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Chapter 20: Problem 114

A voltaic cell is based on \(\mathrm{Cu}^{2+}(a q) / \mathrm{Cu}(s)\) and \(\mathrm{Br}_{2}(l) /\) \(\mathrm{Br}^{-}(a q)\) half-cells. (a) What is the standard emf of the cell? (b) Which reaction occurs at the cathode and which at the anode of the cell? (c) Use \(S^{\circ}\) values in Appendix \(\mathrm{C}\) and the relationship between cell potential and free-energy change to predict whether the standard cell potential increases or decreases when the temperature is raised above \(25^{\circ} \mathrm{C}\). (Thestandard entropy of \(\mathrm{Cu}^{2+}(a q)\) is $\left.S^{\circ}=-99.6 \mathrm{~J} / \mathrm{K}\right)$

Short Answer

Expert verified
The standard emf of the cell is 1.41 V, with the Cu2+ + 2e- -> Cu reaction occurring at the cathode and the 2Br- -> Br2 + 2e- reaction occurring at the anode. The effect of temperature on the standard cell potential is positive, meaning that the standard cell potential increases when the temperature is raised above 25 °C.

Step by step solution

01

Find the Standard Reduction Potentials

Consult a table of standard reduction potentials to find the potentials for the cu 2 /cu and Br2/Br- half-cells. Cu2+ + 2e- -> Cu, E° = +0.34 V (Reduction) Br2 + 2e- -> 2Br-, E° = +1.07 V (Reduction)
02

Determine the Anode and Cathode Reactions

In a voltaic cell, the reduction with the highest potential occurs at the cathode and the one with the lowest potential occurs at the anode. Cathode: Cu2+ + 2e- -> Cu Anode: 2Br- -> Br2 + 2e- (Reverse the reduction reaction)
03

Calculate the Standard Emf

Next, we will calculate the standard emf (E°) of the cell by subtracting the standard potential of the anode reaction from the standard potential of the cathode reaction: E° = E°(cathode) - E°(anode) = 0.34 V - (-1.07 V) = 1.41 V Standard emf of the cell is 1.41 V.
04

Calculate the Standard Free Energy Change

We will use the relationship between cell potential and free-energy change to find the standard free energy change (ΔG°) for the reaction. ΔG° = -nFE° n = 2 (number of electrons in each half-reaction) F = 96485 C/mol (Faraday's constant) ΔG° = -(2)(96485 C/mol)(1.41 V) = -271632 J/mol
05

Calculate the Entropy Change

Calculate the standard entropy change (ΔS°) for the cell reaction using the standard entropy (S°) values. ΔS° = S°(products) - S°(reactants) Entropy of products: S°(Cu) + S°(Br2) = 33.2 J/mol K + 152.3 J/mol K Entropy of reactants: S°(Cu2+) + S°(2Br-) = -99.6 J/mol K + (2 * (10.4 J/mol K)) ΔS° = (33.2 J/mol K + 152.3 J/mol K) - (-99.6 J/mol K + 20.8 J/mol K) = 263.3 J/mol K
06

Determine the Effect of Temperature

Now, we will use the Gibbs-Helmholtz equation to relate the standard free energy change, standard entropy change, and temperature: ΔG° = ΔH° - TΔS° ΔH° = ΔG° + TΔS° We can then find the effect of temperature (dT) on ΔG° and E°: d(ΔG°)/dT = d(ΔH°)/dT - ΔS° d(E°)/dT = -d(ΔG°)/dT/nF = d(ΔH°)/dT/nF - ΔS°/nF Since ΔS° > 0, the term (ΔS°/nF) will be positive and d(E°)/dT will be positive. This means that the standard cell potential increases when the temperature is raised above 25 °C.

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Most popular questions from this chapter

A common shorthand way to represent a voltaic cell is anode \(\mid\) anode solution || cathode solution \(\mid\) cathode A double vertical line represents a salt bridge or a porous barrier. A single vertical line represents a change in phase, such as from solid to solution. (a) Write the half-reactions and overall cell reaction represented by $\mathrm{Fe}\left|\mathrm{Fe}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag} ;$ calculate the standard cell emf using data in Appendix E. (b) Write the half-reactions and overall cell reaction represented by $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{H}^{+}\right| \mathrm{H}_{2} ;$ calculate the standard cell emf using data in Appendix E and use Pt for the hydrogen electrode. (c) Using the notation just described, represent a cell based on the following reaction: $$ \begin{aligned} \mathrm{ClO}_{3}^{-}(a q)+3 \mathrm{Cu}(s) &+6 \mathrm{H}^{+}(a q) \\ & \longrightarrow \mathrm{Cl}^{-}(a q)+3 \mathrm{Cu}^{2+}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ \(\mathrm{Pt}\) is used as an inert electrode in contact with the \(\mathrm{ClO}_{3}^{-}\) and \(\mathrm{Cl}^{-}\). Calculate the standard cell emf given: \(\mathrm{ClO}_{3}^{-}(a q)+\) $6 \mathrm{H}^{+}(a q)+6 \mathrm{e}^{-} \longrightarrow \mathrm{Cl}^{-}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) ; E^{\circ}=1.45 \mathrm{~V}$

During the discharge of an alkaline battery, \(4.50 \mathrm{~g}\) of \(\mathrm{Zn}\) is consumed at the anode of the battery. (a) What mass of \(\mathrm{MnO}_{2}\) is reduced at the cathode during this discharge? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Zn}\) to \(\mathrm{MnO}_{2} ?\)

Copper corrodes to cuprous oxide, \(\mathrm{Cu}_{2} \mathrm{O},\) or cupric oxide, \(\mathrm{CuO},\) depending on environmental conditions. (a) What is the oxidation state of copper in cuprous oxide? (b) What is the oxidation state of copper in cupric oxide? (c) Copper peroxide is another oxidation product of elemental copper. Suggest a formula for copper peroxide based on its name. (d) Copper(III) oxide is another unusual oxidation product of elemental copper. Suggest a chemical formula for copper(III) oxide.

Cytochrome, a complicated molecule that we will represent as \(\mathrm{CyFe}^{2+}\), reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions (Section 19.7). At \(\mathrm{pH} 7.0\) the following reduction potentials pertain to this oxidation of \(\mathrm{CyFe}^{2+}\) $$ \begin{aligned} \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) & & E_{\mathrm{red}}^{\circ}=+0.82 \mathrm{~V} \\\ \mathrm{CyFe}^{3+}(a q)+\mathrm{e}^{-} & \longrightarrow \mathrm{CyFe}^{2+}(a q) & E_{\mathrm{red}}^{\circ} &=+0.22 \mathrm{~V} \end{aligned} $$ (a) What is \(\Delta G\) for the oxidation of \(\mathrm{CyFe}^{2+}\) by air? \((\mathbf{b})\) If the synthesis of \(1.00 \mathrm{~mol}\) of ATP from adenosine diphosphate (ADP) requires a \(\Delta G\) of \(37.7 \mathrm{~kJ},\) how many moles of ATP are synthesized per mole of \(\mathrm{O}_{2} ?\)

Consider a redox reaction for which \(E^{\circ}\) is a negative number. (a) What is the sign of \(\Delta G^{\circ}\) for the reaction? (b) Will the equilibrium constant for the reaction be larger or smaller than \(1 ?\) (c) Can an electrochemical cell based on this reaction accomplish work on its surroundings?
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