The Nernst Equation Concentration and Ecell The voltage

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/n. F)ln(Q) Ecell = E°cell - (0. 0591/n)log(Q) The Nernst Equation

Q Q is the reaction Quotient: a. A + b. B c. C + d. D 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) + Cu 2+(aq) Fe 2+(aq) + Cu(s) Where [Cu 2+] = 0. 3 M and [Fe 2+] = 0. 1 M

Concentration and Ecell (cont. ) • First, need to identify the two half reacions Fe(s) + Cu 2+(aq) + 2 e- Fe(s) + Cu 2+(aq) Fe 2+(aq) + Cu(s) Fe 2+(aq) + 2 e- E° 1/2 = 0. 34 V E° 1/2 = +0. 44 V Fe 2+(aq) + Cu(s) E°cell = +0. 78 V

Concentration and Ecell (cont. ) • Now, calculate Ecell Fe(s) + Cu 2+(aq) Fe 2+(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 [Cu 2+] = 0. 3 M, what [Fe 2+] is needed so that Ecell = 0. 76 V? Fe(s) + Cu 2+(aq) Fe 2+(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) + Cu 2+(aq) Fe 2+(aq) + Cu(s) 4. 7 = Q [Fe 2+] = 1. 4 M