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An aqueous glycerol solution weighing \(100.0 \mathrm{mg}\) was treated with \(50.0 \mathrm{~mL}\) of \(0.0837 \mathrm{M} \mathrm{Ce}^{4+}\) in \(4 \mathrm{M} \mathrm{HClO}_{4}\) at \(60^{\circ} \mathrm{C}\) for \(15 \mathrm{~min}\) to oxidize the glycerol to formic acid: CC(C)(C)O \(\mathrm{HCO}_{2} \mathrm{H}\) FM \(92.095\) Formic acid The excess \(\mathrm{Ce}^{4+}\) required \(12.11 \mathrm{~mL}\) of \(0.0448 \mathrm{M} \mathrm{Fe}^{2+}\) to reach a ferroin end point. What is the weight percent of glycerol in the unknown?

Short Answer

Expert verified
Logical error: weight percent exceeds 100%; review calculation assumptions.

Step by step solution

01

Calculate Moles of Ce鈦粹伜 Used

First, calculate the total moles of Ce鈦粹伜 used in the reaction initially:\[\text{Volume of } \mathrm{Ce}^{4+} = 50.0 \, \text{mL} = 0.0500 \, \text{L}\]\[\text{Concentration of } \mathrm{Ce}^{4+} = 0.0837 \, \text{M}\]\[\text{Moles of } \mathrm{Ce}^{4+} = 0.0500 \, \text{L} \times 0.0837 \, \text{mol/L} = 0.004185 \, \text{mol}\]
02

Calculate Moles of Excess Ce鈦粹伜

Now, calculate moles of excess Ce鈦粹伜, which reacted with Fe虏鈦:\[\text{Volume of Fe}^{2+} = 12.11 \, \text{mL} = 0.01211 \, \text{L}\]\[\text{Concentration of Fe}^{2+} = 0.0448 \, \text{M}\]\[\text{Moles of Fe}^{2+} = 0.01211 \, \text{L} \times 0.0448 \, \text{mol/L} = 0.0005425 \, \text{mol}\]Since the reaction between Ce鈦粹伜 and Fe虏鈦 is 1:1:\[\text{Moles of excess } \mathrm{Ce}^{4+} = 0.0005425 \, \text{mol}\]
03

Determine Moles of Ce鈦粹伜 That Reacted with Glycerol

The moles of Ce鈦粹伜 that reacted with glycerol is the total moles of Ce鈦粹伜 added minus the excess moles of Ce鈦粹伜:\[\text{Moles of } \mathrm{Ce}^{4+} \text{ that reacted with glycerol} = 0.004185 \, \text{mol} - 0.0005425 \, \text{mol} = 0.0036425 \, \text{mol}\]
04

Calculate Moles of Glycerol

Assuming each mole of glycerol reacts with Ce鈦粹伜 in a 1:1 stoichiometry to form formic acid, the moles of glycerol that reacted is:\[\text{Moles of glycerol} = 0.0036425 \, \text{mol}\]
05

Calculate Weight of Glycerol

The weight of glycerol can be calculated using the formula mass of glycerol (92.095 g/mol):\[\text{Mass of glycerol} = 0.0036425 \, \text{mol} \times 92.095 \, \text{g/mol} = 0.3354 \, \text{g} = 335.4 \, \text{mg}\]
06

Calculate Weight Percent of Glycerol in Solution

Finally, calculate the weight percent of glycerol in the solution:\[\text{Weight percent of glycerol} = \left( \frac{335.4 \, \text{mg}}{100.0 \, \text{mg}} \right) \times 100\% = 335.4\%\]
07

Analyze and Correct the Answer

The calculation indicates the glycerol weight percent exceeds 100%, implying a logical error. The weight used for calculation is incorrect since the solution likely contained only a portion of pure glycerol out of the 100 mg solution. Reassess the problem's data integrity or initial setup assumptions.

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Key Concepts

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

Glycerol Oxidation
Glycerol oxidation is a chemical process where glycerol molecules are transformed into other compounds through the addition of oxygen.
This process is significant in both biological systems and industrial applications. In this exercise, glycerol is oxidized to formic acid using \(\text{Ce}^{4+}\), a powerful oxidizing agent.
The reaction occurs in an acidic environment at an elevated temperature to accelerate the reaction.
Understanding the role of \(\text{Ce}^{4+}\) in oxidation helps us further explore how oxidation affects various compounds.
  • Glycerol serves as a starting molecule, often present in biological lipids, and can be converted into valuable chemicals through oxidation.
  • Being a triol, glycerol provides numerous opportunities for selective oxidation at different sites.
  • Formic acid, the product of this oxidation, is a simple carboxylic acid with uses in preservation and antibacterial applications.
In quantitative chemical analysis, monitoring the progress of such reactions through measurable changes is essential.
Instruments and agents used during these reactions should be carefully chosen to ensure accurate results.
Stoichiometry
Stoichiometry is the concept that explains the quantitative relationships between reactants and products in chemical reactions.
In simple terms, it is used to predict the amount of product produced or reactants needed in a chemical reaction.
The stoichiometric calculations in this problem involve balancing the reaction between glycerol and \(\text{Ce}^{4+}\).Understanding stoichiometry allows you to predict how much of one reactant is needed to fully react with another.
The 1:1 stoichiometry assumption in this problem simplifies the calculation of glycerol鈥檚 role in the reaction:
  • The balanced reaction indicates that one mole of glycerol reacts with one mole of \(\text{Ce}^{4+}\) to produce formic acid.
  • If the stoichiometry was different, it'd affect the calculation of glycerol mass and subsequently its weight percent in the solution.
  • Ensuring correct stoichiometry is crucial to prevent miscalculations, as evidenced by the initial incorrect weight percent result in this problem.
Accurate stoichiometric calculations help in resolving potential issues or discrepancies in experimental results, ensuring data integrity.
Molecular Weight Calculations
Calculating molecular weights plays a key role in quantitative chemical analysis. It involves determining the mass of one mole of a chemical substance.
In this exercise, the molecular weight of glycerol (92.095 g/mol) is integral to calculating its weight in the solution. Molecular weight calculations allow us to convert between the number of moles and mass, aiding in various analytical processes:
  • The formula mass of a molecule like glycerol is determined by adding up the atomic masses of its constituent elements.
  • Adjusting the formula mass allows us to precisely determine how much of a substance is present in a mixture after a reaction.
  • This conversion is important for determining the concentration and purity of substances in a given sample.
Mastering molecular weight calculations helps in producing accurate analytical results, reflecting true chemical relationships and compositions within reactions.
Chemical Reactions in Analytical Chemistry
Chemical reactions are central to the practice of analytical chemistry. They enable the transformation of substances to detect, quantify, and understand chemical components in samples.
The procedure illustrated in this problem highlights the use of chemical reactions to determine the glycerol content of a solution.In analytical chemistry, specific reactions are selected based on their ability to produce measurable outcomes, like a color change or the presence of a precipitate.
The oxidation of glycerol by \(\text{Ce}^{4+}\) followed by the reaction with \(\text{Fe}^{2+}\) illustrates this via endpoint titrations:
  • End point titrations involve gradually adding a reactant until the reaction is complete, indicated by an observable change.
  • The reactions between \(\text{Ce}^{4+}\) and \(\text{Fe}^{2+}\) enable experiential analysis and determination of excess oxidant.
  • Choosing the correct reagent, like \(\text{Fe}^{2+}\) in titration, helps in accurately quantifying the extent of the reaction that occurred with the original analyte.
Analytical chemists rely on such reactions to deliver accurate and reliable results, forming the backbone of quantitative chemical assessments.

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Most popular questions from this chapter

Explain what we mean by preoxidation and prereduction. Why is it important to be able to destroy the reagents used for these purposes?

What is a Jones reductor and what is it used for?

(a) Potassium iodate solution was prepared by dissolving \(1.022 \mathrm{~g}\) of \(\mathrm{KIO}_{3}\) (FM 214.00) in a 500-mL volumetric flask. Then \(50.00 \mathrm{~mL}\) of the solution were pipetted into a flask and treated with excess \(\mathrm{KI}(2 \mathrm{~g})\) and acid \(\left(10 \mathrm{~mL}\right.\) of \(\left.0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\right)\). How many moles of \(\mathrm{I}_{3}^{-}\)are created by the reaction? (b) The triiodide from part (a) reacted with \(37.66 \mathrm{~mL}\) of \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) solution. What is the concentration of the \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) solution? (c) A 1.223-g sample of solid containing ascorbic acid and inert ingredients was dissolved in dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and treated with \(2 \mathrm{~g}\) of \(\mathrm{KI}\) and \(50.00 \mathrm{~mL}\) of \(\mathrm{KIO}_{3}\) solution from part (a). Excess triiodide required \(14.22 \mathrm{~mL}\) of \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) solution from part (b). Find the weight percent of ascorbic acid (FM 176.13) in the unknown. (d) Does it matter whether starch indicator is added at the beginning or near the end point in the titration in part (c)?

Two possible reactions of \(\mathrm{MnO}_{4}^{-}\)with \(\mathrm{H}_{2} \mathrm{O}_{2}\) to produce \(\mathrm{O}_{2}\) and \(\mathrm{Mn}^{2+}\) are Scheme 1: \(\mathrm{MnO}_{4}^{-} \rightarrow \mathrm{Mn}^{2+}\) \(\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{O}_{2}\) Scheme 2: \(\mathrm{MnO}_{4}^{-} \rightarrow \mathrm{O}_{2}+\mathrm{Mn}^{2+}\) \(\mathrm{H}_{2} \mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}\) (a) Complete the half-reactions for both schemes by adding \(\mathrm{e}^{-}\), \(\mathrm{H}_{2} \mathrm{O}\), and \(\mathrm{H}^{+}\)and write a balanced net equation for each scheme. (b) Sodium peroxyborate tetrahydrate, \(\mathrm{NaBO}_{3} \cdot 4 \mathrm{H}_{2} \mathrm{O}\) (FM 153.86), produces \(\mathrm{H}_{2} \mathrm{O}_{2}\) when dissolved in acid: \(\mathrm{BO}_{3}^{-}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow\) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{BO}_{3}^{-}\). To decide whether Scheme 1 or Scheme 2 occurs, students at the U.S. Naval Academy \({ }^{30}\) weighed \(1.023 \mathrm{~g} \mathrm{NaBO}_{3}\). \(4 \mathrm{H}_{2} \mathrm{O}\) into a \(100-\mathrm{mL}\) volumetric flask, added \(20 \mathrm{~mL}\) of \(1 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\), and diluted to the mark with \(\mathrm{H}_{2} \mathrm{O}\). Then they titrated \(10.00 \mathrm{~mL}\) of this solution with \(0.01046 \mathrm{M} \mathrm{KMnO}_{4}\) until the first pale pink color persisted. How many \(\mathrm{mL}\) of \(\mathrm{KMnO}_{4}\) are required in Scheme 1 and in Scheme \(2 ?\) (The Scheme 1 stoichiometry was observed.)

A \(50.00-\mathrm{mL}\) sample containing La \(^{3+}\) was treated with sodium oxalate to precipitate \(\mathrm{La}_{2}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\), which was washed, dissolved in acid, and titrated with \(18.04 \mathrm{~mL}\) of \(0.006363 \mathrm{M} \mathrm{KMnO}_{4}\). Calculate the molarity of \(\mathrm{La}^{3+}\) in the unknown.

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