Question

What reaction can occur, if any, when the following experiments are carried out under standard-state conditions? (a) Oxygen gas is bubbled through an acidic solution of \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\) (b) A strip of lead is dipped into an aqueous solution of \(\mathrm{AgNO}_{3}\). (c) Chlorine gas is bubbled through aqueous \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\). (d) A nickel wire is dipped into an aqueous solution of HClO.

Short answer

(a) Cr oxidized, (b) Pb displaces Ag, (c) Cl oxidizes oxalic acid, (d) Ni oxidized by HClO.

Step-by-step solution

Understand the Concepts

To predict possible reactions, you should first understand redox reactions, including standard potential tables, and displacement reactions. Bear in mind that a reaction will occur if it results in a net positive change in cell potential (voltage).

Analyze Reaction (a)

Review the standard potential tables. Oxygen can oxidize chromium ions from Cr(III) to Cr(VI) in acidic conditions. Check potentials: \(\mathrm{O}_2 + 4\mathrm{H}^+ + 4e^- \rightarrow 2\mathrm{H}_2\mathrm{O}\), \(E^\circ = 1.23\,\mathrm{V}\). \(\mathrm{Cr}^{3+} + 7\mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ + 6e^-\), \(E^\circ = 1.33\,\mathrm{V}\). The overall reaction is: \(2\mathrm{Cr}^{3+} + 3\mathrm{O}_2 + 2\mathrm{H}_2\mathrm{O} \rightarrow \mathrm{Cr}_2\mathrm{O}_7^{2-} + 4\mathrm{H}^+\) which occurs because \(E^\circ_{\text{cell}}\) is positive.

Analyze Reaction (b)

Check if lead can be oxidized by silver ions. Lead has a standard reduction potential of \(-0.13\,\mathrm{V}\) (\(\mathrm{Pb}^{2+} + 2e^- \rightarrow \mathrm{Pb}\)), and silver has \(E^\circ = 0.80\,\mathrm{V}\) (\(\mathrm{Ag}^+ + e^- \rightarrow \mathrm{Ag}\)). Since silver has a higher positive potential, it can be reduced and displace lead, given the reaction: \(2\mathrm{Ag}^+ + \mathrm{Pb} \rightarrow 2\mathrm{Ag} + \mathrm{Pb}^{2+}\).

Analyze Reaction (c)

Check the ability of chlorine gas to oxidize oxalic acid. Chlorine can be reduced from \(\mathrm{Cl}_2\) to \(\mathrm{Cl}^-\) with \(E^\circ = 1.36 \, \mathrm{V}\), and oxalic acid can be oxidized, making the overall process favorable. The reaction occurs: \(\mathrm{Cl}_2 + \mathrm{H}_2\mathrm{C}_2\mathrm{O}_4 \rightarrow 2\mathrm{Cl}^- + 2\mathrm{CO}_2 + 2\mathrm{H}^+\).

Analyze Reaction (d)

Determine if nickel can displace hypochlorous acid. Nickel's standard reduction potential is \(-0.25\,\mathrm{V}\) (\(\mathrm{Ni}^{2+} + 2e^- \rightarrow \mathrm{Ni}\)), while \(\mathrm{HClO}\) can be reduced to \(\mathrm{Cl}^-\) with \(E^\circ = 1.49\,\mathrm{V}\). Based on these potentials, \(\mathrm{HClO}\) is reduced and \(\mathrm{Ni}\) is oxidized: \(\mathrm{Ni} + 2\mathrm{HClO} \rightarrow \mathrm{Ni}^{2+} + 2\mathrm{Cl}^- + \mathrm{H}_2\mathrm{O}\).

Key concepts

Standard Potential Tables

Standard potential tables are essential tools in understanding redox reactions. They list the standard electrode potentials, expressed as \(E^\circ\), for various half-reactions. These potentials are measured under standard conditions: 25°C, 1 atm pressure, and 1 M concentrations of solutions. Such tables allow us to predict the behavior of substances in electrochemical reactions.

In these tables, each half-reaction is shown with its corresponding standard potential. A positive \(E^\circ\) indicates a strong tendency for reduction, while a negative value suggests a stronger oxidation. By comparing potentials, one can identify the likelihood of a reaction occurring, depending on which substance is more readily reduced or oxidized. This is crucial in predicting if a given redox reaction will proceed and in which direction.

When analyzing potential reactions, selection of the relevant half-reactions from the standard potential tables helps in calculating the overall cell potential, guiding us in determining the spontaneity of the reaction. A positive cell potential signifies a spontaneous reaction under standard conditions.

Displacement Reactions

Displacement reactions involve the replacement of one element in a compound with another. These reactions often occur in solutions where metals compete to be in oxidized or reduced states. Understanding these reactions is key in studying how metals and ions interact in different environments.

For example, if a metal has a higher reduction potential compared to another, it can displace the latter's ions in solution. This is because it more readily gains electrons (reduction), and the less favorable metal loses electrons (oxidation). The classic example is the reaction between silver ions and lead, where silver, having a higher potential, gets reduced and displaces lead to form solid silver.

Studying displacement reactions allows chemists to predict which reactions might occur when different metals and their ions are mixed. Factors like the reactivity series and standard potential tables inform these predictions. Such reactions are fundamental in processes like metal extraction and electrochemistry.

Cell Potential

Cell potential, or electromotive force (EMF), is the potential difference between two electrodes in an electrochemical cell. It is measured in volts (V) and is a measure of the cell's ability to perform work in driving electrons through a circuit. The cell potential is derived from subtracting the potential of the anode (oxidation) from the cathode (reduction).

The formula for cell potential is given by:

• \(E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \)

A positive \(E^\circ_{\text{cell}}\) often indicates a spontaneous reaction. Cells are designed to maximize this potential, typically by selecting materials that have vastly different electrode potentials.

Understanding cell potential is critical when designing batteries and other energy-storage devices. Concepts like internal resistance, efficiency, and power output are directly related to the measured cell potential. This understanding enables the engineering of cells that store and deliver energy more efficiently in various applications.