© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Balance the redox equation. 1. Assign oxidation states to all atoms and identify the substances being oxidized and reduced. 2. Separate the overall reaction into two half-reactions: one for oxidation and one for reduction. 3. Balance each half-reaction with respect to mass in the following order: Balance all elements other than H and O. Balance O by adding H 2 O. Balance H by adding H +. All elements are balanced, so proceed to next step. SOLUTION Example 18.1 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition 4. Balance each half-reaction with respect to charge by adding electrons. (Make the sum of the charges on both sides of the equation equal by adding as many electrons as necessary.) 5. Make the number of electrons in both half-reactions equal by multiplying one or both half-reactions by a small whole number. 6. Add the two half-reactions together, canceling electrons and other species as necessary. Example 18.1 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution Continued

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued 7. Verify that the reaction is balanced both with respect to mass and with respect to charge. For Practice 18.1 Balance the redox reaction in acidic solution. Example 18.1 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.2 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution 1. Assign oxidation states to all atoms and identify the substances being oxidized and reduced. 2. Separate the overall reaction into two half-reactions: one for oxidation and one for reduction. 3. Balance each half-reaction with respect to mass in the following order: Balance all elements other than H and O. Balance O by adding H 2 O. Balance H by adding H +. Balance the redox equation. SOLUTION

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued Example 18.2 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution 4. Balance each half-reaction with respect to charge by adding electrons. (Make the sum of the charges on both sides of the equation equal by adding as many electrons as necessary.) 5. Make the number of electrons in both half-reactions equal by multiplying one or both half-reactions by a small whole number. 6. Add the two half-reactions together, canceling electrons and other species as necessary.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued Example 18.2 Half-Reaction Method of Balancing Aqueous Redox Equations in Acidic Solution 7. Verify that the reaction is balanced both with respect to mass and with respect to charge. For Practice 18.2 Balance the redox reaction in acidic solution.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.3 Balancing Redox Reactions Occurring in Basic Solution Balance the equation occurring in basic solution: SOLUTION To balance redox reactions occurring in basic solution, we follow the half-reaction method outlined in Examples 18.1 and 18.2, but add an extra step to neutralize the acid with OH − as shown in step 3 below. 1. Assign oxidation states. 2. Separate the overall reaction into two half-reactions. 3. Balance each half-reaction with respect to mass. Balance all elements other than H and O. Balance O by adding H 2 O. Balance H by adding H +. Neutralize H + by adding enough OH − to neutralize each H +. Add the same number of OH − ions to each side of the equation.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued Example 18.3 Balancing Redox Reactions Occurring in Basic Solution 4. Balance each half-reaction with respect to charge. 5. Make the number of electrons in both half- reactions equal. 6. Add the half-reactions together. 7. Verify that the reaction is balanced. For Practice 18.3 Balance the redox reaction occurring in basic solution.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Use tabulated standard electrode potentials to calculate the standard cell potential for the reaction occurring in an electrochemical cell at 25 ○ C. (The equation is balanced.) Example 18.4 Calculating Standard Potentials for Electrochemical Cells from Standard Electrode Potentials of the Half-Reactions SOLUTION Begin by separating the reaction into oxidation and reduction half-reactions. [In this case, you can readily see that Al(s) is oxidized. In cases where it is not so apparent, you many want to assign oxidation states to determine the correct half-reactions.] Look up the standard electrode potentials for each half-reaction. Add the half-cell reactions together to obtain the overall redox equation. Calculate the standard cell potential by subtracting the electrode potential of the anode from the electrode potential of the cathode.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.4 Calculating Standard Potentials for Electrochemical Cells from Standard Electrode Potentials of the Half-Reactions Continued For Practice 18.4 Use tabulated standard electrode potentials to calculate the standard cell potential for the reaction occurring in an electrochemical cell at 25 ○ C. (The equation is balanced.)

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.5 Predicting Spontaneous Redox Reactions and Sketching Electrochemical Cells Without calculating E ○ cell, predict whether each redox reaction is spontaneous. If the reaction is spontaneous as written, make a sketch of the electrochemical cell in which the reaction could occur. If the reaction is not spontaneous as written, write an equation for the spontaneous direction in which the reaction would occur and make a sketch of the electrochemical cell in which the spontaneous reaction would occur. In your sketches, make sure to label the anode (which should be drawn on the left), the cathode, and the direction of electron flow. SOLUTION

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued For Practice 18.5 Is each redox reaction spontaneous under standard conditions? Example 18.5 Predicting Spontaneous Redox Reactions and Sketching Electrochemical Cells

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.6 Relating ΔG ○ and E ○ cell Use the tabulated electrode potentials to calculate ΔG ○ for the reaction: Is the reaction spontaneous? SORT You are given a redox reaction and asked to find ΔG ○. STRATEGIZE Use the tabulated values of electrode potentials to calculate E ○ cell. Then use Equation 18.3 to calculate ΔG ○ from E ○ cell. SOLVE Separate the reaction into oxidation and reduction half- reactions and find the standard electrode potentials for each. Determine E ○ cell by subtracting E an from E cat.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued Calculate ΔG ○ from E ○ cell. The value of n (the number of moles of electrons) corresponds to the number of electrons that are canceled in the half-reactions. Remember that 1 V = 1 J/C. For Practice 18.6 Use tabulated electrode potentials to calculate ΔG ○ for the reaction: Is the reaction spontaneous? CHECK The answer is in the correct units (joules) and seems reasonable in magnitude (≈110 kJ) since you have seen (in Chapter 17) that values of ΔG ○ are typically in the range of plus or minus tens to hundreds of kilojoules. The sign is positive, as expected for a reaction in which E ○ cell is negative. Example 18.6 Relating ΔG ○ and E ○ cell

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.7 Relating E ○ cell and K Use the tabulated electrode potentials to calculate K for the oxidation of copper by H + : SORT You are given a redox reaction and asked to find K. STRATEGIZE Use the tabulated values of electrode potentials to calculate E ○ cell. Then use Equation 18.6 to calculate K from E ○ cell. SOLVE Separate the reaction into oxidation and reduction half-reactions and find the standard electrode potentials for each. Find E ○ cell by subtracting E an from E cat.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Continued Calculate K from E ○ cell. The value of n (the number of moles of electrons) corresponds to the number of electrons canceled in the half-reactions. CHECK The answer has no units, as expected for an equilibrium constant. The magnitude of the answer is small, meaning that the reaction lies far to the left at equilibrium, as expected for a reaction in which E ○ cell is negative. For Practice 18.7 Use the tabulated electrode potentials to calculate K for the oxidation of iron by H + : Example 18.7 Relating E ○ cell and K

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Example 18.8 Calculating E cell under Nonstandard Conditions An electrochemical cell is based on these two half-reactions: Calculate the cell potential. SORT You are given the half-reactions for a redox reaction and the concentrations of the aqueous reactants and products. You are asked to find the cell potential. STRATEGIZE Use the tabulated values of electrode potentials to calculate E ○ cell. Then use Equation 18.9 to calculate E cell. SOLVE Write the oxidation and reduction half-reactions, multiplying by the appropriate coefficients to cancel the electrons. Find the standard electrode potentials for each and find E ○ cell.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Calculate the cell potential. Continued Calculate E cell from E ○ cell. The value of n (the number of moles of electrons) corresponds to the number of electrons (in this case 6) that are canceled in the half- reactions. Determine Q based on the overall balanced equation and the given concentrations of the reactants and products. (Note that pure liquid water, solid MnO 2, and solid copper are omitted from the expression for Q.) CHECK The answer has the correct units (V). The value of E cell is larger than E ○ cell, as expected based on Le Châtelier’s principle because one of the aqueous reactants has a concentration greater than standard conditions and the one aqueous product has a concentration less than standard conditions. Therefore, the reaction would have a greater tendency to proceed toward products and a greater cell potential. For Practice 18.8 An electrochemical cell is based on these two half-reactions: Example 18.8 Calculating E cell under Nonstandard Conditions

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition Gold can be plated out of a solution containing Au 3+ according to the half-reaction: Example 18.9 Stoichiometry of Electrolysis What mass of gold (in grams) is plated by the flow of 5.5 A of current for 25 minutes? SORT You are given the half-reaction for the plating of gold, which shows the stoichiometric relationship between moles of electrons and moles of gold. You are also given the current and time. You are asked to find the mass of gold that will be deposited in that time. STRATEGIZE You need to find the amount of gold, which is related stoichiometrically to the number of electrons that have flowed through the cell. Begin with time in minutes and convert to seconds. Then, since current is a measure of charge per unit time, use the given current and the time to find the number of coulombs. You can then use Faraday’s constant to calculate the number of moles of electrons and the stoichiometry of the reaction to find the number of moles of gold. Finally, use the molar mass of gold to convert to mass of gold.

© 2013 Pearson Education, Inc. Nivaldo J. Tro: Principles of Chemistry: A Molecular Approach, Second Edition CHECK The answer has the correct units (g Au). The magnitude of the answer is also reasonable considering that 10 amps of current for 1 hour is the equivalent of about mol of electrons (check for yourself), which would produce mol (or about 20 g) of gold. Continued SOLVE Follow the conceptual plan to solve the problem, canceling units to arrive at mass of gold. For Practice 18.9 Silver can be plated out of a solution containing Ag + according to the half-reaction: How much time (in minutes) does it take to plate 12 g of silver using a current of 3.0 A? Example 18.9 Stoichiometry of Electrolysis