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Complete and balance each half-reaction in acid solution, and identify it as an oxidation or a reduction. (a) \(\mathrm{Cr}^{3+}(\mathrm{aq}) \rightarrow \mathrm{Cr}(\mathrm{s})\) (b) \(\mathrm{I}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}_{2}(\mathrm{aq})\) (c) \(\mathrm{NO}_{2}^{-}(\mathrm{aq}) \rightarrow \mathrm{NO}_{3}^{-}(\mathrm{aq})\)

Short Answer

Expert verified
(a) Reduction: \(\mathrm{Cr^{3+} + 3e^- \rightarrow Cr}\); (b) Oxidation: \(\mathrm{2I^- \rightarrow I_2 + 2e^-}\); (c) Oxidation: \(\mathrm{NO_2^- + H_2O \rightarrow NO_3^- + 2H^+ + 2e^-}\).

Step by step solution

01

Determine the Oxidation States and Electrons Exchange in Reaction (a)

For the reaction \(Cr^{3+} \rightarrow Cr\), the oxidation state of chromium changes from +3 in \(Cr^{3+}\) to 0 in \(Cr\). Since chromium goes from an oxidation state of +3 to 0, it gains 3 electrons. This is a reduction process. The half-reaction can be written and balanced as: \[\mathrm{Cr^{3+} + 3e^- \rightarrow Cr}\]\.
02

Determine the Oxidation States and Electrons Exchange in Reaction (b)

For \(I^- \rightarrow I_2\), each iodine ion \(I^-\) has an oxidation state of -1. In \(I_2\), each iodine atom has an oxidation state of 0. To form one \(I_2\) molecule, two \(I^-\) ions must lose 2 electrons total. This is an oxidation process. The balanced half-reaction is: \[\mathrm{2I^- \rightarrow I_2 + 2e^-}\]\.
03

Determine the Oxidation States and Electrons Exchange in Reaction (c)

In the half-reaction \(NO_2^- \rightarrow NO_3^-\), the oxidation state of nitrogen changes from +3 in \(NO_2^-\) to +5 in \(NO_3^-\). This change requires the loss of 2 electrons, indicating it's an oxidation process. The half-reaction balanced in acid solution is: \[\mathrm{NO_2^- + H_2O \rightarrow NO_3^- + 2H^+ + 2e^-}\]\.

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Key Concepts

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

Half-Reaction Balancing
Balancing half-reactions is a key step in understanding redox chemistry. In redox reactions, you separate the oxidation and reduction processes into two separate equations, or half-reactions. The main goal in half-reaction balancing is to ensure the charges and atoms are balanced on both sides of the equation.
To balance a redox reaction in acidic solution, first write the unbalanced half-reaction. Then balance all the elements except for oxygen and hydrogen. Next, balance the oxygen atoms by adding water ( H_2O ) molecules. Following this, balance the hydrogen atoms by adding H^+ ions.
Finally, balance the charges by adding electrons ( e^- ). Ensure that the number of electrons lost in the oxidation process equals the number of electrons gained in the reduction process. This balance is crucial for the overall reaction to be legitimate.
Oxidation States
Oxidation states, or oxidation numbers, are important for tracking electron transfer in redox reactions. These numbers help indicate how many electrons an atom gains, loses, or shares when it forms chemical bonds.
For example, consider chromium in the reaction Cr^{3+} ightarrow Cr . Initially, chromium has an oxidation state of +3 in Cr^{3+} , and it changes to 0 in Cr . This transition indicates it gains three electrons.
Understanding oxidation states is crucial because it helps determine whether a substance is undergoing oxidation or reduction. Typically, a loss in electrons results in an increase in oxidation state, denoting oxidation, while a gain in electrons decreases the oxidation state, indicating reduction.
Electrons Exchange
Electrons exchange is at the heart of redox reactions. Electrons are transferred from the reducing agent to the oxidizing agent. This transfer can occur wholly or partially, depending on the participating substances.
Consider the equation 2I^- ightarrow I_2 + 2e^- . Here, the two I^- ions lose electrons to form I_2 . This example shows the typical electron exchange in oxidation processes.
In all balanced redox reactions, the number of electrons lost should equal the number of electrons gained. This equality is essential for confirming that matter and charge are conserved during the reaction.
Reduction Process
The reduction process occurs when a substance gains electrons, resulting in the decrease of its oxidation state. A prime example is chromium in the reaction Cr^{3+} + 3e^- ightarrow Cr . Chromium gains three electrons, reducing its oxidation state from +3 to 0.
Reduction is always paired with oxidation; while one species undergoes reduction, another species is oxidized. This coupling ensures the balance of overall electrons in the equation. Recognizing reduction involves tracking the electrons added to particular species and understanding how their oxidation states decrease through this gain.
Oxidation Process
The oxidation process involves the loss of electrons from a substance, leading to an increase in oxidation state. For instance, in the reaction 2I^- ightarrow I_2 + 2e^- , each iodine ion loses one electron when forming diatomic iodine, making it an oxidation process.
Identifying oxidation processes involves two key steps: observing the increase in oxidation state and counting the electrons lost. Often in complex reactions, multiple atoms or molecules will undergo oxidation simultaneously, and it becomes important to track each change individually to maintain the reaction's balance. Through oxidation, an atom, ion, or molecule serves as the reducing agent, which loses electrons and increases its oxidation potential.

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Most popular questions from this chapter

Assign the oxidation states of all elements in each of the following: (a) \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) (b) \(\mathrm{Ba}\left(\mathrm{ClO}_{4}\right)_{2}\) (c) \(\mathrm{T} 1^{3+}\)

The equilibrium constant at \(25^{\circ} \mathrm{C}\) is \(1.58 \times 10^{2}\) for $$\begin{aligned} 2 \mathrm{VO}^{2+}(\mathrm{aq})+\mathrm{Br}_{2}(\ell)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \\\& 2 \mathrm{VO}_{2}^{2+}(\mathrm{aq})+2 \mathrm{Br}^{-}(\mathrm{aq})+4 \mathrm{H}^{+}(\mathrm{aq}) \end{aligned} $$ Calculate \(\Delta G^{\circ}\) and \(E^{\circ}\) for this reaction.

Balance each of the following redox reactions in acid solution. (a) \(\mathrm{Fe}(\mathrm{s})+\mathrm{Ag}^{+}(\mathrm{aq}) \rightarrow \mathrm{Ag}(\mathrm{s})+\mathrm{Fe}^{2+}(\mathrm{aq})\) (b) \(\mathrm{I}_{2}(\mathrm{aq})+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})\) (c) \(\mathrm{MnO}_{4}^{-}(\mathrm{aq})+\mathrm{Fe}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Mn}^{2+}(\mathrm{aq})\)

Complete and balance each half-reaction in acid solution, and identify it as an oxidation or a reduction. (a) \(\mathrm{UO}_{2}^{2+}(\mathrm{aq}) \rightarrow \mathrm{U}^{4+}(\mathrm{aq})\) (b) \(\mathrm{Zn}(\mathrm{s}) \rightarrow \mathrm{Zn}^{2+}(\mathrm{aq})\) (c) \(\mathrm{IO}_{3}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})\)

A Consider the standard reduction potentials of cesium and lithium. $$ \begin{array}{ll} \mathrm{Cs}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Cs}(\mathrm{s}) & E^{\circ}=-3.026 \mathrm{~V} \\\ \mathrm{Li}^{+}(\mathrm{aq})+\mathrm{e}^{-} \rightarrow \mathrm{Li}(\mathrm{s}) & E^{\circ}=-3.095 \mathrm{~V} \end{array} $$ The periodic trends in the properties of the element indicate that fluorine is the most chemically reactive nonmetal, so perhaps it is not surprising that the standard reduction potential of fluorine has the highest positive value for a nonmetallic element. However, periodic properties of the elements also indicate that cesium should be the most reactive metal. Comparison of the voltage of the cesium half-reaction with that of lithium shows that the standard reduction potential of lithium is less negative than that of cesium, indicating that lithium is a better oxidizer than is cesium. (a) Calculate the standard cell voltages of the voltaic cells based on the reaction $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{M}^{+}(\mathrm{aq})+2 \mathrm{~F}^{-}(\mathrm{aq}) $$ where \(\mathrm{M}\) is \(\mathrm{Cs}\) and \(\mathrm{Li}\). (b) Assuming that the pressure of \(\mathrm{F}_{2}(\mathrm{~g})\) stays at \(1.00 \mathrm{~atm}\), what concentration does \(\mathrm{Li}^{+}(\mathrm{aq})\) have to be for the voltage of the \(\mathrm{Li} / \mathrm{F}_{2}\) voltaic cell to equal the standard voltage of the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cell? (c) Can you suggest a reason why the standard reduction potential of lithium is lower than that of cesium, even though periodic trends indicate that cesium is the more reactive metal? (d) Calculate \(\Delta G^{o}\) for both the \(\mathrm{Li} / \mathrm{F}_{2}\) and the \(\mathrm{Cs} / \mathrm{F}_{2}\) voltaic cells from their \(E^{\circ} \mathrm{s}\). Compare this with the Gibbs' free energies of formation of \(2 \mathrm{~mol} \mathrm{LiF}\) and CsF. Can you explain the difference? (e) Given the fact that alkali metals react rather violently with water, it would be unlikely that any voltaic cell can be constructed using Li(s) or \(\mathrm{Cs}(\mathrm{s})\) in the presence of water. A more likely scenario is that the voltaic cell would have no solvent, so that the voltaic cell reaction would be $$ 2 \mathrm{M}(\mathrm{s})+\mathrm{F}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{MF}(\mathrm{xtal}) $$ where \(\mathrm{M}\) is \(\mathrm{Cs}\) or \(\mathrm{Li}\). What would be the \(E^{\circ}\) s of the two different voltaic cells if this were the reaction? (Hint: See your answer to part d.)

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