Given that E°_red = -1.66 V for Al³⁺/Al at 25°C,find E° and E for the concentration cell expressed using shorthand notation below.
Al(s) ∣ Al³⁺(1.0 × 10^-5 M) ∣∣ Al³⁺(0.100 M) ∣ Al(s)

Question

Quizplus · Accepted Answer

The shorthand notation for the concentration cell can be written as: Al(s)∣ Al³⁺(0.100 M)∣∣ Al³⁺(1.0 × 10^-5 M)∣ Al(s) The standard potential, E°, for the cell can be calculated using the Nernst equation: Ecell = E° - (0.0592 V/n) log(Q) where Q is the reaction quotient and n is the number of electrons transferred in the reaction. For this cell, the reaction is: Al³⁺ + 3e- → Al + 13H+ + P Using the concentrations given in the shorthand notation, the reaction quotient is: Q = [Al3+][H+]13/[Al³⁺] = 1.0 × 1013 Plugging in the values: E° = Ecell + (0.0592 V/n) log(Q) E° = (-1.66 V) + (0.0592 V/3) log(1.0 × 1013) E° = 0.00 V Therefore, the answer is either A or B. The voltage, E, for the cell can be calculated using the Nernst equation: Ecell = E° - (0.0592 V/n) log(Q) + (0.0592 V/n) log([H+]left/[H+]right) where [H+]left and [H+]right are the hydrogen ion concentrations on the left and right sides of the cell, respectively. For this cell, the hydrogen ion concentrations are: [H+]left = 1.0 × 10-5 M [H+]right = 0.100 M Plugging in the values: E = Ecell + (0.0592 V/n) log(Q) - (0.0592 V/n) log([H+]left/[H+]right) E = (0.00 V) + (0.0592 V/3) log(1.0 × 1013) - (0.0592 V/3) log(1.0 × 10-5/0.100) E = 0.12 V Therefore, the answer is B: E° = 0.00 V and E = +0.12 V.

Given That E°red = -1

Given That E°_red = -1