For a galvanic cell operating at 298 K , the overall cell reaction is given as: 2 Al(s) + 3 Cu ²⁺(0.001 M ) 2 Al ³⁺(0.001 M ) + 3 Cu(s) If the standard cell potential ( E^ _ cell ) for this reaction is 2.00 V , what is the operating electromotive force (emf) of the cell? (Assume 2.303 RT F = 0.059 V at 298 K )

Step-by-step solution

The given cell reaction is: 2 Al(s) + 3 Cu ²⁺(0.001 M ) 2 Al ³⁺(0.001 M ) + 3 Cu(s) The number of electrons transferred in the balanced reaction is n = 6 . The reaction quotient Q is given by: Q = [ Al ³⁺]^2 [ Cu ²⁺]^3 Substituting the given concentrations: Q = (10⁻³)^2 (10⁻³)^3 = 10⁻⁶ 10⁻⁹ = 10^3 Using the Nernst equation: E_ cell = E^ _ cell - 0.059 n Q Substituting the values: E_ cell = 2.00 - 0.059 6 (10^3) E_ cell = 2.00 - 0.059 6 3 E_ cell = 2.00 - 0.059 2 E_ cell = 2.00 - 0.0295 = 1.9705 V Answer: 1.9705 V