Ksp2 is crossed, i.e., [Ag+]end2·[CrO42−]end = Ksp2. At pH = pHend = pH0, CrO42− predominates significantly over all other chromium species (Fig. 1) and it is still not consumed by silver nitrate, which acts mainly as a diluent at V ≤ Vend. Hence, Since AgCl is also the equilibrium solid phase in this system, [Cl−]end = Ksp1/[Ag+]end. Gathering these expressions, we can rewrite Eq. 15: Ksp1 rffiffiffiffiffiffiffiffiffiffiVffiffiffi0ffiffiffiffiffiffiffiffiVffiffiffiffieffinffiffidffi Ksp2 þ CindV 0 − rffiffiffiffiffiffiffiffiffiffiVffiffiffi0ffiffiffiffiffiffiffiffiVffiffiffiffieffinffiffidffi Ksp2 þ CindV 0 ¼ C0V 0−CV end ð19Þ V 0 þ V end Equation 19 can be solved for Vend iteratively by inserting all known numerical values (C, Cind, C0, V0, Ksp1, Ksp2). For the value Cind = 0.002 mol/L, we find that Vend = 10.022 mL satisfies Eq. 19. Given that simple chemical stoichiometry suggests the equivalence point at Veq = 10 mL, ignoring the corrections due to solubility and other chemical processes leads to a 0.22% error. Results for other values of Cind are summarized in Table 1. As we can see from Table 1, errors in chloride determination are affected by the initial concentration of K2CrO4, Cind. With the increase of Cind, the systematic error decreases, assumes zero at Cind = 0.0078 mol/L, and then increases gradually. On the basis of the data obtained from calculations, one can also check whether the solubility products Ksp3 for Ag2Cr2O7 and Ksp4 for Ag2O are crossed. At Cind = 0.002 mol/L, we calculate [Ag+]end = 2.632 × 10−5 mol/L from Eq. 18. At pH = 8.99 we have [Cr2O72−] = 3.46 × 10−8 mol/L and [Ag+]2[Cr2O72−] = 2.4 × 10−17 < 10−6.7, [Ag+][OH−] = 2.6 × 10−10 < 10−7.84. Hence, these solubility products are not crossed. Titration is still considered as a primary method of chemical analysis. From this example it is evident that the accuracy of the titration results can be significantly improved by better understanding of the physicochemical conditions of the system. Meija J , Michałowska-Kaczmarczyk AM , Michałowski T. Mohr's method challenge . Anal Bioanal Chem . 2016 ; 408 : 1721 - 22 .

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Juris Meija, Anna Maria Michałowska-Kaczmarczyk, Tadeusz Michałowski. Solution to Mohr’s method challenge, Analytical and Bioanalytical Chemistry, 2016, 4469-4471, DOI: 10.1007/s00216-016-9555-3