The Nernst Equation

Concentration and Ecell The voltage of a cell depends on the conditions of the cell. In non-standard conditions the voltage of a cell will be different: Ecell = E°cell - (RT/nF)ln(Q) Ecell = E°cell - (0.0591/n)log(Q) The Nernst Equation

Q not liquids or solids Q is the reaction Quotient: aA + bB  cC + dD Q = [C]c [D]d [A]a [B]b not liquids or solids

Concentration and Ecell With the Nernst Eq., we can determine the effect of concentration on cell potentials. Ecell = E°cell - (0.0591/n)log(Q) Example. Calculate the cell potential for the following: Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) Where [Cu2+] = 0.3 M and [Fe2+] = 0.1 M

Concentration and Ecell (cont.) • First, need to identify the two half reacions Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) Cu2+(aq) + 2e- Cu(s) E°1/2 = 0.34 V Fe(s) Fe 2+(aq) + 2e- E°1/2 = +0.44 V Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V

Concentration and Ecell (cont.) • Now, calculate Ecell Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V Ecell = E°cell - (0.0591/n)log(Q) Ecell = 0.78 V - (0.0591 /2)log(0.33) Ecell = 0.78 V - (-0.014 V) = 0.794 V

Determining Concentration • If [Cu2+] = 0.3 M, what [Fe2+] is needed so that Ecell = 0.76 V? Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) E°cell = +0.78 V Ecell = E°cell - (0.0591/n)log(Q) 0.76 V = 0.78 V - (0.0591/2)log(Q) 0.02 V = (0.0591/2)log(Q) 0.676 = log(Q) 4.7 = Q

Concentration and Ecell (cont.) Fe(s) + Cu2+(aq) Fe2+(aq) + Cu(s) 4.7 = Q [Fe2+] = 1.4 M