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Chapter 9: Problem 36

The amount of calcium in physiological fluids is determined by a complexometric titration with EDTA. In one such analysis a \(0.100-\mathrm{mL}\) sample of a blood serum is made basic by adding 2 drops of \(\mathrm{NaOH}\) and titrated with \(0.00119 \mathrm{M}\) EDTA, requiring \(0.268 \mathrm{~mL}\) to reach the end point. Report the concentration of calcium in the sample as milligrams Ca per \(100 \mathrm{~mL}\).

Short Answer

Expert verified
12.774 mg of calcium per 100 mL.

Step by step solution

01

Calculate Moles of EDTA

To determine the amount of calcium, we start by calculating the moles of EDTA used in the titration. The volume of EDTA used is given as 0.268 mL and its concentration is 0.00119 M. First, convert the volume to liters by dividing by 1000, which gives 0.000268 L. Then, multiply the volume by the molarity to get the moles: \[ \text{Moles of EDTA} = 0.000268 \, \text{L} \times 0.00119 \, \text{mol/L} = 3.1892 \times 10^{-7} \, \text{mol} \].
02

Determine Moles of Calcium

In complexometric titrations with EDTA, calcium reacts with EDTA in a 1:1 mole ratio. Therefore, the moles of EDTA used equal the moles of calcium in the sample: \[ \text{Moles of Ca} = 3.1892 \times 10^{-7} \, \text{mol} \].
03

Convert Moles of Calcium to Milligrams

To find the mass of the calcium, multiply the moles of calcium by its molar mass. The molar mass of calcium is approximately 40.08 g/mol: \[ \text{Mass of Ca} = 3.1892 \times 10^{-7} \, \text{mol} \times 40.08 \, \text{g/mol} = 1.2774 \times 10^{-5} \, \text{g} \]. Convert this mass to milligrams by multiplying by 1000: \[ 1.2774 \times 10^{-5} \, \text{g} \times 1000 = 0.012774 \, \text{mg} \].
04

Express Calcium Concentration per 100 mL

Since the sample size is 0.100 mL, we need to express the concentration per 100 mL. Multiply the calcium mass by 1000 to scale up from 0.100 mL to 100 mL: \[ 0.012774 \, \text{mg} \times 1000 = 12.774 \, \text{mg} \].

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Key Concepts

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

EDTA
EDTA, or ethylenediaminetetraacetic acid, is a chelating agent that is widely used in complexometric titrations for its ability to bind tightly with metal ions. This characteristic makes it exceptional for quantitative analyses, especially when determining the concentration of metal ions such as calcium in various solutions. EDTA acts as a polyvalent ligand that can form stable complexes with metal ions by surrounding them completely. The resulting complex is very stable, leading to precise measurements.
  • Because of its ability to form one-on-one complexes with metal ions, it鈥檚 perfect for determining the amount of metal present through titration.
  • In a titration involving EDTA, two primary components are essential: the concentration of EDTA and the volume added to the sample, enabling accurate calculations of the analyte concentration.
Calcium Analysis
Calcium analysis in complexometric titration generally involves the use of EDTA as it can specifically and effectively bind to calcium ions. Calcium is a crucial element found in various biological systems, and precise measurement is often necessary in physiological and environmental samples, like blood serum.
  • The titration process allows for accurate assessment of the calcium content because EDTA binds directly to the calcium ions in a 1:1 ratio.
  • In the process described, a small volume of blood serum sample was used to determine the presence of calcium, highlighting the sensitivity and efficiency of the method.
  • The analysis requires the sample to be made basic, which facilitates the formation of the EDTA-metal complex.
Moles Calculation
Calculating moles is a vital step in complexometric titrations. It involves converting measurable physical quantities, like volume and concentration, into moles, to understand how much of a particular substance is present in the solution. In the outlined problem, the volume and molarity of EDTA were used to calculate the moles of the substance added.
In this case:
  • The concentration (molarity) given as 0.00119 M indicates moles of solute per liter of solution.
  • By converting the EDTA volume from milliliters to liters (by dividing by 1000), we ensure consistency in the units.
  • Multiplying the volume in liters by the molarity gives the total moles of EDTA used in the titration.
Understanding this concept is essential for translating the raw titrimetric data into meaningful chemical quantities.
Titration Chemistry
Titration chemistry involves the controlled addition of a solution of known concentration to react with a solution of unknown concentration until the reaction reaches completion, indicated by an endpoint. This method is essential in determining quantities in a solution with a high degree of accuracy.
  • In the practice of complexometric titration, EDTA is used to determine the concentration of metal ions, taking advantage of its binding properties.
  • The endpoint of the titration, often indicated by a color change with an appropriate indicator, signals complete reaction between the titrant and the analyte.
  • Understanding the stoichiometry, such as the 1:1 binding ratio of calcium ions to EDTA, is crucial for accurate calculation of ion concentrations.
This method is widely used in various fields, including medicine and environmental science, due to its precision and dependability.

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Most popular questions from this chapter

The concentration of \(o\) -phthalic acid in an organic solvent, such as \(n\) butanol, is determined by an acid-base titration using aqueous \(\mathrm{NaOH}\) as the titrant. As the titrant is added, the \(o\) -phthalic acid extracts into the aqueous solution where it reacts with the titrant. The titrant is added slowly to allow sufficient time for the extraction to take place. (a) What type of error do you expect if the titration is carried out too quickly? (b) Propose an alternative acid-base titrimetric method that allows for a more rapid determination of the concentration of \(o\) -phthalic acid in \(n\) -butanol.

Before the introduction of EDTA most complexation titrations used \(\mathrm{Ag}^{+}\) or \(\mathrm{CN}^{-}\) as the titrant. The analysis for \(\mathrm{Cd}^{2+},\) for example, was accomplished indirectly by adding an excess of \(\mathrm{KCN}\) to form \(\mathrm{Cd}(\mathrm{CN})_{4}^{2-}\), and back titrating the excess \(\mathrm{CN}^{-}\) with \(\mathrm{Ag}^{+},\) forming \(\mathrm{Ag}(\mathrm{CN})_{2}^{-} .\) In one such analysis a \(0.3000-\mathrm{g}\) sample of an ore is dissolved and treated with \(20.00 \mathrm{~mL}\) of \(0.5000 \mathrm{M} \mathrm{KCN}\). The excess \(\mathrm{CN}^{-}\) requires \(13.98 \mathrm{~mL}\) of \(0.1518 \mathrm{M} \mathrm{AgNO}_{3}\) to reach the end point. Determine the \(\% \mathrm{w} / \mathrm{w}\) Cd in the ore.

A \(0.5131-\mathrm{g}\) sample that contains \(\mathrm{KBr}\) is dissolved in \(50 \mathrm{~mL}\) of distilled water. Titrating with \(0.04614 \mathrm{M} \mathrm{AgNO}_{3}\) requires \(25.13 \mathrm{~mL}\) to reach the Mohr end point. A blank titration requires \(0.65 \mathrm{~mL}\) to reach the same end point. Report the \(\% \mathrm{w} / \mathrm{w} \mathrm{KBr}\) in the sample.

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.

Using a ladder diagram, explain why the presence of dissolved \(\mathrm{CO}_{2}\) leads to a determinate error for the standardization of \(\mathrm{NaOH}\) if the end point's \(\mathrm{pH}\) is between \(6-10\), but no determinate error if the end point's \(\mathrm{pH}\) is less than 6.
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