Nernst equation

The Nernst equation (named after Walther Nernst, rarely also Peterssche equation) describes the concentration dependence of the electrode potential of a redox couple (Ox z e -Red )

3.1 reduction
3.2 oxyhydrogen reaction
3.3 concentration elements
3.4 Concentration elements with different elements
3.6 lambda probes
3.7 Nernst equation in biology

Interpretation and Meaning

Any combination of two electrodes is called Galvanic cell (eg batteries or biological cells). Your open-circuit voltage U0 ( historically: Electromotive force ) is equal to the potential difference E of the electrodes on the half-cells as U0 = E = EAkzeptor when applying the Nernst equation - EDonator can be calculated. Similarly, it allows the calculation of the self-adjusting equilibrium activities when the half-cell voltage is applied.

The Nernst equation has central importance in electrochemistry, electroplating and electrochemical analysis because they are the electrical variable voltage (or electrode potential ) with the chemical Scale connects concentration. It is strictly valid only for cells without transfer and electroless processes, but provides a starting point for the derivation of equations in current-carrying electrochemical systems. The Nernst potential U0 multiplied by the charge zF for a molar metabolism zFUo gives the free energy. =? G - zFU0. The Nernst potential is therefore made to the chemical energy of the electrochemical reaction, divided by the charge involved.

Alternative formulations

The term Nernst equation is used depending on the application for different derived or advanced equations.

Special (historical ) Nernst equation

The original form, launched in 1889, the German physicist and chemist Walther Nernst using concentrations from c.

The factor RT / ze F is called the Nernst factor or electrode slope; a table of values for RT / ze F at different temperatures is located in the Item to the electrode slope.

General Nernst equation ( derivation )

For the change of the Gibbs energy ( free enthalpy ) of a chemical reaction, according to the substances

Involved applies

The relationship between and the logarithm is plausible, because on the one hand proportional to the number of particles (or the spelling of the chemical equation) is, on the other hand, in the activity quotient individual activities are considered with the power of the stoichiometric coefficients. The logarithm converts the exponent into a factor.

Obtained per the same ( electro) chemical potential as

Is at constant pressure and constant temperature of the reaction, maximum work that can be completely converted into useful electrical work. Due to the energy conservation law applies

Resulting in the general Nernst equation

The general Nernst equation allows for the considered reaction, the calculation of the equilibrium constants ( for ), direction ( for voluntary, enforced on ) and voltage supplied by the reaction is allowed to proceed if their redox half reactions in separate half-cells.

See also: chemical potential, electrochemical potential

Application

For the potentiometric titration

Reduction

For the reduction of

Is the general form directly into the former equation. This identity has two practical meanings:

The electrochemical series lists in principle reductions.
Since one can decompose any chemical reaction in the oxidation and reduction reaction steps of the redox pairs AE is the sum of the multiplied with the corresponding stoichiometric coefficients Nernst equations for the component reactions. The oxidation reactions are part of a negative stoichiometric coefficients.

Oxyhydrogen reaction

The partial reactions of the so-called hydrogen-oxygen reaction

Run as an oxidizing

Or reduction

Spatially separated into hydrogen-oxygen fuel cells. The resulting achievable voltage can be calculated using the Nernst equation and under standard conditions ΔE0 = 1.23 V.

Concentration elements

A condensing element is composed of two half cells, the electrolytes containing the same ingredients, but with a different ion concentration. Therefore, it is particularly suitable for demonstrating the Nernst equation.

An example is a copper concentration cell composed of two copper electrodes, and two copper sulfate solutions, which differ only in the concentration. When current flows then the concentrations in the cells of the same, for it then run from the following reactions:

The reduction in the half-cell with the greater concentration of copper ions CG:

The oxidation in the half-cell having a smaller copper ion concentration CK:

Using the Nernst equation for the sub- reaction or the general Nernst equation the total response obtained for the voltage of the copper concentration of the element AE:

As a general rule for the voltage of a concentration element:

In the temperature range of 22 to 26 ° C applies:

Concentration elements with different elements

When concentration cells with different elements and concentrations that deviate from normal conditions, the following formula is used:

A = factor in front of the oxidation side (example 4)
B = factor in front of the reduction side (example 2)

We consider H concentration elements ( ), then the Nernst equation is at room temperature ( T = 298.15 K ≙ 25 ° C), conversion of the natural logarithm of the logarithm (log a ( H ) = ln a ( H ) / ln 10) and in accordance with the definition of the pH value (pH = - lg A (H )) in the form

About. Glass electrodes for pH measurement in principle provide such a H - concentration elements dar. In them is a solution with a known pH. If contact with a solution of unknown pH produced, measures the associated meter a voltage directly to a pH - value is converted and displayed by the factor 0.059 V. The factor can vary the preparation, and must be calibrated before use, however, is always close to 0.059 V.

Lambda probes

With a lambda sensor, the sensor element is conductive for oxygen ions, is due to the concentration gradient of the oxygen between the air and exhaust gas, a voltage, which is used to adjust the lambda control, a desired mixture.

Nernst equation in biology

In biological systems, cell membranes separate areas from different ion concentrations. The membrane is selectively permeable to a specific ion, it will diffuse along the concentration gradient is formed at the same time, however, since the ion is charged, a voltage ( resting membrane potential). The Nernst equation can be the equilibrium position of this process describe.

Commonly used is a simplified form of the equation, where R, F and T ( 310 K) and the conversion factor for the logarithm to be put into a constant: