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Chapter 15: Problem 13

Write balanced half-reactions in which \(\mathrm{MnO}_{4}^{-}\)acts as an oxidant at (a) \(\mathrm{pH}=0\); (b) \(\mathrm{pH}=10\); (c) \(\mathrm{pH}=15\).

Short Answer

Expert verified
Acidic: \( \mathrm{MnO}_4^- + 8\,\mathrm{H}^+ + 5\,\mathrm{e}^- \rightarrow \mathrm{Mn}^{2+} + 4\,\mathrm{H_2O} \); Basic: \( \mathrm{MnO}_4^- + 2\,\mathrm{H_2O} + 3\,\mathrm{e}^- \rightarrow \mathrm{MnO_2} + 4\,\mathrm{OH}^- \); Strong Basic: \( \mathrm{MnO}_4^- + \mathrm{e}^- \rightarrow \mathrm{MnO}_4^{2-} \).

Step by step solution

01

Understanding the Problem

We need to write balanced half-reactions for the permanganate ion \( \mathrm{MnO}_4^- \) acting as an oxidant under three different pH conditions: \( \mathrm{pH} = 0 \), \( \mathrm{pH} = 10 \), and \( \mathrm{pH} = 15 \). Oxidation involves losing electrons, and the permanganate ion will reduce in these reactions.
02

Half-Reaction at \( \mathrm{pH} = 0 \)

At \( \mathrm{pH} = 0 \), the reaction environment is highly acidic, meaning excess \( \mathrm{H}^+ \) ions are present. The permanganate ion is often reduced to \( \mathrm{Mn}^{2+} \) in acidic conditions. The balanced half-reaction is:\[ \mathrm{MnO}_4^- + 8\,\mathrm{H}^+ + 5\,\mathrm{e}^- \rightarrow \mathrm{Mn}^{2+} + 4\,\mathrm{H_2O} \]
03

Half-Reaction at \( \mathrm{pH} = 10 \)

At \( \mathrm{pH} = 10 \), which is basic, there are fewer \( \mathrm{H}^+ \) ions. The permanganate ion can be reduced directly to manganese dioxide \( \mathrm{MnO}_2 \), a common product in slightly basic conditions. The balanced half-reaction is:\[ \mathrm{MnO}_4^- + 2\,\mathrm{H_2O} + 3\,\mathrm{e}^- \rightarrow \mathrm{MnO_2} + 4\,\mathrm{OH}^- \]
04

Half-Reaction at \( \mathrm{pH} = 15 \)

At \( \mathrm{pH} = 15 \), the environment is strongly basic. Under strongly basic conditions, permanganate usually reduces to \( \mathrm{MnO}_4^{2-} \) rather than all the way to \( \mathrm{MnO}_2 \). The balanced half-reaction is:\[ \mathrm{MnO}_4^- + \mathrm{e}^- \rightarrow \mathrm{MnO}_4^{2-} \]

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Key Concepts

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

Half-Reactions
Half-reactions are a fundamental part of redox (reduction-oxidation) chemistry. They are simply one side of the overall redox equation and either involve the process of oxidation or reduction.
In a redox reaction:
  • Oxidation involves the loss of electrons.
  • Reduction involves the gain of electrons.
Redox reactions are balanced separately in terms of mass and charge to form half-reactions. Once these are set, they can be combined to give the final balanced redox equation. The half-reaction method simplifies balancing complex redox reactions by focusing on one reaction at a time.
This method is useful when dealing with reactions that occur in different pH conditions, since the environment significantly affects electron transfer.
Permanganate Ion
The permanganate ion, represented chemically as \( \mathrm{MnO}_4^- \), is a strong oxidizing agent. This means it readily accepts electrons from other substances in a chemical reaction. It is notable for its deep purple color in solutions.
Depending on the pH conditions in which it is acting:
  • In acidic environments, permanganate typically reduces to \( \mathrm{Mn}^{2+} \).
  • In neutral or slightly basic environments, it reduces to \( \mathrm{MnO}_2 \).
  • In strongly basic conditions, it often reduces only to \( \mathrm{MnO}_4^{2-} \).
These different products show how the same substance can play different roles based on external conditions. This versatility makes permanganate an important agent in various chemical reactions.
pH Conditions
The pH level of a solution significantly influences the outcome of redox reactions, especially for substances like the permanganate ion. pH is a measure of the acidity or basicity of a solution:
  • Acidic solutions have a pH less than 7, with a high concentration of \( \mathrm{H}^+ \) ions.
  • Neutral solutions have a pH of about 7.
  • Basic (alkaline) solutions have a pH greater than 7, with a low concentration of \( \mathrm{H}^+ \) ions.
At different pH levels, certain chemical species will be more stable or prevalent, influencing the direction and product of a redox reaction.
For instance:
  • At \( \mathrm{pH} = 0 \), the high concentration of \( \mathrm{H}^+ \) ions in an acidic medium allows the permanganate ion to more easily reduce to \( \mathrm{Mn}^{2+} \).
  • At \( \mathrm{pH} = 10 \), in a basic condition, it reduces to \( \mathrm{MnO}_2 \).
  • At \( \mathrm{pH} = 15 \), in a very strongly basic environment, permanganate reduces minimally to \( \mathrm{MnO}_4^{2-} \).
Understanding pH is thus crucial to predicting the behavior of redox reactions in different environments.

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Most popular questions from this chapter

\(\mathrm{Li}_{1}+{ }_{y} \mathrm{CoO}_{2}\) is an anode for lithium batteries. Cobalt is present as a mixture of \(\mathrm{Co}(\mathrm{III})\) and \(\mathrm{Co}(\mathrm{II})\). Most preparations also contain inert lithium salts and moisture. To find the stoichiometry, Co was measured by atomic absorption and its average oxidation state was measured by a potentiometric tritration. \({ }^{33}\) For the titration, \(25.00 \mathrm{mg}\) of solid were dissolved under \(\mathrm{N}_{2}\) in \(5.000 \mathrm{~mL}\) containing \(0.1000 \mathrm{M}\) \(\mathrm{Fe}^{2+}\) in \(6 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) plus \(6 \mathrm{M} \mathrm{H}_{3} \mathrm{PO}_{4}\) to give a clear pink solution: $$ \mathrm{Co}^{3+}+\mathrm{Fe}^{2+} \rightarrow \mathrm{Co}^{2+}+\mathrm{Fe}^{3+} $$ Unreacted \(\mathrm{Fe}^{2+}\) required \(3.228 \mathrm{~mL}\) of \(0.01593 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) for complete titration. (a) How many mmol of \(\mathrm{Co}^{3+}\) are contained in \(25.00 \mathrm{mg}\) of the material? (b) Atomic absorption found \(56.4 \mathrm{wt} \%\) Co in the solid. What is the average oxidation state of Co? (c) Find \(y\) in the formula \(\mathrm{Li}_{1}+y \mathrm{CoO}_{2}\). (d) What is the theoretical quotient \(\mathrm{wt} \% \mathrm{Li} / \mathrm{wt} \%\) Co in the solid? The observed quotient, after washing away inert lithium salts, was \(0.1388 \pm 0.0006\). Is the observed quotient consistent with the average cobalt oxidation state?

Consider the titration of \(25.0 \mathrm{~mL}\) of \(0.0500 \mathrm{M} \mathrm{Sn}^{2+}\) with \(0.100 \mathrm{M} \mathrm{Fe}^{3+}\) in \(1 \mathrm{M} \mathrm{HCl}\) to give \(\mathrm{Fe}^{2+}\) and \(\mathrm{Sn}^{4+}\), using \(\mathrm{Pt}\) and calomel electrodes. (a) Write a balanced titration reaction. (b) Write two half-reactions for the indicator electrode. (c) Write two Nernst equations for the cell voltage. (d) Calculate \(E\) at the following volumes of \(\mathrm{Fe}^{3+}: 1.0,12.5,24.0\), \(25.0,26.0\), and \(30.0 \mathrm{~mL}\). Sketch the titration curve.

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State two ways to make standard triiodide solution.

Some people have an allergic reaction to the food preservative sulfite \(\left(\mathrm{SO}_{3}^{2-}\right)\). Sulfite in wine was measured by the following procedure: To \(50.0 \mathrm{~mL}\) of wine were added \(5.00 \mathrm{~mL}\) of solution containing \(\left(0.8043 \mathrm{~g} \mathrm{KIO}_{3}+5 \mathrm{~g} \mathrm{KI}\right) / 100 \mathrm{~mL}\). Acidification with \(1.0 \mathrm{~mL}\) of \(6.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) quantitatively converted \(\mathrm{IO}_{3}^{-}\)into \(\mathrm{I}_{3}^{-}\). The \(\mathrm{I}_{3}^{-}\)reacted with \(\mathrm{SO}_{3}^{2-}\) to generate \(\mathrm{SO}_{4}^{2-}\), leaving excess \(\mathrm{I}_{3}^{-}\)in solution. The excess \(\mathrm{I}_{3}^{-}\)required \(12.86 \mathrm{~mL}\) of \(0.04818 \mathrm{M} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) to reach a starch end point. (a) Write the reaction that occurs when \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added to \(\mathrm{KIO}_{3}+\mathrm{KI}\) and explain why \(5 \mathrm{~g}\) KI were added to the stock solution. Is it necessary to measure out \(5 \mathrm{~g}\) very accurately? Is it necessary to measure \(1.0 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) very accurately? (b) Write a balanced reaction between \(\mathrm{I}_{3}^{-}\)and sulfite. (c) Find the concentration of sulfite in the wine. Express your answer in \(\mathrm{mol} / \mathrm{L}\) and in \(\mathrm{mg} \mathrm{SO}_{3}^{2-}\) per liter. (d) \(t\) test. Another wine was found to contain \(277.7 \mathrm{mg} \mathrm{SO}_{3}^{2-} / \mathrm{L}\) with a standard deviation of \(\pm 2.2 \mathrm{mg} / \mathrm{L}\) for three determinations by the iodimetric method. A spectrophotometric method gave \(273.2 \pm\) 2.1 \(\mathrm{mg} / \mathrm{L}\) in three determinations. Are these results significantly different at the \(95 \%\) confidence level?
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