The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal M is: M(s)|M+(aq;0.05molar)||M+(aq), 1molar)|M(s). For the above electrolytic cell the magnitude of the cell potential |Ecell|=70mV. For the above cell:

M(s) + M+(aq) 1M → M+(aq) 0.05M + M(s)

The given cell is a concentration cell. In a concentration cell, the cell potential is generated due to a difference in the concentration of the same ion in two half-cells. The Nernst equation can be used to calculate the cell potential:

Ecell = E°cell - (RT/nF)lnQ

where:

• Ecell is the cell potential
• E°cell is the standard cell potential (which is 0 for a concentration cell)
• R is the ideal gas constant
• T is the temperature in Kelvin
• n is the number of electrons transferred (in this case, n=1)
• F is Faraday's constant
• Q is the reaction quotient

For the given concentration cell, the reaction quotient Q is:

Q = [M+(aq, 0.05M)] / [M+(aq, 1M)] = 0.05

Since E°cell = 0 for a concentration cell, the Nernst equation simplifies to:

Ecell = - (RT/nF)lnQ

Since Q = 0.05 < 1, lnQ will be negative. Therefore, Ecell will be positive.

The Gibbs free energy change (ΔG) is related to the cell potential by:

ΔG = -nFEcell

Since Ecell > 0, ΔG will be negative. Therefore, the correct option is Ecell > 0; ΔG < 0