Passage
The tendency of a chemical species to undergo reduction during an electrochemical reaction is indicated by the standard potential E° for the reaction. As represented generally by Reaction 1, E° measures the potential Z at which element X with oxidation number N accepts N electrons and is reduced to its elemental state.X(N) + Ne⁻ → X(0) , E° = Z voltsReaction 1In a galvanic cell, E° > 0 indicates a spontaneous reaction. Therefore, chemical species with higher positive E° values are reduced more easily than those with lower E° values.Using E° as a basis of comparison, the relative thermodynamic stabilities of different chemical species involving the same element at different oxidation states can be presented graphically using a Frost diagram. For a series of compounds containing element X, a Frost diagram plots the value of NE° for each compound against the corresponding oxidation number N of element X within the species. Frost diagrams for several species containing manganese or chlorine are shown in Figure 1.
Figure 1 Frost diagrams for manganese and chlorineOn a Frost diagram, NE° is proportional to the standard Gibbs free energy ΔG° according to the relationshipΔG° = −FNE° = −nFE°Equation 1where n is the number of moles of electrons transferred during the electrochemical process and F is the Faraday constant. Free energy considerations also show that a species is prone to disproportionation if its position on the Frost diagram lies above a line connecting the points of two adjacent species, as seen for species B in Figure 2.
Figure 2 General Frost diagram for an element forming species A, B, C, and D.The slope of a line segment joining two species on a Frost diagram is equal to the standard reduction potential for the couple. A greater slope indicates a higher corresponding reduction potential. As a result, in Figure 2, the reduction potential for B to A is lower than that for D to C.
-What is the standard potential E° for the half-reaction below?ClO₃⁻(aq) + 3H⁺(aq) + 2e⁻ → HClO₂(aq) + H₂O(l)

Question

Passage
The tendency of a chemical species to undergo reduction during an electrochemical reaction is indicated by the standard potential E° for the reaction. As represented generally by Reaction 1, E° measures the potential Z at which element X with oxidation number N accepts N electrons and is reduced to its elemental state.X(N) + Ne⁻ → X(0) , E° = Z voltsReaction 1In a galvanic cell, E° > 0 indicates a spontaneous reaction. Therefore, chemical species with higher positive E° values are reduced more easily than those with lower E° values.Using E° as a basis of comparison, the relative thermodynamic stabilities of different chemical species involving the same element at different oxidation states can be presented graphically using a Frost diagram. For a series of compounds containing element X, a Frost diagram plots the value of NE° for each compound against the corresponding oxidation number N of element X within the species. Frost diagrams for several species containing manganese or chlorine are shown in Figure 1.

Figure 1 Frost diagrams for manganese and chlorineOn a Frost diagram, NE° is proportional to the standard Gibbs free energy ΔG° according to the relationshipΔG° = −FNE° = −nFE°Equation 1where n is the number of moles of electrons transferred during the electrochemical process and F is the Faraday constant. Free energy considerations also show that a species is prone to disproportionation if its position on the Frost diagram lies above a line connecting the points of two adjacent species, as seen for species B in Figure 2.

Figure 2 General Frost diagram for an element forming species A, B, C, and D.The slope of a line segment joining two species on a Frost diagram is equal to the standard reduction potential for the couple. A greater slope indicates a higher corresponding reduction potential. As a result, in Figure 2, the reduction potential for B to A is lower than that for D to C.
-What is the standard potential E° for the half-reaction below?ClO₃⁻(aq) + 3H⁺(aq) + 2e⁻ → HClO₂(aq) + H₂O(l)

Quizplus · Accepted Answer

11ecba2d_1222_86c2_a3bf_51490e8dcd31_MD0008_00 As stated in the passage, the slope of a line segment joining two species on a Frost diagram equals the standard reduction potential E° for the couple. Accordingly, the slope between two points on an x,y-coordinate system is found by dividing the change in the y-axis values by the change in the x-axis values: 11ecba2d_1222_86c3_a3bf_79db0e5c6c16_MD0008_00 In the given half-reaction, ClO₃⁻(aq) is reduced by accepting two electrons under acidic conditions to form HClO₂(aq). The point on the Frost diagram (Figure 1) corresponding to ClO₃⁻ under acidic conditions (pH 0) therefore represents the initial condition of the half-reaction, whereas the point corresponding to HClO₂ represents the final condition. The change in oxidation number between the two species (Δx) equals the number of electrons transferred, and the slope of the line segment between these points equals the standard potential for the reduction. Substituting the x- and y-coordinate values for the ClO₃⁻ and HClO₂ points on the Frost diagram into the slope equation above gives: 11ecba2d_1222_86c4_a3bf_29d3d083adb1_MD0008_00 Therefore, the Frost diagram for chlorine indicates that the standard potential E° for the reduction of ClO₃⁻ to HClO₂ is approximately +1.2 V. (Choice A) A value of +2.4 V·e⁻ is obtained if the change in NE° (y-axis) is not divided by the change in the oxidation state N (x-axis). The slope (Δy/Δx), not Δy, is equal to E° for the reduction, as confirmed by the units. (Choice C) A standard potential of +0.3 V is required for the reduction of ClO₃⁻ to ClO₂⁻ (instead of HClO₂), which occurs only under basic conditions. The given half-reaction occurs under acidic conditions (H⁺ in the reactants). (Choice D) A value of −0.6 V·e⁻ results if the change in NE° (y-axis) calculated under basic conditions for the reduction of ClO₃⁻ to ClO₂⁻ is not divided by the change in N (x-axis). A calculation error gives a negative slope. Educational objective: The standard reduction potential E° for an oxidation-reduction couple can be evaluated graphically using electrochemical data. The slope of a line segment between two points on an x,y-coordinate system is found by dividing the change in the y-axis values by the change in the x-axis values.

Passage The Tendency of a Chemical Species to Undergo Reduction During