Question

Nernst equation for a electrochemistry cell​

Answer 1

Answer:

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction (half-cell or full cell reaction) to the standard electrode potential, temperature, and activities (often approximated by concentrations) of the chemical species undergoing reduction and oxidation ...

Answer 2

Explanation:

The Nernst equation is derived from the standard changes in the Gibbs free energy associated with an electrochemical transformation. For any electrochemical reduction reaction of the form

Ox + z e− → Red

standard thermodynamics says that the actual free energy change ΔG is related to the free energy change under standard state ΔGo by the relationship

{\displaystyle \Delta G=\Delta G^{\ominus }+RT\ln Q,} {\displaystyle \Delta G=\Delta G^{\ominus }+RT\ln Q,}

where Q is the reaction quotient. The electrochemical potential E associated with the electrochemical reaction is defined as the decrease in Gibbs free energy per coulomb of charge transferred, which leads to the relationship

{\displaystyle \Delta G=-zFE.} {\displaystyle \Delta G=-zFE.}

The constant F (the Faraday constant) is a unit conversion factor F = NAq, where NA is Avogadro's number and q is the fundamental electron charge. This immediately leads to the Nernst equation.

The Nernst equation for an electrochemical half-cell is

{\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln Q=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {a_{\text{Red}}}{a_{\text{Ox}}}}.} {\displaystyle E_{\text{red}}=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln Q=E_{\text{red}}^{\ominus }-{\frac {RT}{zF}}\ln {\frac {a_{\text{Red}}}{a_{\text{Ox}}}}.}

For a complete electrochemical reaction (full cell), the equation can also be written as

{\displaystyle E_{\text{cell}}=E_{\text{cell}}^{\ominus }-{\frac {RT}{zF}}\ln Q_{r},} {\displaystyle E_{\text{cell}}=E_{\text{cell}}^{\ominus }-{\frac {RT}{zF}}\ln Q_{r},} (total cell potential)

where

Ered is the half-cell reduction potential at the temperature of interest,

Eo

red is the standard half-cell reduction potential,

Ecell is the cell potential (electromotive force) at the temperature of interest,

Eo

cell is the standard cell potential,

R is the universal gas constant: R = 8.314472(15) J K−1 mol−1,

T is the temperature in kelvins,

a is the chemical activity for the relevant species, where aRed is the activity of the reduced form and aOx is the activity of the oxidized form. Similarly to equilibrium constants, activities are always measured with respect to the standard state (1 mol/L for solutes, 1 atm for gases). The activity of species x, aX , can be related to the physical concentrations cX via aX = γXcX, where γX is the activity coefficient of species X. Because activity coefficients tend to unity at low concentrations, activities in the Nernst equation are frequently replaced by simple concentrations.

F is the Faraday constant, the number of coulombs per mole of electrons: F = 9.64853399(24)×104 C mol−1,

z is the number of electrons transferred in the cell reaction or half-reaction,

Qr is the reaction quotient of the cell reaction.

At room temperature (25 °C),

RT

/

F

may be treated as a constant and replaced by 25.693 mV for cells.

The Nernst equation is frequently expressed in terms of base-10 logarithms (i.e., common logarithms) rather than natural logarithms, in which case it is written, for a cell at 25 °C:

{\displaystyle E=E^{0}+{\frac {0.059\;{\text{V}}}{z}}\log _{10}{\frac {a_{\text{Ox}}}{a_{\text{Red}}}}.} {\displaystyle E=E^{0}+{\frac {0.059\;{\text{V}}}{z}}\log _{10}{\frac {a_{\text{Ox}}}{a_{\text{Red}}}}.}

The Nernst equation is used in physiology for finding the electric potential of a cell membrane with respect to one type of ion.