Problem 21 - Analytical Chemistry

Question

Chloride in serum is determined by titration with \(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2} ; 2 \mathrm{Cl}^{-}+\mathrm{Hg}^{2+} \rightleftharpoons \mathrm{HgCl}_{2} .\) The \(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}\) is standardized by titrating \(2.00 \mathrm{~mL}\) of a \(0.0108 \mathrm{M} \mathrm{NaCl}\) solution, requiring \(1.12 \mathrm{~mL}\) to reach the diphenylcarbazone end point. A \(0.500-\mathrm{mL}\) serum sample is treated with \(3.50 \mathrm{~mL}\) water, \(0.50 \mathrm{~mL} 10 \%\) sodium tungstate solution, and \(0.50 \mathrm{~mL}\) of \(0.33 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) solution to precipitate proteins. After the proteins are precipitated, the sample is filtered through a dry filter into a dry flask. A \(2.00-\mathrm{mL}\) aliquot of the filtrate is titrated with the \(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}\) solution, requiring \(1.23 \mathrm{~mL}\). Calculate the \(\mathrm{mg} / \mathrm{L}\) chloride in the serum. (Note: mercury is rarely used today due to its toxicity. The problem is illustrative.)

Step-by-Step Solution

Answer

The chloride concentration in the serum is 1682 mg/L.

Step 1: Calculate Moles of NaCl in Standardization

First, calculate the moles of NaCl using its concentration and volume. The concentration is given as \(0.0108\, \text{M}\), and the volume is \(2.00 \times 10^{-3}\, \text{L}\). Thus, the moles of NaCl are:\[\text{moles of NaCl} = 0.0108 \times 2.00 \times 10^{-3} = 2.16 \times 10^{-5}\, \text{moles}\.\]

Step 2: Determine Molarity of Hg(NO₃)₂ Solution

The reaction stoichiometry is 1:2, meaning each mole of \(\text{Hg(NO}_3\text{)}_2\) reacts with 2 moles of \(\text{Cl}^-\). Therefore, the moles of \(\text{Hg(NO}_3\text{)}_2\) used in standardization are:\[\text{moles of } \text{Hg(NO}_3\text{)}_2 = \frac{2.16 \times 10^{-5}}{2} = 1.08 \times 10^{-5}\, \text{moles}\.\]From the equation, \(1.12 \text{ mL}\) was the volume used, which is \(1.12 \times 10^{-3} \text{ L}\), thus the molarity of \(\text{Hg(NO}_3\text{)}_2\) is:\[\text{Molarity of } \text{Hg(NO}_3\text{)}_2 = \frac{1.08 \times 10^{-5}}{1.12 \times 10^{-3}} = 0.00964\, \text{M}\.\]

Step 3: Calculate Moles of Cl⁻ in the Serum Sample

Now calculate the number of moles of \(\text{Hg(NO}_3\text{)}_2\) used for the serum by multiplying its molarity by the volume used for titration \(1.23 \times 10^{-3} \text{ L}\):\[\text{moles of } \text{Hg(NO}_3\text{)}_2 = 0.00964 \times 1.23 \times 10^{-3} = 1.18572 \times 10^{-5}\, \text{moles}\.\]Because the stoichiometry is 1:2, the moles of chloride are:\[\text{moles of } \text{Cl}^- = 2 \times 1.18572 \times 10^{-5} = 2.37144 \times 10^{-5}\, \text{moles}\.\]

Step 4: Convert Moles of Cl⁻ to Mass

Convert the moles of \(\text{Cl}^-\) to grams. The molar mass of \(\text{Cl}^-\) is approximately \(35.45\, \text{g/mol}\).\[\text{mass of } \text{Cl}^- = 2.37144 \times 10^{-5} \times 35.45 = 8.410 \times 10^{-4}\, \text{g}\.\]

Step 5: Calculate Concentration in mg/L

Finally, calculate the chloride concentration in the serum. Given that \(0.500\, \text{mL}\) of serum was used, convert the mass from grams to milligrams \((1\, \text{g} = 1000\, \text{mg})\), and adjust for the per liter reference:\[\text{Concentration of } \text{Cl}^- = \frac{8.410 \times 10^{-4} \times 1000}{0.500 \times 10^{-3}} = 1682\, \text{mg/L}\.\]

Key Concepts

Chloride Determination

Chloride determination in serum is an important analytical procedure often carried out to measure chloride ions, which are vital electrolytes in the human body. The determination involves titration, a technique to find the concentration of a solute in a solution.
A common method for chloride determination uses a titration reaction with mercuric nitrate (\(\mathrm{Hg}\left(\mathrm{NO}_{3}\right)_{2}\)), as represented in our exercise. In this method, the chloride ions (\(\mathrm{Cl^-}\)) react with mercuric ions (\(\mathrm{Hg}^{2+}\)) to form mercurous chloride (\(\mathrm{HgCl}_2\)), an insoluble product.

• This precipitation makes it possible to determine the amount of chloride in the serum, helping in calculating the sample's overall chloride concentration efficiently.
• The endpoint of the titration is often indicated by a color change, such as when using diphenylcarbazone as an indicator.

Serum Analysis

Serum analysis is crucial for assessing various components of blood plasma, excluding clotting factors. When analyzing serum for chloride content, it's essential to prepare the sample properly.
For instance, proteins often interfere with the analysis, thus being removed by precipitation. In our case, the serum sample is mixed with reagents, namely water, sodium tungstate solution, and sulfuric acid, to precipitate these proteins out of the solution.

• Once proteins are out, the serum filtrate can be used for chloride determination.
• The clear serum filtrate ensures that there are no interferences during the titration process, leading to more accurate results.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. In chloride determination by titration, understanding stoichiometry is crucial.
The balanced chemical equation \(2\mathrm{Cl}^-+\mathrm{Hg}^{2+} \rightleftharpoons \mathrm{HgCl}_{2} \) illustrates the molar relationship between chloride ions and mercuric nitrate.

• According to the reaction, every mole of mercuric nitrate reacts with two moles of chloride ions. This 1:2 ratio is essential for calculating how many moles of chloride are present in the sample after titration.
• By understanding stoichiometry, we can accurately determine the molarity of solutions and the number of moles involved in reactions.

Concentration Calculation

Concentration calculation is the final step in determining the amount of chloride in the serum. Once we know the moles of chloride from the stoichiometry analysis, we can convert these moles into mass using the molar mass of chloride (35.45 g/mol).
Calculation involves converting moles into grams, and then adjusting this mass for the concentration by accounting for the sample size.

• The concentration is reported in mg/L (milligrams per liter) for serum samples, providing a clear measure of how much chloride is present per liter of solution.
• Understanding and performing these calculations accurately are crucial for meaningful interpretation of serum analysis results.
• The conversion presumes 1 liter equals 1000 milliliters, facilitating a straightforward conversion from the amount measured in the sample to the standardized concentration units.