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Chapter 4: Problem 73

Limonite, an ore of iron, is brought into solution in acidic medium and titrated with \(\mathrm{KMnO}_{4}\). The unbalanced equation for the reaction is $$ \mathrm{MnO}_{4}^{-}(a q)+\mathrm{Fe}^{2+}(a q) \longrightarrow \mathrm{Fe}^{3+}(a q)+\mathrm{Mn}^{2+}(a q) $$ It is found that a \(1.000-\mathrm{g}\) sample of the ore requires \(75.52 \mathrm{~mL}\) of \(0.0205 \mathrm{M}\) \(\mathrm{KMnO}_{4}\). What is the percent of Fe in the sample?

Short Answer

Expert verified
Answer: The percent of Fe in the limonite sample is 69.22%.

Step by step solution

01

Balance the chemical equation

To balance the chemical equation, we need 8 moles of H2O on the right side and 5 moles of H+ ions on the left side. The balanced equation becomes: $$ 5 \mathrm{H}_{2}\mathrm{O}(l)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{Fe}^{2+}(a q) \longrightarrow 5 \mathrm{H}^{+}(a q)+8 \mathrm{Fe}^{3+}(a q)+\mathrm{Mn}^{2+}(a q) $$
02

Calculate moles of KMnO4 used

To calculate the moles of KMnO4 used in the titration, we start with the given volume and concentration: Moles of KMnO4 = \(\text{volume (L)} \times \text{concentration (M)}\) Moles of KMnO4 = \((75.52\times10^{-3})\, \text{L} \times 0.0205\,\text{M} = 1.5486 \times10^{-3}\,\text{moles}\)
03

Calculate moles of Fe in the sample

Using the balanced equation and stoichiometry, we can find the moles of Fe in the sample: $$ \frac{1.5486\times10^{-3}\,\text{moles KMnO}_4}{1} \times \frac{8\,\text{moles Fe}^2+}{1\,\text{mole KMnO}_4} = 1.239\times10^{-2}\,\text{moles Fe}^2+ $$
04

Calculate the mass and percent of Fe in the sample

Now that we have the moles of Fe, we can convert it to mass using the molar mass of Fe: Mass of Fe = moles of Fe 脳 molar mass of Fe Mass of Fe = \(1.239\times10^{-2}\,\text{moles} \times 55.85\, \frac{\text{g}}{\text{mole}} = 0.6922\,\text{g}\) Now, we can find the percent of Fe in the sample: Percent of Fe = \(\frac{\text{Mass of Fe}}{\text{Mass of limonite sample}}\times100\) Percent of Fe = \(\frac{0.6922\,\text{g}}{1.000\,\text{g}}\times100 = 69.22\%\) Therefore, the percent of Fe in the limonite sample is 69.22%.

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Key Concepts

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

Stoichiometry in Chemistry
Stoichiometry is a section of chemistry that involves using relationships from the balanced chemical equations to calculate the quantities of reactants and products. It's like a recipe for chemistry where you need to know the precise amounts of ingredients you need and how much you'll end up with.

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Most popular questions from this chapter

What is the volume of \(1.222 \mathrm{M}\) sodium hydroxide required to react with (a) \(32.5 \mathrm{~mL}\) of \(0.569 \mathrm{M}\) sulfurous acid? (One mole of sulfurous acid reacts with two moles of hydroxide ion.) (b) \(5.00 \mathrm{~g}\) of oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) ? (One mole of oxalic acid reacts with two moles of hydroxide ion.) (c) \(15.0 \mathrm{~g}\) of concentrated acetic acid \(\left(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\right)\) that is \(88 \%\) by mass pure?

Write net ionic equations for the formation of (a) a precipitate when solutions of magnesium nitrate and potassium hydroxide are mixed. (b) two different precipitates when solutions of silver(I) sulfate and barium chloride are mixed.

A solution of potassium permanganate reacts with oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) to form carbon dioxide and solid manganese(IV) oxide \(\left(\mathrm{MnO}_{2}\right)\). (a) Write a balanced net ionic equation for the reaction. (b) If \(20.0 \mathrm{~mL}\) of \(0.300 M\) potassium permanganate is required to react with \(13.7 \mathrm{~mL}\) of oxalic acid, what is the molarity of the oxalic acid? (c) What is the mass of manganese(IV) oxide formed?

Calcium in blood or urine can be determined by precipitation as call cium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4}\). The precipitate is dissolved in strong acid and titrated with potassium permanganate. The products of the reaction are carbon dioxide and manganese(II) ion. A 24-hour urine sample is collected from an adult patient, reduced to a small volume, and titrated with \(26.2 \mathrm{~mL}\) of \(0.0946 \mathrm{M} \mathrm{KMnO}_{4}\). How many grams of calcium oxalate are in the sample? Normal range for \(\mathrm{Ca}^{2+}\) output for an adult is 100 to \(300 \mathrm{mg}\) per 24 hour. Is the sample within the normal range?

When solutions of aluminum sulfate and sodium hydroxide are mixed, a white gelatinous precipitate forms. (a) Write a balanced net ionic equation for the reaction. (b) What is the mass of the precipitate when \(2.76 \mathrm{~g}\) of aluminum sulfate in \(125 \mathrm{~mL}\) of solution is combined with \(85.0 \mathrm{~mL}\) of \(0.2500 \mathrm{M} \mathrm{NaOH}\) ? (c) What is the molarity of the ion in excess? (Ignore spectator ions and assume that volumes are additive.)
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