A galvanic cell is constructed using two generic metals A and B . The cell reaction is given as: A(s) + B²⁺(aq) A²⁺(aq) + B(s) The equilibrium constant K for this reaction is 10¹⁶ at 298 K . If the concentrations of the aqueous ions are [A²⁺] = 10⁻⁴ M and [B²⁺] = 10⁻² M , the actual cell potential E_ cell is ________ 10⁻² V . (Given: 2.303RT F = 0.06 V )

Step-by-step solution

The standard cell potential E^ _ cell is related to the equilibrium constant K by the equation: E^ _ cell = 2.303RT nF K For the given reaction, the number of electrons transferred is n = 2 . E^ _ cell = 0.06 2 (10¹⁶) E^ _ cell = 0.03 16 = 0.48 V The reaction quotient Q is: Q = [A²⁺] [B²⁺] = 10⁻⁴ 10⁻² = 10⁻² Using the Nernst equation to find the non-standard cell potential E_ cell : E_ cell = E^ _ cell - 2.303RT nF Q E_ cell = 0.48 - 0.06 2 (10⁻²) E_ cell = 0.48 - 0.03 (-2) E_ cell = 0.48 + 0.06 = 0.54 V Converting