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Chapter 8: Problem 19

The amount of iron and manganese in an alloy is determined by precipitating the metals with 8 -hydroxyquinoline, \(\mathrm{C}_{9} \mathrm{H}_{7} \mathrm{NO}\). After weighing the mixed precipitate, the precipitate is dissolved and the amount of 8-hydroxyquinoline determined by another method. In a typical analysis a 127.3 -mg sample of an alloy containing iron, manganese, and other metals is dissolved in acid and treated with appropriate masking agents to prevent an interference from other metals. The iron and manganese are precipitated and isolated as \(\mathrm{Fe}\left(\mathrm{C}_{9} \mathrm{H}_{6} \mathrm{NO}\right)_{3}\) and \(\mathrm{Mn}\left(\mathrm{C}_{9} \mathrm{H}_{6} \mathrm{NO}\right)_{2},\) yielding a total mass of \(867.8 \mathrm{mg}\). The amount of 8 -hydroxyquinolate in the mixed precipitate is determined to be \(5.276 \mathrm{mmol}\). Calculate the \(\% \mathrm{w} / \mathrm{w} \mathrm{Fe}\) and \(\% \mathrm{w} / \mathrm{w} \mathrm{Mn}\) in the alloy.

Short Answer

Expert verified
Calculate molar masses, use mole ratios, set up and solve the equations to find Fe and Mn percentages.

Step by step solution

01

Understanding the Chemical Formulas

Identify the chemical formulas involved. We have two precipitates: \( \mathrm{Fe}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{3} \) and \( \mathrm{Mn}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{2} \). Each precipitate contains 8-hydroxyquinoline, and we need to find their molar masses to use in calculations.
02

Molar Mass Calculation

Calculate the molar mass of 8-hydroxyquinoline \( \mathrm{C}_{9}\mathrm{H}_{7}\mathrm{NO} \) as 145.16 g/mol. Now, calculate the molar mass of \( \mathrm{Fe}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{3} \), adding iron鈥檚 molar mass (55.85 g/mol) to three times that of 8-hydroxyquinoline minus three hydrogens. Similarly, calculate for \( \mathrm{Mn}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{2} \).
03

Mole Ratio from Total Precipitate

Determine the mol ratio from the mass of 8-hydroxyquinoline in the total precipitation. The total moles of 8-hydroxyquinoline are given as 5.276 mmol, distributed among the precipitates.
04

Set Up Equations for Masses

Set up the equations for the mass balance based on the moles of the ligands: \( 3x + 2y = 5.276 \) (where \( x \) and \( y \) are moles of \( \mathrm{Fe}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{3} \) and \( \mathrm{Mn}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{2} \) respectively), and \( M_{Fe} x + M_{Mn} y = 867.8 \, \text{mg} \).
05

Solving the System of Equations

Solve the system of equations to find the values of \( x \) and \( y \). Substitute the known values into these equations and solve for the mole numbers of each metal complex.
06

Calculate Mass of Fe and Mn

Using the molar amounts from the solutions, convert the moles into grams using their respective molar masses. This step gives us the mass of iron and manganese in the precipitate.
07

Determine Percentage Composition

Calculate the percentage weight by dividing the mass of each metal by the initial 127.3 mg sample mass, then multiply by 100 to obtain the percentage composition. Thus, calculate \( \% \mathrm{w} / \mathrm{w} \mathrm{Fe} \) and \( \% \mathrm{w} / \mathrm{w} \mathrm{Mn} \).

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Key Concepts

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

Precipitation Method
The precipitation method is a pivotal technique in analytical chemistry used to separate and identify components in a mixture. This approach involves converting a substance into an insoluble solid, called a precipitate, by reacting it with a precipitating agent. In the context of the given exercise, iron and manganese are isolated from a metal alloy using 8-hydroxyquinoline as a precipitating agent. This compound reacts with the metals to form specific precipitates - \( \mathrm{Fe}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{3} \) and \( \mathrm{Mn}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{2} \). Key steps in this method:
  • Addition of a precise quantity of 8-hydroxyquinoline to the dissolved metal sample.
  • Formation and isolation of solid precipitates by the metals bonding with the reagent.
  • Separation of these precipitates from the solution for further analysis.
The success of this technique hinges on correct chemical conditions, such as pH and temperature, to ensure complete precipitation of the target metals.
Molar Mass Calculation
Molar mass calculation is crucial for translating the chemical formula of a compound into a practical value used in quantitative analysis. Determining the molar mass lets chemists convert moles into grams, a necessary step in analyzing compound compositions.Let's consider the compound 8-hydroxyquinoline, with its chemical formula \( \mathrm{C}_{9}\mathrm{H}_{7}\mathrm{NO} \). The molar mass is calculated by summing the atomic masses of all atoms in the formula:
  • Carbon: \( 9 \times 12.01 \text{ g/mol} \)
  • Hydrogen: \( 7 \times 1.008 \text{ g/mol} \)
  • Nitrogen: \( 1 \times 14.01 \text{ g/mol} \)
  • Oxygen: \( 1 \times 16.00 \text{ g/mol} \)
The total comes out to 145.16 g/mol.For the compounds \( \mathrm{Fe}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{3} \) and \( \mathrm{Mn}\left(\mathrm{C}_{9}\mathrm{H}_{6}\mathrm{NO}\right)_{2} \), similar calculations incorporate the metal's molar mass:
  • Add the metal molar mass to three or two times the hydroxyquinoline molar mass (minus hydrogens).
  • For example, for iron, add 55.85 g/mol to three times the 8-hydroxyquinoline mass.
This makes further mass calculations possible and allows determination of metal content after isolation.
Percentage Composition
Percentage composition helps determine the proportion of each component in a mixture, providing specific insights into the contents of a sample. This is especially useful when assessing the purity or formulation of chemical products.To calculate the percentage composition, follow these steps:
  • Determine the exact mass of the metal in the precipitate using molar mass and mole conversions from the chemical reactions.
  • The mass is then compared to the original sample mass (127.3 mg in the exercise).
  • This ratio is multiplied by 100 to convert it to a percentage.
In this exercise, after obtaining the masses of iron and manganese, their individual percentage weights in the alloy can be calculated. For instance, if the mass of iron obtained is 50 mg, its percentage composition is \( \frac{50}{127.3} \times 100 \), resulting in the percentage weight of iron in the alloy.By calculating these percentages, you learn the concentration of each metal in the sample, tying back to the overall composition and quality of the alloy.

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Most popular questions from this chapter

A \(516.7-\mathrm{mg}\) sample that contains a mixture of \(\mathrm{K}_{2} \mathrm{SO}_{4}\) and \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) is dissolved in water and treated with \(\mathrm{BaCl}_{2},\) precipitating the \(\mathrm{SO}_{4}^{2-}\) as \(\mathrm{BaSO}_{4}\). The resulting precipitate is isolated by filtration, rinsed free of impurities, and dried to a constant weight, yielding \(863.5 \mathrm{mg}\) of \(\mathrm{BaSO}_{4} .\) What is the \(\% \mathrm{w} / \mathrm{w} \mathrm{K}_{2} \mathrm{SO}_{4}\) in the sample?

In the presence of water vapor the surface of zirconia, \(\mathrm{ZrO}_{2}\), chemically adsorbs \(\mathrm{H}_{2} \mathrm{O},\) forming surface hydroxyls, \(\mathrm{ZrOH}\) (additional water is physically adsorbed as \(\mathrm{H}_{2} \mathrm{O}\) ). When heated above \(200^{\circ} \mathrm{C}\), the surface hydroxyls convert to \(\mathrm{H}_{2} \mathrm{O}(g),\) releasing one molecule of water for every two surface hydroxyls. Below \(200^{\circ} \mathrm{C}\) only physically absorbed water is lost. Nawrocki, et al. used thermogravimetry to determine the density of surface hydroxyls on a sample of zirconia that was heated to \(700^{\circ} \mathrm{C}\) and cooled in a desiccator containing humid \(\mathrm{N}_{2}{ }^{15}\) Heating the sample from \(200^{\circ} \mathrm{C}\) to \(900^{\circ} \mathrm{C}\) released \(0.006 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) for every gram of dehy- droxylated \(\mathrm{ZrO}_{2}\). Given that the zirconia had a surface area of \(33 \mathrm{~m}^{2} / \mathrm{g}\) and that one molecule of \(\mathrm{H}_{2} \mathrm{O}\) forms two surface hydroxyls, calculate the density of surface hydroxyls in \(\mu \mathrm{mol} / \mathrm{m}^{2}\).

After preparing a sample of alum, \(\mathrm{K}_{2} \mathrm{SO}_{4} \cdot \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3} \cdot 24 \mathrm{H}_{2} \mathrm{O},\) an ana- lyst determines its purity by dissolving a \(1.2931-\mathrm{g}\) sample and precipitating the aluminum as \(\mathrm{Al}(\mathrm{OH})_{3}\). After filtering, rinsing, and igniting, \(0.1357 \mathrm{~g}\) of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) is obtained. What is the purity of the alum preparation?

Calcium is determined gravimetrically by precipitating \(\mathrm{CaC}_{2} \mathrm{O}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) and isolating \(\mathrm{CaCO}_{3}\). After dissolving a sample in \(10 \mathrm{~mL}\) of water and \(15 \mathrm{~mL}\) of \(6 \mathrm{M} \mathrm{HCl}\), the resulting solution is heated to boiling and a warm solution of excess ammonium oxalate is added. The solution is maintained at \(80^{\circ} \mathrm{C}\) and \(6 \mathrm{M} \mathrm{NH}_{3}\) is added dropwise, with stirring, until the solution is faintly alkaline. The resulting precipitate and solution are removed from the heat and allowed to stand for at least one hour. After testing the solution for completeness of precipitation, the sample is filtered, rinsed with \(0.1 \% \mathrm{w} / \mathrm{v}\) ammonium oxalate, and dried for one hour at \(100-120^{\circ} \mathrm{C}\). The precipitate is transferred to a muffle furnace where it is converted to \(\mathrm{CaCO}_{3}\) by drying at \(500 \pm 25^{\circ} \mathrm{C}\) until constant weight. (a) Why is the precipitate of \(\mathrm{CaC}_{2} \mathrm{O}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) converted to \(\mathrm{CaCO}_{3} ?\) (b) In the final step, if the sample is heated at too high of a temperature some \(\mathrm{CaCO}_{3}\) is converted to \(\mathrm{CaO}\). What effect would this have on the reported \(\% \mathrm{w} / \mathrm{w}\) Ca? (c) Why is the precipitant, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) added to a hot, acidic solution instead of a cold, alkaline solution?

A 1.4639 -g sample of limestone is analyzed for \(\mathrm{Fe}, \mathrm{Ca}\), and \(\mathrm{Mg}\). The iron is determined as \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) yielding \(0.0357 \mathrm{~g} .\) Calcium is isolated as \(\mathrm{CaSO}_{4},\) yielding a precipitate of \(1.4058 \mathrm{~g},\) and \(\mathrm{Mg}\) is isolated as \(0.0672 \mathrm{~g}\) of \(\mathrm{Mg}_{2} \mathrm{P}_{2} \mathrm{O}_{7} .\) Report the amount of Fe, \(\mathrm{Ca}\), and \(\mathrm{Mg}\) in the limestone sample as \(\% \mathrm{w} / \mathrm{w} \mathrm{Fe}_{2} \mathrm{O}_{3}, \% \mathrm{w} / \mathrm{w} \mathrm{CaO},\) and \(\% \mathrm{w} / \mathrm{w} \mathrm{MgO} .\)
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