/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 51 The amount of uranium in an ore ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 51

The amount of uranium in an ore is determined by an indirect redox titration. The analysis is accomplished by dissolving the ore in sulfuric acid and reducing \(\mathrm{UO}_{2}^{2+}\) to \(\mathrm{U}^{4+}\) with a Walden reductor. The solution is treated with an excess of \(\mathrm{Fe}^{3+}\), forming \(\mathrm{Fe}^{2+}\) and \(\mathrm{U}^{6+}\). The \(\mathrm{Fe}^{2+}\) is titrated with a standard solution of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} .\) In a typical analysis a 0.315 -g sample of ore is passed through the Walden reductor and treated with \(50.00 \mathrm{~mL}\) of \(0.0125 \mathrm{M} \mathrm{Fe}^{3+}\). Back titrating with 0.00987 \(\mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) requires \(10.52 \mathrm{~mL}\). What is the \(\% \mathrm{w} / \mathrm{w} \mathrm{U}\) in the sample?

Short Answer

Expert verified
The %w/w of uranium in the sample is 0.2082%.

Step by step solution

01

Calculate Moles of Fe3+ Added

Using the concentration and volume of the \(\mathrm{Fe}^{3+}\) solution, calculate the moles of \(\mathrm{Fe}^{3+}\) added. Use the formula \(\text{moles} = \text{concentration} \times \text{volume}\). Thus, \[0.0125 \text{ M} \times 0.05000 \text{ L} = 6.25 \times 10^{-4} \text{ moles Fe}^{3+}.\]
02

Calculate Moles of K2Cr2O7 Used

Using the concentration and volume of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\) used in the back titration, calculate the moles of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\). Use the formula \(\text{moles} = \text{concentration} \times \text{volume}\). Thus, \[0.00987 \text{ M} \times 0.01052 \text{ L} = 1.037074 \times 10^{-4} \text{ moles K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}.\]
03

Calculate Moles of Fe2+ Oxidized

Since the reaction ratio of \(\mathrm{Fe}^{2+}\) to \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) is 6:1, calculate the moles of \(\mathrm{Fe}^{2+}\) oxidized using the moles of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\). Thus, \[1.037074 \times 10^{-4} \text{ moles K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7} \times 6 = 6.22244 \times 10^{-4} \text{ moles Fe}^{2+}.\]
04

Calculate Initial Moles of Fe2+ Before Titration

Since all \(\mathrm{U}^{4+}\) converts \(\mathrm{Fe}^{3+}\) to \(\mathrm{Fe}^{2+}\), calculate the initial moles of \(\mathrm{Fe}^{2+}\) before titration. These were equal to the moles of \(\mathrm{Fe}^{3+}\) added, or \(6.25 \times 10^{-4} \text{ moles}.\)
05

Calculate Moles of U4+

The difference in moles of \(\mathrm{Fe}^{3+}\) added and \(\mathrm{Fe}^{2+}\) titrated indicates the moles of \(\mathrm{Fe}^{2+}\) reacted with \(\mathrm{U}^{4+}\). Calculate these moles: \[6.25 \times 10^{-4} - 6.22244 \times 10^{-4} = 2.756 \times 10^{-6} \text{ moles U}^{4+}.\]
06

Convert Moles of U4+ to Mass of Uranium

Use the molar mass of uranium \(238.03 \text{ g/mol}\) to convert moles to grams. Thus, \[2.756 \times 10^{-6} \text{ moles} \times 238.03 \text{ g/mol} = 0.00065638 \text{ g U}.\]
07

Calculate %w/w Uranium in the Ore

Calculate the mass percent of uranium in the ore by dividing the mass of uranium by the total mass of the ore and multiplying by 100. Thus, \[\left( \frac{0.00065638}{0.315} \right) \times 100 \% = 0.2082\% \,w/w \, \mathrm{U}.\]

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 91影视!

Key Concepts

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

Redox Titration
Redox titration is a technique used to determine the concentration of an unknown solution. This method involves a reduction-oxidation reaction, where one component is oxidized, and the other is reduced. In the context of Analytical Chemistry, this process is used to analyze metals like uranium, as presented in the original exercise. Redox titration helps understand the amounts of reactants involved and the completion of the chemical reaction.

In the given exercise, a uranium ore is dissolved and treated with an excess of \( ext{Fe}^{3+} \), which is reduced to \( ext{Fe}^{2+} \). The \( ext{Fe}^{2+} \) ions are then titrated with a standard solution of \( ext{K}_2 ext{Cr}_2 ext{O}_7 \). This forms the basis of the redox titration, by measuring how much \( ext{K}_2 ext{Cr}_2 ext{O}_7 \) is needed to oxidize the \( ext{Fe}^{2+} \), we can understand how much uranium was present originally. For a successful titration, it is crucial that the endpoints are clearly visible, often indicated by a color change in the solution being titrated.
Moles Calculation
Understanding how to calculate moles is fundamental in chemistry, especially when dealing with titrations and molar solutions. Moles provide a measurement to count atoms, molecules, or ions in a given sample based on Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) entities per mole.
To compute the number of moles, use the formula:
  • \( ext{moles} = ext{concentration} \times ext{volume} \).

For accurate calculations, ensure that the volume is in liters. In the example given, the concentration and volume of \( ext{Fe}^{3+} \) and \( ext{K}_2 ext{Cr}_2 ext{O}_7 \) are used to find their respective moles. Through this calculation, one can determine how much of each substance participates in the chemical reaction. Accurately calculating moles helps predict yields, evaluate reaction extents, and for balancing chemical equations.
Mass Percent Composition
Mass percent composition allows chemists to describe how much of a particular element is present in a compound relative to its total mass. In practical applications, it helps identify the richness of elements in ores, solutions, and mixtures.
In our exercise scenario, after finding the mass of uranium, the mass percent composition is calculated by dividing the mass of an element (in this case, uranium) by the total mass of the sample, then multiplying by 100 to present it as a percentage.
  • Formula: \[ \text{mass percent} = \left( \frac{\text{mass of element}}{\text{total mass of sample}} \right) \times 100 \% \]
By applying this concept, the exercise determines the percentage of uranium in the ore sample, finding it to be 0.2082% w/w U. This percentage provides important data in mining and material sciences, helping optimize the extraction process and evaluate the quality of mineral deposits.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The amount of \(\mathrm{Cr}^{3+}\) in an inorganic salt is determined by a redox titration. A portion of sample that contains approximately \(0.25 \mathrm{~g}\) of \(\mathrm{Cr}^{3+}\) is accurately weighed and dissolved in \(50 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{O} .\) The \(\mathrm{Cr}^{3+}\) is oxidized to \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) by adding \(20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{AgNO}_{3}\), which serves as a catalyst, and \(50 \mathrm{~mL}\) of \(10 \% \mathrm{w} / \mathrm{v}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{~S}_{2} \mathrm{O}_{8}\), which serves as the oxidizing agent. After the reaction is complete, the resulting solution is boiled for 20 minutes to destroy the excess \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-},\) cooled to room temperature, and diluted to \(250 \mathrm{~mL}\) in a volumetric flask. A \(50-m L\) portion of the resulting solution is transferred to an Erlenmeyer flask, treated with \(50 \mathrm{~mL}\) of a standard solution of \(\mathrm{Fe}^{2+}\), and acidified with \(200 \mathrm{~mL}\) of \(1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\), reducing the \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) to \(\mathrm{Cr}^{3+}\). The excess \(\mathrm{Fe}^{2+}\) is then determined by a back titration with a standard solution of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) using an appropriate indicator. The results are reported as \(\% \mathrm{w} / \mathrm{w} \mathrm{Cr}^{3+}\). (a) There are several places in the procedure where a reagent's volume is specified (see italicized text). Which of these measurements must be made using a volumetric pipet. (b) Excess peroxydisulfate, \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\) is destroyed by boiling the solution. What is the effect on the reported \(\% \mathrm{w} / \mathrm{w} \mathrm{Cr}^{3+}\) if some of the \(\mathrm{S}_{2} \mathrm{O}_{8}^{2-}\) is not destroyed during this step? (c) Solutions of \(\mathrm{Fe}^{2+}\) undergo slow air oxidation to \(\mathrm{Fe}^{3+}\). What is the effect on the reported \(\% \mathrm{w} / \mathrm{w} \mathrm{Cr}^{3+}\) if the standard solution of \(\mathrm{Fe}^{2+}\) is inadvertently allowed to be partially oxidized?

The amount of iron in a meteorite is determined by a redox titration using \(\mathrm{KMnO}_{4}\) as the titrant. A \(0.4185-\mathrm{g}\) sample is dissolved in acid and the liberated \(\mathrm{Fe}^{3+}\) quantitatively reduced to \(\mathrm{Fe}^{2+}\) using a Walden reductor. Titrating with \(0.02500 \mathrm{M} \mathrm{KMnO}_{4}\) requires \(41.27 \mathrm{~mL}\) to reach the end point. Determine the \(\% \mathrm{w} / \mathrm{w} \mathrm{Fe}_{2} \mathrm{O}_{3}\) in the sample of meteorite.

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.

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.

The following data for the titration of a monoprotic weak acid with a strong base were collected using an automatic titrator. Prepare normal, first derivative, second derivative, and Gran plot titration curves for this data, and locate the equivalence point for each. $$ \begin{array}{cccc} \text { Volume of } \mathrm{NaOH}(\mathrm{ml}) & \mathrm{pH} & \text { Volume of } \mathrm{NaOH}(\mathrm{mL}) & \mathrm{pH} \\ \hline 0.25 & 3.0 & 49.95 & 7.8 \\ 0.86 & 3.2 & 49.97 & 8.0 \\ 1.63 & 3.4 & 49.98 & 8.2 \\ 2.72 & 3.6 & 49.99 & 8.4 \\ 4.29 & 3.8 & 50.00 & 8.7 \\ 6.54 & 4.0 & 50.01 & 9.1 \\ 9.67 & 4.2 & 50.02 & 9.4 \\ 13.79 & 4.4 & 50.04 & 9.6 \\ 18.83 & 4.6 & 50.06 & 9.8 \\ 24.47 & 4.8 & 50.10 & 10.0 \\ 30.15 & 5.0 & 50.16 & 10.2 \\ 35.33 & 5.2 & 50.25 & 10.4 \\ 39.62 & 5.4 & 50.40 & 10.6 \\ 42.91 & 5.6 & 50.63 & 10.8 \\ 45.28 & 5.8 & 51.01 & 11.0 \\ 46.91 & 6.0 & 51.61 & 11.2 \\ 48.01 & 6.2 & 52.58 & 11.4 \\ 48.72 & 6.4 & 54.15 & 11.6 \\ 49.19 & 6.6 & 56.73 & 11.8 \\ 49.48 & 6.8 & 61.11 & 12.0 \\ 49.67 & 7.0 & 68.83 & 12.2 \\ 49.79 & 7.2 & 83.54 & 12.4 \\ 49.87 & 7.4 & 116.14 & 12.6 \\ 49.92 & 7.6 & & \end{array} $$
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation

Chemistry Branches

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.