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Chapter 1: Problem 26

Use the following information to answer questions 25-28. A voltaic cell is created using the following half-cells: $\begin{array}{ll}{\mathrm{Cr}^{3+}+3 e \rightarrow \mathrm{Cr}(s)} & {E^{\circ}=-0.41 \mathrm{V}} \\ {\mathrm{Pb}^{2+}+2 e \rightarrow \mathrm{Pb}(s)} & {E^{\circ}=-0.12 \mathrm{V}}\end{array}$ The concentrations of the solutions in each half-cell are 1.0 M. Which net ionic equation below represents a possible reaction that takes place when a strip of magnesium metal is oxidized by a solution of chromium (III) nitrate? (A) $\operatorname{Mg}(s)+\operatorname{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cr}^{3+}(a q)+3 \mathrm{NO}_{3}^{-}(a q)$ (B) $3 \mathrm{Mg}(s)+2 \mathrm{Cr}^{3+} \rightarrow 3 \mathrm{Mg}^{2+}+2 \mathrm{Cr}(s)$ (C) $\mathrm{Mg}(s)+\mathrm{Cr}^{3+} \rightarrow \mathrm{Mg}^{2+}+\mathrm{Cr}(s)$ (D) $3 \mathrm{Mg}(s)+2 \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}(a q) \rightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{Cr}(s)+\mathrm{NO}_{3}^{-}(a q)$

Short Answer

Expert verified
The correct net ionic equation is: \(3 \mathrm{Mg}(s)+2 \mathrm{Cr}^{3+}(a q) \rightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{Cr}(s)\). Hence, choice (B) is correct.

Step by step solution

01

Determine the standard potentials

From the provided half-cell reactions, the standard reduction potential \(E^\circ\) for chromium and lead are -0.41 V and -0.12 V respectively. The standard potential for magnesium is not given, but can be looked up in a standard electrode potentials table as -2.37 V.
02

Determine the direction of the reaction

In a voltaic cell, reduction occurs at the cathode and oxidation at the anode. The element with higher (more positive) standard potential gets reduced while the one with lower (more negative) standard potential gets oxidized. In this case, since magnesium has a lower standard potential than chromium, magnesium will be oxidized and chromium will be reduced.
03

Write the half-cell reactions

The oxidation of magnesium can be represented as: \[\mathrm{Mg}(s) \rightarrow \mathrm{Mg}^{2+}(a q)+2 e^-\] The reduction of chromium can be represented as: \[\mathrm{Cr}^{3+}(a q)+3 e^- \rightarrow \mathrm{Cr}(s)\]
04

Balance the half-cell reactions

To balance the charges, multiply the oxidation half-reaction by 3 and the reduction half-reaction by 2. This gives: \[3\mathrm{Mg}(s) \rightarrow 3\mathrm{Mg}^{2+}(a q)+6 e^-\] \[2\mathrm{Cr}^{3+}(a q)+6 e^- \rightarrow 2\mathrm{Cr}(s)\]
05

Write the net ionic equation

The net ionic equation is found by adding the half-reactions together and cancelling out the electrons. This results in the equation: \[3 \mathrm{Mg}(s)+2 \mathrm{Cr}^{3+}(a q) \rightarrow 3 \mathrm{Mg}^{2+}(a q)+2 \mathrm{Cr}(s)\]

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Most popular questions from this chapter

In an experiment 2 moles of \(\mathrm{H}_{2}(g)\) and 1 mole of \(\mathrm{O}_{2}(g)\) were completely reacted, according to the following equation in a sealed container of constant volume and temperature: $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)$$ If the initial pressure in the container before the reaction is denoted as \(P_{i}\) which of the following expressions gives the final pressure, assuming ideal gas behavior? (A) \(P_{i}\) (B) 2\(P_{i}\) (C) \((3 / 2) P_{i}\) (D) \((2 / 3) P_{i}\)

A laboratory technician wishes to create a buffered solution with a pH of 5. Which of the following acids would be the best choice for the buffer? (A) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \quad K_{a}=5.9 \times 10^{-2}\) (B) \(\mathrm{H}_{3} \mathrm{AsO}_{4} \quad K_{a}=5.6 \times 10^{-3}\) (C) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \quad K_{a}=1.8 \times 10^{-5}\) (D) \(\mathrm{HOCl}\) \(\quad K_{a}=3.0 \times 10^{-8}\)

Which gas has the strongest IMFs? (A) He (B) Ne (C) NO (D) All gases have identical IMFs.

150 \(\mathrm{mL}\) of saturated \(\mathrm{SrF}_{2}\) solution is present in a 250 \(\mathrm{mL}\) beaker at room temperature. The molar solubility of \(\mathrm{SrF}_{2}\) at 298 \(\mathrm{K}\) is \(1.0 \times 10^{-3} \mathrm{M}\) . What are the concentrations of \(\mathrm{Sr}^{2+}\) and \(\mathrm{F}^{-}\) in the beaker? (A) \(\left[\mathrm{Sr}^{2+}\right]=1.0 \times 10^{-3} M\left[\mathrm{F}^{-}\right]=1.0 \times 10^{-3} M\) (B) \(\left[\mathrm{Sr}^{2+}\right]=1.0 \times 10^{-3} M\left[\mathrm{F}^{-}\right]=2.0 \times 10^{-3} M\) (C) \(\left[\mathrm{Sr}^{2+}\right]=2.0 \times 10^{-3} M\left[\mathrm{F}^{-}\right]=1.0 \times 10^{-3} M\) (D) \(\left[\mathrm{Sr}^{2+}\right]=2.0 \times 10^{-3} \mathrm{M}\left[\mathrm{F}^{-}\right]=2.0 \times 10^{-3} M\)

Use the following information to answer questions 29-31. Pennies are made primarily of zinc, which is coated with a thin layer of copper through electroplating, using a setup like the one above. The solution in the beaker is a strong acid (which produces H' ions), and the cell is wired so that the copper electrode is the anode and zinc penny is the cathode. Use the following reduction potentials to answer questions \(29-31 .\) $$\begin{array}{|l|l|}\hline \text { Half-Reaction } & {\text { Standard Reduction Potential }} \\ \hline \mathrm{Cu}^{2++2 e^{-} \rightarrow \mathrm{Cu}(s)} & {+0.34 \mathrm{V}} \\ \hline 2 \mathrm{H}^{++2 e^{-} \rightarrow \mathrm{H}_{2}(g)} & {0.00 \mathrm{V}} \\ \hline \mathrm{Ni}^{2++2 e^{-} \rightarrow \mathrm{Ni}(s)} & {-0.25 \mathrm{V}} \\\ \hline \mathrm{Zn}^{2++2 e^{-} \rightarrow \mathrm{Zn}(s)} & {-0.76 \mathrm{V}} \\ \hline\end{array}$$ If, instead of copper, a nickel bar were to be used, could nickel be plated onto the zinc penny effectively? Why or why not? (A) Yes, nickel’s SRP is greater than that of zinc, which is all that is required for nickel to be reduced at the cathode (B) Yes, nickel is able to take electrons from the \(\mathrm{H}^{+}\) ions in solution, allowing it to be reduced (C) No, nickel's SRP is lower than that of \(\mathrm{H}^{+}\) ions, which means the only product being produced at the cathode would be hydrogen gas (D) No, nickel's SRP is negative, meaning it cannot be reduced in an electrolytic cell
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