91Ó°ÊÓ

Prada and colleagues described an indirect method for determining sulfate in natural samples, such as seawater and industrial effluents. \({ }^{12}\) The method consists of three steps: precipitating the sulfate as \(\mathrm{PbSO}_{4}\); dissolving the \(\mathrm{PbSO}_{4}\) in an ammonical solution of excess EDTA to form the soluble \(\mathrm{Pb} \mathrm{Y}^{2-}\) complex; and titrating the excess EDTA with a standard solution of \(\mathrm{Mg}^{2+}\). The following reactions and equilibrium constants are known $$ \begin{array}{ll} \mathrm{PbSO}_{4}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{SO}_{4}^{2-}(a q) & K_{\mathrm{sp}}=1.6 \times 10^{-8} \\ \mathrm{~Pb}^{2+}(a q)+\mathrm{Y}^{4-}(a q) \rightleftharpoons \mathrm{Pb} \mathrm{Y}^{2-}(a q) & K_{\mathrm{f}}=1.1 \times 10^{18} \\ \mathrm{Mg}^{2+}(a q)+\mathrm{Y}^{4-}(a q) \rightleftharpoons \mathrm{Mg} \mathrm{Y}^{2-}(a q) & K_{\mathrm{f}}=4.9 \times 10^{8} \\ \mathrm{Zn}^{2+}(a q)+\mathrm{Y}^{4-}(a q)=\mathrm{Zn} \mathrm{Y}^{2-}(a q) & K_{\mathrm{f}}=3.2 \times 10^{16} \end{array} $$ (a) Verify that a precipitate of \(\mathrm{PbSO}_{4}\) will dissolve in a solution of \(\mathrm{Y}^{4-}\). (b) Sporek proposed a similar method using \(\mathrm{Zn}^{2+}\) as a titrant and found that the accuracy frequently was poor. \(^{13}\) One explanation is that \(\mathrm{Zn}^{2+}\) might react with the \(\mathrm{PbY}^{2-}\) complex, forming \(\mathrm{ZnY}^{2-}\). Show that this might be a problem when using \(\mathrm{Zn}^{2+}\) as a titrant, but that it is not a problem when using \(\mathrm{Mg}^{2+}\) as a titrant. Would such a displacement of \(\mathrm{Pb}^{2+}\) by \(\mathrm{Zn}^{2+}\) lead to the reporting of too much or too little sulfate? (c) In a typical analysis, a 25.00 -mL sample of an industrial effluent is carried through the procedure using \(50.00 \mathrm{~mL}\) of \(0.05000 \mathrm{M}\) EDTA. Titrating the excess EDTA requires \(12.42 \mathrm{~mL}\) of \(0.1000 \mathrm{M}\) \(\mathrm{Mg}^{2+}\). Report the molar concentration of \(\mathrm{SO}_{4}^{2-}\) in the sample of effluent.

Step by step solution

01

Determining Solubility of PbSO4 in Y4- Solution

To verify if PbSO4 will dissolve in a solution containing Y4-, we need to verify if the reaction \( \mathrm{PbSO}_{4}(s) \rightleftharpoons \mathrm{Pb}^{2+}(aq) + \mathrm{SO}_{4}^{2-}(aq) \) will shift to the right when \( \mathrm{Pb}^{2+}(aq) \) is complexed with \( \mathrm{Y}^{4-} \). The formation constant for \( \mathrm{PbY}^{2-} \) is very large (\( K_f = 1.1 \times 10^{18} \)). Since \( K_{sp} = 1.6 \times 10^{-8} \), the equilibrium is greatly shifted to the right, indicating \( \mathrm{PbSO_{4}} \) will dissolve by forming \( \mathrm{PbY}^{2-} \).

02

Analyzing Potential Reaction of PbY2- with Zn2+

Sporek's method may encounter problems with Zn2+ because \( \mathrm{Zn}^{2+} \) could form \( \mathrm{ZnY}^{2-} \), thus displacing Pb2+ from \( \mathrm{PbY}^{2-} \) complex. The complex formation constant for \( \mathrm{ZnY}^{2-} \) is \( K_f = 3.2 \times 10^{16} \), which is quite significant, though much lower than that for \( \mathrm{PbY}^{2-} \). This could lead to insufficient displacement of \( \mathrm{Y}^{4-} \) for accurate titration. This displacement is not an issue with \( \mathrm{Mg}^{2+} \), as its formation constant \( (4.9 \times 10^8) \) is lower, preventing significant competition for \( \mathrm{Y}^{4-} \).

03

Impact of Zn2+ Displacement Reaction on Sulfate Results

If \( \mathrm{Zn}^{2+} \) displaces \( \mathrm{Pb}^{2+} \) in the \( \mathrm{PbY}^{2-} \) complex, there would be fewer \( \mathrm{Y}^{4-} \) complexed with \( \mathrm{Pb}^{2+} \), leading to inaccurate measurements. More free \( \mathrm{Y}^{4-} \) would remain than expected, which would consume more titrant, suggesting a higher sulfate concentration than actual.

04

Calculating Molar Concentration of SO42-

Firstly, calculate the moles of EDTA used: \( n = C \times V = 0.05000\, \text{M} \times 0.05000\, \text{L} = 0.00250\, \text{mol}\). The moles of \( \mathrm{Mg}^{2+} \) titrant used is \( 0.1000\, \text{M} \times 0.01242\, \text{L} = 0.001242\, \text{mol}\). The moles of EDTA that were not used to complex sulfate ions: \( 0.00250 - 0.001242 = 0.001258\, \text{mol}\). Thus, moles of sulfate is \( 0.001258\, \text{mol} \), and the concentration in \( 0.02500\, \text{L} \): \( \frac{0.001258}{0.02500} = 0.05032\, \text{M} \).

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sulfate Determination

Determining sulfate levels in various samples, such as natural waters and industrial effluents, is crucial for environmental and quality control. Sulfates, particularly in natural samples like seawater, can have significant impacts on the environment and human health. The method described by Prada involves an interesting indirect approach to sulfate determination. This method includes:

• Precipitating sulfate as lead sulfate (\(\mathrm{PbSO}_4\)).
• Dissolving this precipitate in an ammoniacal solution with excess ethylenediaminetetraacetic acid (EDTA), leading to the formation of a soluble lead-EDTA complex (\(\mathrm{PbY}^{2-}\)).
• Finally, titrating the excess EDTA with a standardized magnesium solution.

This approach is robust because the initial precipitation step separates the sulfate ions, allowing for precise interaction with EDTA. The release of lead ions, once the insoluble lead sulfate is dissolved by EDTA, is a key step. It ensures that the sulfate ions are also released and quantified indirectly using the EDTA that is not bound by lead.

Complexometric Titration

Complexometric titration is a type of volumetric analysis widely used to determine the concentration of metal ions in solution. In the context of sulfate determination, EDTA plays a critical role due to its ability to form stable complexes with various metal ions. EDTA acts as a chelating agent, meaning it can bind tightly to metal ions, creating a ring-like structure. This property makes complexometric titration very effective for the measurement of sulfate when lead is involved.
During the process:

• The dissolved \(\mathrm{PbSO}_4\) reacts with EDTA, forming the complex \(\mathrm{PbY}^{2-}\).
• Unreacted EDTA is titrated against a \(\mathrm{Mg}^{2+}\) solution.

The advantage of using magnesium over other metals, like zinc, relates to their differing affinities for EDTA, highlighted through their formation constants. Low affinity of magnesium ensures it does not displace lead from \(\mathrm{PbY}^{2-}\), which is essential for maintaining the integrity of the analytical process.

Equilibrium Constants

Equilibrium constants are pivotal parameters in chemical reactions, indicating the extent to which reactants are converted to products. In sulfate determination via complexometric titration, two key equilibrium constants govern the process.
The solubility product constant (\(K_{sp}\)) and the formation constant (\(K_{f}\)) play critical roles:

• \(K_{sp}\) of lead sulfate (\(\mathrm{PbSO}_4\)), valued at \(1.6 \times 10^{-8}\), suggests low solubility, making the precipitation step effective.
• \(K_{f}\) of the \(\mathrm{PbY}^{2-}\) complex, at an extraordinary \(1.1 \times 10^{18}\), supports nearly complete chelation of \(\mathrm{Pb}^{2+}\) by EDTA.

Equilibrium constants essentially determine the reaction direction and completion. The notably high \(K_{f}\) for \(\mathrm{PbY}^{2-}\) indicates a strong "pull" driving the dissolution of \(\mathrm{PbSO}_4\) in the presence of EDTA. This efficiency relies on these constants directing the processes towards desirable outcomes, such as precise sulfate quantification.