Standard cell potential

When two half cells are combined using an external circuit and salt bridge, a potential difference arises due to the different electrode potentials of the two half cells.

The cell with the more negative potential will attempt to push electrons around the external circuit towards the less negative half cell. The measured potential (using a high resistance voltmeter) is called the cell potential - it is equal to the DIFFERENCE between the electrode potentials of the two half cells.

The direction of (attempted) flow is from the cell with the most negative potential to the cell with the least negative (most positive) potential.

Example:In the following cell made up of two half cells the standard electrode potential of zinc = -0.76V and that of copper is +0.34V

The cell potential is the difference between the standard electrode potential values

= -0.76 - +0.34 = -1.10V

The zinc half cell has the most negative potential and so the direction of electron flow would be from the zinc half cell to the copper half cell.

Reactions occuring in the half cells

As the zinc half-cell releases electrons then..

Zn ⇋ Zn²⁺ + 2e

As the copper half-cell accepts electrons then..

Cu²⁺ + 2e → Cu

Adding these two reactions gives the overall cell reaction as:

Zn + Cu²⁺ → Zn²⁺ + Cu

cell potential = 1.10 V

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Spontaneity of a reaction

Spontaneous in this context does not mean 'happens immediately'. It just means that the reaction is possible in terms of the energetics (thermodynamics) of the process. Another word that could be used is 'feasible'.

Feasible reactions can be identified from the relative electrode potential values of the reacting species.

Any combination of an oxidising agent with a reducing agent, where the difference in electrode potentials is greater than 0.3 V. Basically something on the left will react with something higher up from the right hand side.

The equations for the reactions can be constructed by first balancing the number of electrons in each half-equation and then adding the half-equations together.

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Prediction of spontaneity

Electrode potentials for redox systems can be used to predict whether or not a proposed reaction could proceed. Take the reaction between copper ions and zinc metal. The two half-equations are:

Zn²⁺ + 2e ⇋ Zn

Cu²⁺ + 2e ⇋ Cu

The zinc half-equation is reversed and added to the copper half-equation:

Cu²⁺ + Zn ⇋ Cu + Zn²⁺

This is the proposed reaction. By inspection we can see that if the reaction proceeds the copper ions are going to be reduced (they have electrons added) and the zinc atoms are going to be oxidised (they have electrons removed).

The zinc is said to be the oxidised state (the part getting oxidised) and the copper ions the reduced state (the part getting reduced).

To find spontaneity we apply the equation:

E^o (species that gets reduced) - E^o (species that gets oxidised) = E^o (cell potential)

• If the E (cell potential) is negative then there is no reaction between these species
• If the value given lies between 0 and 0.3 then an equilibrium is established
• If the value for E (cell) is greater than +0.3 then reaction between these species is spontaneous

As:

Cu²⁺ + 2e ⇋ Cu      E^o = +0.34V

and

Zn²⁺ + 2e ⇋ Zn     E^o = -0.76V

then

E = E (red) - E (ox)

E = +0.34 - (-0.76)V

E = + 1.10V

The answer is positive and greater than 0.3V therefore the reaction is spontaneous - zinc reacts with copper ions.

Feasible reactions can be identified by any combination of an oxidising agent with a reducing agent, where the difference in electrode potentials is greater than 0.3 V. Basically something on the left will react with something higher up from the right hand side.

The equations for the reactions can be constructed by first balancing the number of electrons in each half-equation and then adding the half-equations together.

Example: Construct the equation for the reaction between dichromate ions and tin 2+ ions

The dichromate half-equation is:

1Cr₂O₇^2-(aq) + 14H⁺(aq) + 6e^- → 2Cr³⁺(aq) + 7H₂O(l)      (E^o = + 1.33 V)

And the tin 2+ half-equation is:

2Sn⁴⁺(aq) + 2e^- → Sn²⁺(aq)     (E^o = 0.55 V)

By inspection we can see that the dichromate equation needs six electrons on the left hand side whereas the tin 2+ equation has only two electrons on the right hand side. We must, then, multiply the tin 2+ equation by three before adding them.

Whether or not the reaction will be spontaneous is decided by applying E = E (red) - E (ox)

In this case the Cr₂O₇^2- is reduced and the Sn²⁺ oxidised therefore

E = 1.33 - 0.55 = 0.78 V

This is a positive value greater than 0.3 therefore the reaction is spontaneous.

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Exceptions

1 These standard electrode potential values refer to standard conditions i.e. 1.0 Molar concentrations at 25^oC and atmospheric pressure. If these conditions change then so does the electrode potential. In other words, for calculating cell potential, or spontaneity of reaction, it is important to understand that variations occur.

For example, according to standard electrode potentials, manganese IV oxide will not react spontaneously with hydrochloric acid, however this is the standard preparation of chlorine in the laboratory.

In the lab preparation the manganese IV oxide is heated with the concentrated HCl - these are not standard conditions, the temperature is much greater than 25^oC and the concentration of the acid much greater than 1.0 mol dm^-3. Under these new conditions the reaction becomes spontaneous and proceeds at a comfortable rate to collect the chlorine gas produced.

MnO₂(s) + 4H⁺(aq) + 2Cl^-(aq) → Mn2+ + 2H₂O(l) + Cl₂(g)

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