Calculate E°_cell for each balanced redox reaction and determine if the reaction is spontaneous as written. a. O₂(g) + 2 H₂O(l) + 4 Ag(s) → 4 OH^–(aq) + 4 Ag⁺(aq) b. Br₂(l) + 2 I^–(aq) → 2 Br^–(aq) + I₂(s)

Verified step by step guidance

1. Step 1: Identify the half-reactions. The reduction half-reaction is O2(g) + 2 H2O(l) + 4 e- → 4 OH-(aq). The oxidation half-reaction is 4 Ag(s) → 4 Ag+(aq) + 4 e-.
2. Step 2: Look up the standard reduction potentials for each half-reaction in a table of standard reduction potentials. The standard reduction potential for the reduction of O2 to OH- is +0.40 V. The standard reduction potential for the oxidation of Ag to Ag+ is +0.80 V.
3. Step 3: Calculate the standard cell potential (Ec°ell) using the formula Ec°ell = E°cathode - E°anode. In this case, the cathode is the reduction half-reaction and the anode is the oxidation half-reaction.
4. Step 4: If the calculated Ec°ell is positive, the reaction is spontaneous as written. If it is negative, the reaction is non-spontaneous as written.
5. Step 5: Remember that standard cell potentials are calculated under standard conditions (1 M concentrations, 1 atm pressure, 25°C). If the conditions are different, the actual cell potential may be different from the standard cell potential.

Key Concepts

Standard Electrode Potential (Ec°ell)

The standard electrode potential, Ec°ell, is a measure of the tendency of a chemical species to be reduced, expressed in volts. It is determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). The overall cell potential for a redox reaction can be calculated by subtracting the reduction potential of the anode from that of the cathode, indicating whether the reaction can occur spontaneously.

Redox Reactions

Redox reactions involve the transfer of electrons between two species, where one is oxidized (loses electrons) and the other is reduced (gains electrons). In these reactions, the oxidation state of the elements changes, and they can be balanced using half-reactions. Understanding the oxidation states and identifying the oxidizing and reducing agents is crucial for analyzing redox processes.

Spontaneity of Reactions

A reaction is considered spontaneous if it occurs without external intervention, which can be determined by the sign of the cell potential (Ec°ell). If Ec°ell is positive, the reaction is spontaneous as written; if negative, it is non-spontaneous. This concept is rooted in thermodynamics, where spontaneous processes tend to increase the overall entropy of the system.