Complexation titrations, however, are more selective. Although each method is unique, the following description of the determination of the hardness of water provides an instructive example of a typical procedure. As shown in Table 9.11, the conditional formation constant for CdY2– becomes smaller and the complex becomes less stable at more acidic pHs. The resulting spectrophotometric titration curve is shown in Figure 9.31a. The quantitative relationship between the titrand and the titrant is determined by the stoichiometry of the titration reaction. Add 1–2 drops of indicator and titrate with a standard solution of EDTA until the red-to-blue end point is reached (Figure 9.32). Complexometric, How to Use Excel in Analytical Chemistry and in General Scientific Data Analysis. With the help of back titration this list can be mad e much longer, as back titration can be used in the cases when the complex is created too slowly (as it happens in the case of Al and Cr), when it is not possible to choose good end point indicator, or when metal could precipitate at as hydroxide at pH required for a direct titration. EDTA stands for ethylenediaminetetraacetic acid. 2. Titrating with 0.05831 M EDTA required 35.43 mL to reach the murexide end point. Titration 2: moles Ni + moles Fe = moles EDTA, Titration 3: moles Ni + moles Fe + moles Cr + moles Cu = moles EDTA, We can use the first titration to determine the moles of Ni in our 50.00-mL portion of the dissolved alloy. The value of αCd2+ depends on the concentration of NH3. An alloy of chromel containing Ni, Fe, and Cr was analyzed by a complexation titration using EDTA as the titrant. which means the sample contains 1.524×10–3 mol Ni. After the equilibrium point we know the equilibrium concentrations of CdY2- and EDTA. The amount of EDTA reacting with Cu is, \[\mathrm{\dfrac{0.06316\;mol\;Cu^{2+}}{L}\times0.00621\;L\;Cu^{2+}\times\dfrac{1\;mol\;EDTA}{mol\;Cu^{2+}}=3.92\times10^{-4}\;mol\;EDTA}\]. This displacement is stoichiometric, so the total concentration of hardness cations remains unchanged. 9.3.2 Complexometric EDTA Titration Curves. Because EDTA has many forms, when we prepare a solution of EDTA we know it total concentration, CEDTA, not the concentration of a specific form, such as Y4–. Approximately 0.004M of disodium EDTA solution is titrated into a standardized stock solution to verify molarity and is then titrated into the unknown solution labeled #50 to determine the amount of calcium carbonate within it. Sketch titration curves for the titration of 50.0 mL of 5.00×10–3 M Cd2+ with 0.0100 M EDTA (a) at a pH of 10 and (b) at a pH of 7. Engineering Chemistry Lab ( Rajasthan Technical University) EDTA Complexometric Titration of Hydroxyapatite Column Effiuent Bulletin 067 Esteban Freydell, Larry Cummings, and Mark Snyder Bio-Rad Laboratories, Inc., 2000 Alfred Nobel Drive, Hercules, CA 94547 Introduction Ceramic Hydroxyapatite (CHT™) is a mixed-mode chromatographic resin widely used for the purification of proteins and monoclonal antibodies. Finally, we complete our sketch by drawing a smooth curve that connects the three straight-line segments (Figure 9.29e). Figure 9.29c shows the third step in our sketch. The second titration uses, \[\mathrm{\dfrac{0.05831\;mol\;EDTA}{L}\times0.03543\;L\;EDTA=2.066\times10^{-3}\;mol\;EDTA}\]. Of the cations contributing to hardness, Mg2+ forms the weakest complex with EDTA and is the last cation to be titrated. Complexation titrimetry continues to be listed as a standard method for the determination of hardness, Ca2+, CN–, and Cl– in waters and wastewaters. There is a second method for calculating [Cd2+] after the equivalence point. Report the purity of the sample as %w/w NaCN. The concentration of Cl– in the sample is, \[\dfrac{0.0226\textrm{ g Cl}^-}{0.1000\textrm{ L}}\times\dfrac{\textrm{1000 mg}}{\textrm g}=226\textrm{ mg/L}\]. The stoichiometry between EDTA and each metal ion is 1:1. A time limitation suggests that there is a kinetically controlled interference, possibly arising from a competing chemical reaction. After transferring a 50.00-mL portion of this solution to a 250-mL Erlenmeyer flask, the pH was adjusted by adding 5 mL of a pH 10 NH3–NH4Cl buffer containing a small amount of Mg2+–EDTA. Recall that an acid–base titration curve for a diprotic weak acid has a single end point if its two Ka values are not sufficiently different. To evaluate the titration curve, therefore, we first need to calculate the conditional formation constant for CdY2–. Calcium Analysis by EDTA Titration One of the factors that establish the quality of a water supply is its degree of hardness. A 50.00-mL aliquot of the sample, treated with pyrophosphate to mask the Fe and Cr, required 26.14 mL of 0.05831 M EDTA to reach the murexide end point. The reaction between Cl– and Hg2+ produces a metal–ligand complex of HgCl2(aq). In section 9B we learned that an acid–base titration curve shows how the titrand’s pH changes as we add titrant. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. As we add EDTA it reacts first with free metal ions, and then displaces the indicator from MInn–. Using back titration it is also possible to determine some anions - for example SO42- can be determined by BaSO4 precipitation with the use of BaCl2 and titration of excess barium left in the solution. Why does the procedure specify that the titration take no longer than 5 minutes? To do so we need to know the shape of a complexometric EDTA titration curve. The sample, therefore, contains 4.58×10–4 mol of Cr. The solid lines are equivalent to a step on a conventional ladder diagram, indicating conditions where two (or three) species are equal in concentration. Other metal–ligand complexes, such as CdI42–, are not analytically useful because they form a series of metal–ligand complexes (CdI+, CdI2(aq), CdI3– and CdI42–) that produce a sequence of poorly defined end points. Finally, complex titrations involving multiple analytes or back titrations are possible. Complexometric Titrations. See Chapter 11 for more details about ion selective electrodes. The accuracy of an indicator’s end point depends on the strength of the metal–indicator complex relative to that of the metal–EDTA complex. At a pH of 9 an early end point is possible, leading to a negative determinate error. Before the equivalence point, Cd2+ is present in excess and pCd is determined by the concentration of unreacted Cd2+. Figure 9.29a shows the result of the first step in our sketch. A red to blue end point is possible if we maintain the titrand’s pH in the range 8.5–11. The ladder diagram defines pMg values where MgIn– and HIn– are predominate species. The red arrows indicate the end points for each analyte. The analogous result for a complexation titration … Report the weight percents of Ni, Fe, and Cr in the alloy. Hardness is reported as mg CaCO3/L. Hardness of water is determined by titrating with a standard solution of ethylene diamine tetra acetic acid (EDTA) which is a complexing agent. At the equivalence point the initial moles of Cd2+ and the moles of EDTA added are equal. A 0.4482-g sample of impure NaCN is titrated with 0.1018 M AgNO3, requiring 39.68 mL to reach the end point. Calmagite is a useful indicator because it gives a distinct end point when titrating Mg2+. Complexometric titration (sometimes chelatometry) is a form of volumetric analysis in which the In practice, the use of EDTA as a titrant is well established . In section 9B we learned that an acid–base titration curve shows how the titrand’s pH changes as we add titrant. Correcting the absorbance for the titrand’s dilution ensures that the spectrophotometric titration curve consists of linear segments that we can extrapolate to find the end point. For example, an NH4+/NH3 buffer includes NH3, which forms several stable Cd2+–NH3 complexes. Although many quantitative applications of complexation titrimetry have been replaced by other analytical methods, a few important applications continue to be relevant. Note that the titration curve’s y-axis is not the actual absorbance, A, but a corrected absorbance, Acorr, \[A_\textrm{corr}=A\times\dfrac{V_\textrm{EDTA}+V_\textrm{Cu}}{V_\textrm{Cu}}\]. An important limitation when using an indicator is that we must be able to see the indicator’s change in color at the end point. &=\dfrac{(5.00\times10^{-3}\textrm{ M})(\textrm{50.0 mL})}{\textrm{50.0 mL + 30.0 mL}}=3.13\times10^{-3}\textrm{ M} The sample is acidified to a pH of 2.3–3.8 and diphenylcarbazone, which forms a colored complex with excess Hg2+, serves as the indicator. It reacts directly with Mg, Ca, Zn, Cd, Pb, Cu, Ni, Co, Fe, Bi, Th, Zr and others. The molarity of EDTA in the titrant is, \[\mathrm{\dfrac{4.068\times10^{-4}\;mol\;EDTA}{0.04263\;L\;EDTA} = 9.543\times10^{-3}\;M\;EDTA}\]. Although EDTA forms strong complexes with most metal ion, by carefully controlling the titrand’s pH we can analyze samples containing two or more analytes. Figure 9.32 End point for the titration of hardness with EDTA using calmagite as an indicator; the indicator is: (a) red prior to the end point due to the presence of the Mg2+–indicator complex; (b) purple at the titration’s end point; and (c) blue after the end point due to the presence of uncomplexed indicator. Figure 9.29 Illustrations showing the steps in sketching an approximate titration curve for the titration of 50.0 mL of 5.00 × 10–3 M Cd2+ with 0.0100 M EDTA in the presence of 0.0100 M NH3: (a) locating the equivalence point volume; (b) plotting two points before the equivalence point; (c) plotting two points after the equivalence point; (d) preliminary approximation of titration curve using straight-lines; (e) final approximation of titration curve using a smooth curve; (f) comparison of approximate titration curve (solid black line) and exact titration curve (dashed red line). Because the pH is 10, some of the EDTA is present in forms other than Y4–. Both analytes react with EDTA, but their conditional formation constants differ significantly. This method, called a complexometric titration, is used to find the calcium content of milk, the ‘hardness’ of water and the amount of calcium carbonate in various solid materials. See the final side comment in the previous section for an explanation of why we are ignoring the effect of NH3 on the concentration of Cd2+. EDTA titration can be used for direct determination of many metal cations. Record the titration volumes. 3rd ed. \end{align}\]. This is often a problem when analyzing clinical samples, such as blood, or environmental samples, such as natural waters. For example, when titrating Cu2+ with EDTA, ammonia is used to adjust the titrand’s pH. When the titration is complete, raising the pH to 9 allows for the titration of Ca2+. To prevent an interference the pH is adjusted to 12–13, precipitating Mg2+ as Mg(OH)2. A 100.0-mL sample is analyzed for hardness using the procedure outlined in Representative Method 9.2, requiring 23.63 mL of 0.0109 M EDTA. Let’s calculate the titration curve for 50.0 mL of 5.00 × 10–3 M Cd2+ using a titrant of 0.0100 M EDTA. The operational definition of water hardness is the total concentration of cations in a sample capable of forming insoluble complexes with soap. After the equivalence point, EDTA is in excess and the concentration of Cd2+ is determined by the dissociation of the CdY2– complex. A indirect complexation titration with EDTA can be used to determine the concentration of sulfate, SO42–, in a sample. Most indicators for complexation titrations are organic dyes—known as metallochromic indicators—that form stable complexes with metal ions. Our derivation here is general and applies to any complexation titration using EDTA as a titrant. Report the sample’s hardness as mg CaCO3/L. APCH Chemical Analysis. Because not all the unreacted Cd2+ is free—some is complexed with NH3—we must account for the presence of NH3. Let’s use the titration of 50.0 mL of 5.00×10–3 M Cd2+ with 0.0100 M EDTA in the presence of 0.0100 M NH3 to illustrate our approach. :N HO2CCH2 HO 2CCH CH2 2 CH2CO2H CH2CO2H N: 1 H4Y: ethylenediaminetetraacetic acid (EDTA) We can solve for the equilibrium concentration of CCd using Kf´´ and then calculate [Cd2+] using αCd2+. C_\textrm{EDTA}&=\dfrac{M_\textrm{EDTA}V_\textrm{EDTA}-M_\textrm{Cd}V_\textrm{Cd}}{V_\textrm{Cd}+V_\textrm{EDTA}}\\ Although EDTA is the usual titrant when the titrand is a metal ion, it cannot be used to titrate anions. EDTA, which is shown in Figure 9.26a in its fully deprotonated form, is a Lewis acid with six binding sites—four negatively charged carboxylate groups and two tertiary amino groups—that can donate six pairs of electrons to a metal ion. where Kf´ is a pH-dependent conditional formation constant. 3. The hardness of water is defined in terms of its content of calcium and magnesium ions. Figure 9.33 shows the titration curve for a 50-mL solution of 10–3 M Mg2+ with 10–2 M EDTA at pHs of 9, 10, and 11. Complexometric Titration (1): Standardization of an EDTA Solution with Zinc Ion Solution and Analysis of Zinc Supplement Tablets OBJECTIVE Complexometric volumetric titrations withEDTA (ethylene diaminetetraacetic acid) will be performed. The red arrows indicate the end points for each titration curve. Here the concentration of Cd2+ is controlled by the dissociation of the Cd2+–EDTA complex. Why is a small amount of the Mg2+–EDTA complex added to the buffer? For a titration using EDTA, the stoichiometry is always 1:1. The sample was acidified and titrated to the diphenylcarbazone end point, requiring 6.18 mL of the titrant. The third step in sketching our titration curve is to add two points after the equivalence point. Solving equation 9.13 for [Cd2+] and substituting into equation 9.12 gives, \[K_\textrm f' =K_\textrm f \times \alpha_{\textrm Y^{4-}} = \dfrac{[\mathrm{CdY^{2-}}]}{\alpha_\mathrm{Cd^{2+}}C_\textrm{Cd}C_\textrm{EDTA}}\], Because the concentration of NH3 in a buffer is essentially constant, we can rewrite this equation, \[K_\textrm f''=K_\textrm f\times\alpha_\mathrm{Y^{4-}}\times\alpha_\mathrm{Cd^{2+}}=\dfrac{[\mathrm{CdY^{2-}}]}{C_\textrm{Cd}C_\textrm{EDTA}}\tag{9.14}\]. Figure 9.33 Titration curves for 50 mL of 10–3 M Mg2+ with 10–3 M EDTA at pHs 9, 10, and 11 using calmagite as an indicator. After adding calmagite as an indicator, the solution was titrated with the EDTA, requiring 42.63 mL to reach the end point. The determination of Ca2+ is complicated by the presence of Mg2+, which also reacts with EDTA. The ability of EDTA to potentially donate its six lone pairs of electrons for the formation of coordinate covalent bonds to metal cations makes EDTA a hexadentate ligand. Next, we draw our axes, placing pCd on the y-axis and the titrant’s volume on the x-axis. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. A variety of methods are available for locating the end point, including indicators and sensors that respond to a change in the solution conditions. Suppose we need to analyze a mixture of Ni2+ and Ca2+. (Note that in this example, the analyte is the titrant. At the titration’s end point, EDTA displaces Mg2+ from the Mg2+–calmagite complex, signaling the end point by the presence of the uncomplexed indicator’s blue form. Adjust the sample’s pH by adding 1–2 mL of a pH 10 buffer containing a small amount of Mg2+–EDTA. Standardization is accomplished by titrating against a solution prepared from primary standard grade NaCl. COMPLEXOMETRIC TITRATIONS Introduction The complete applications package At Radiometer Analytical, we put applications first. When the titration is complete, we adjust the titrand’s pH to 9 and titrate the Ca2+ with EDTA. Calmagite is used as an indicator. The titration uses, \[\mathrm{\dfrac{0.05831\;mol\;EDTA}{L}\times 0.02614\;L\;EDTA=1.524\times10^{-3}\;mol\;EDTA}\]. The third titration uses, \[\mathrm{\dfrac{0.05831\;mol\;EDTA}{L}\times0.05000\;L\;EDTA=2.916\times10^{-3}\;mol\;EDTA}\], of which 1.524×10–3 mol are used to titrate Ni and 5.42×10–4 mol are used to titrate Fe. For more information contact us at or check out our status page at Step 1: Calculate the conditional formation constant for the metal–EDTA complex. Titrating with EDTA using murexide or Eriochrome Blue Black R as the indicator gives the concentration of Ca2+. Legal. EDTA Complexometric Titration EDTA called as ethylenediaminetetraacetic acid is a complexometric indicator consisting of 2 amino groups and four carboxyl groups called as Lewis bases. A late end point and a positive determinate error are possible if we use a pH of 11. In addition, EDTA must compete with NH3 for the Cd2+. Figure 9.30 (a) Predominance diagram for the metallochromic indicator calmagite showing the most important form and color of calmagite as a function of pH and pMg, where H2In–, HIn2–, and In3– are uncomplexed forms of calmagite, and MgIn– is its complex with Mg2+. The initial solution is a greenish blue, and the titration is carried out to a purple end point. Add 6 drops of indicator and 3 mL of buffer solution. If MInn– and Inm– have different colors, then the change in color signals the end point. Hardness is determined by titrating with EDTA at a buffered pH of 10. Complex titration with EDTA EDTA, ethylenediaminetetraacetic acid , has four carboxyl groups and two amine groups that can act as electron pair donors, or Lewis bases . We present here recent developments on chelators and indicators for complexometric titrations. The indicator, Inm–, is added to the titrand’s solution where it forms a stable complex with the metal ion, MInn–. Complexometric Titration Is a type of volumetric analysis wherein colored complex is used to determine the endpoint of titration. Explore more on EDTA. \end{align}\], \[\begin{align} Figure 9.30 is essentially a two-variable ladder diagram. Finally, what makes EDTA a convenient reagent is fact, that it always reacts with metals on the 1:1 basis, making calculations easy. (a) Titration of 50.0 mL of 0.010 M Ca2+ at a pH of 3 and a pH of 9 using 0.010 M EDTA. Ethylenediaamine tetra-acetic acid (EDTA) has risen from an obscure chemical … In this section we will learn how to calculate a titration curve using the equilibrium calculations from Chapter 6. Complexometric titrations are titrations that can be used to discover the hardness of water or to discover metal ions in a solution. Determination of the Hardness of Tap Water 1. to give a conditional formation constant, Kf´´, that accounts for both pH and the auxiliary complexing agent’s concentration. a pCd of 15.32. In this case the interference is the possible precipitation of CaCO3 at a pH of 10. Step 4: Calculate pM at the equivalence point using the conditional formation constant. The best way to appreciate the theoretical and practical details discussed in this section is to carefully examine a typical complexation titrimetric method. The earliest examples of metal–ligand complexation titrations are Liebig’s determinations, in the 1850s, of cyanide and chloride using, respectively, Ag+ and Hg2+ as the titrant. The buffer is at its lower limit of pCd = logKf´ – 1 when, \[\dfrac{C_\textrm{EDTA}}{[\mathrm{CdY^{2-}}]}=\dfrac{\textrm{moles EDTA added} - \textrm{initial moles }\mathrm{Cd^{2+}}}{\textrm{initial moles }\mathrm{Cd^{2+}}}=\dfrac{1}{10}\], Making appropriate substitutions and solving, we find that, \[\dfrac{M_\textrm{EDTA}V_\textrm{EDTA}-M_\textrm{Cd}V_\textrm{Cd}}{M_\textrm{Cd}V_\textrm{Cd}}=\dfrac{1}{10}\], \[M_\textrm{EDTA}V_\textrm{EDTA}-M_\textrm{Cd}V_\textrm{Cd}=0.1 \times M_\textrm{Cd}V_\textrm{Cd}\], \[V_\textrm{EDTA}=\dfrac{1.1 \times M_\textrm{Cd}V_\textrm{Cd}}{M_\textrm{EDTA}}=1.1\times V_\textrm{eq}\]. A 0.1557-g sample is dissolved in water, any sulfate present is precipitated as BaSO4 by adding Ba(NO3)2. Page was last modified on April 28 2009, 17:00:52. titration at © 2009 ChemBuddy. of which 1.524×10–3 mol are used to titrate Ni. \[K_\textrm f''=\dfrac{[\mathrm{CdY^{2-}}]}{C_\textrm{Cd}C_\textrm{EDTA}}=\dfrac{3.33\times10^{-3}-x}{(x)(x)}= 9.5\times10^{14}\], \[x=C_\textrm{Cd}=1.9\times10^{-9}\textrm{ M}\]. Next, we solve for the concentration of Cd2+ in equilibrium with CdY2–. Although most divalent and trivalent metal ions contribute to hardness, the most important are Ca2+ and Mg2+. Furthermore, let’s assume that the titrand is buffered to a pH of 10 with a buffer that is 0.0100 M in NH3. Even if a suitable indicator does not exist, it is often possible to complete an EDTA titration by introducing a small amount of a secondary metal–EDTA complex, if the secondary metal ion forms a stronger complex with the indicator and a weaker complex with EDTA than the analyte., \[C_\textrm{Cd}=[\mathrm{Cd^{2+}}]+[\mathrm{Cd(NH_3)^{2+}}]+[\mathrm{Cd(NH_3)_2^{2+}}]+[\mathrm{Cd(NH_3)_3^{2+}}]+[\mathrm{Cd(NH_3)_4^{2+}}]\], Conditional Metal–Ligand Formation Constants, 9.3.2 Complexometric EDTA Titration Curves, 9.3.3 Selecting and Evaluating the End point, Finding the End point by Monitoring Absorbance, Selection and Standardization of Titrants, 9.3.5 Evaluation of Complexation Titrimetry, information contact us at, status page at 1. The concentration of Cl– in a 100.0-mL sample of water from a freshwater aquifer was tested for the encroachment of sea water by titrating with 0.0516 M Hg(NO3)2. If the sample does not contain any Mg2+ as a source of hardness, then the titration’s end point is poorly defined, leading to inaccurate and imprecise results. Compare your results with Figure 9.28 and comment on the effect of pH and of NH3 on the titration of Cd2+ with EDTA. Next, we add points representing pCd at 110% of Veq (a pCd of 15.04 at 27.5 mL) and at 200% of Veq (a pCd of 16.04 at 50.0 mL). C_\textrm{Cd}&=\dfrac{\textrm{initial moles Cd}^{2+} - \textrm{moles EDTA added}}{\textrm{total volume}}=\dfrac{M_\textrm{Cd}V_\textrm{Cd}-M_\textrm{EDTA}V_\textrm{EDTA}}{V_\textrm{Cd}+V_\textrm{EDTA}}\\ Hard water should be not used for washing (it reduces effectiveness of detergents) nor in water heaters and kitchen appliances like coffee makers (that can be destroyed by scale). Missed the LibreFest? This may be difficult if the solution is already colored. [\mathrm{CdY^{2-}}]&=\dfrac{\textrm{initial moles Cd}^{2+}}{\textrm{total volume}}=\dfrac{M_\textrm{Cd}V_\textrm{Cd}}{V_\textrm{Cd}+V_\textrm{EDTA}}\\ This provides some control over an indicator’s titration error because we can adjust the strength of a metal–indicator complex by adjusted the pH at which we carry out the titration. Figure 9.30, for example, shows the color of the indicator calmagite as a function of pH and pMg, where H2In–, HIn2–, and In3– are different forms of the uncomplexed indicator, and MgIn– is the Mg2+–calmagite complex. Calcium is also of biological importance and is contained in teeth and bone. \end{align}\], To calculate the concentration of free Cd2+ we use equation 9.13, \[[\mathrm{Cd^{2+}}] = \alpha_\mathrm{Cd^{2+}} \times C_\textrm{Cd} = (0.0881)(3.64\times10^{-4}\textrm{ M})=3.21\times10^{-4}\textrm{ M}\], \[\textrm{pCd}=-\log[\mathrm{Cd^{2+}}]=-\log(3.21\times10^{-4}) = 3.49\]. EDTA titration can be used for direct determination of many metal cations. To use equation 9.10, we need to rewrite it in terms of CEDTA. If the metal–indicator complex is too strong, the change in color occurs after the equivalence point. Because the calculation uses only [CdY2−] and CEDTA, we can use Kf´ instead of Kf´´; thus, \[\dfrac{[\mathrm{CdY^{2-}}]}{[\mathrm{Cd^{2+}}]C_\textrm{EDTA}}=\alpha_\mathrm{Y^{4-}}\times K_\textrm f\], \[\dfrac{3.13\times10^{-3}\textrm{ M}}{[\mathrm{Cd^{2+}}](6.25\times10^{-4}\textrm{ M})} = (0.37)(2.9\times10^{16})\]. The estimation of hardness is based on complexometric titration. In this titration standard EDTA solution is added to given sample containing metals using burette till the end point is achieved. Figure 9.29b shows the pCd after adding 5.00 mL and 10.0 mL of EDTA. The calculations are straightforward, as we saw earlier. As is the case with acid–base titrations, we estimate the equivalence point of a complexation titration using an experimental end point. \[\textrm{MIn}^{n-}+\textrm Y^{4-}\rightarrow\textrm{MY}^{2-}+\textrm{In}^{m-}\]. Beginning with the conditional formation constant, \[K_\textrm f'=\dfrac{[\mathrm{CdY^{2-}}]}{[\mathrm{Cd^{2+}}]C_\textrm{EDTA}}=\alpha_\mathrm{Y^{4-}} \times K_\textrm f = (0.37)(2.9\times10^{16})=1.1\times10^{16}\], we take the log of each side and rearrange, arriving at, \[\log K_\textrm f'=-\log[\mathrm{Cd^{2+}}]+\log\dfrac{[\mathrm{CdY^{2-}}]}{C_\textrm{EDTA}}\], \[\textrm{pCd}=\log K_\textrm f'+\log\dfrac{C_\textrm{EDTA}}{[\mathrm{CdY^{2-}}]}\]. Calculate titration curves for the titration of 50.0 mL of 5.00×10–3 M Cd2+ with 0.0100 M EDTA (a) at a pH of 10 and (b) at a pH of 7. Contrast this with αY4-, which depends on pH. As we add EDTA, however, the reaction, \[\mathrm{Cu(NH_3)_4^{2+}}(aq)+\textrm Y^{4-}(aq)\rightarrow\textrm{CuY}^{2-}(aq)+4\mathrm{NH_3}(aq)\], decreases the concentration of Cu(NH3)42+ and decreases the absorbance until we reach the equivalence point. Note that after the equivalence point, the titrand’s solution is a metal–ligand complexation buffer, with pCd determined by CEDTA and [CdY2–]. Why is the sample buffered to a pH of 10? For each of the three titrations, therefore, we can easily equate the moles of EDTA to the moles of metal ions that are titrated. Having determined the moles of Ni, Fe, and Cr in a 50.00-mL portion of the dissolved alloy, we can calculate the %w/w of each analyte in the alloy.
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