Electrode potentials and calculations

​​In a nutshell

Electrode potentials of the half-cells are used to calculate the cell potential of an electrochemical cell in volts $$V$$. Standard electrode potentials are calculated using a hydrogen half-cell under standard conditions of $$298\ K, 100\ kPa$$ and solutions of $$1.00\ mol\ dm^{-3}$$ to compare the electrode potentials of different metals.

​​Equations

Electrode potentials in half-cells

In an electrochemical cell, the half-cells (electrodes) each have an electrode potential. The electrode potential $$E$$, is a measure of the electrode's ability to lose electrons (oxidation) and is measured in volts $$V$$​. 

The half-cell which is oxidised (anode) will have a positive electrode potential whereas the half-cell which is reduced (cathode) will have a negative electrode potential. The potential difference is the charge difference between the electrode and the ions in the solution.

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Example

For the reaction in an electrochemical cell: 

​​1. Anode (Oxidation) 2. Salt bridge 3. Voltmeter 4. Cathode (Reduction)

$$Zn+Cu^{2+}\leftrightharpoons Cu+Zn^{2+}$$

Anode: $$Zn\rightarrow Zn^{2+}+2e^-$$

Cathode: $$Cu^{2+}+2e^-\rightarrow Cu$$​​

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At the anode, as electrons build up to produce a negative charge, there will be more positive $$Zn^{2+}$$ions built up in the solution which creates a potential difference.​

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Electrochemical cells can be represented in a simplistic way to show the two half-cells. The anode is shown on the left and the cathode is shown on the right which are separated by two dotted lines. The oxidised species are in the middle and reduced species on the outside, separated by single dotted lines.

For standard hydrogen electrodes, these are always shown on the left of the diagram. The oxidised and reduced forms of hydrogen are shown and the inert electrode $$(Pt,Pb)$$ is shown furthest left. ​

Example

Draw a simplified drawing for a $$Zn/Cu$$ electrochemical cell.

Standard hydrogen electrodes

Standard hydrogen electrodes are used as a reference electrode to measure standard electrode potentials of half-cells and has a value of $$0.00\ V$$​. The standard electrode potential $$E^{\theta}$$ is the voltage of a half-cell when connected to a standard hydrogen electrode under standard conditions. 

Standard conditions 

The standard conditions required is a temperature of $$298\ K\ (25\ ^oC)$$, a pressure of $$100\ kPa\ (1\ atm)$$, and an ion concentration of $$1.00\ mol\ dm^{-3}$$ in the solutions. 

These conditions can impact the equilibrium position, therefore affect the electrode potentials. Standard conditions are used to eliminate these factors and allow comparisons of different cell potentials. 

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Example

This is a typical standard hydrogen electrode which would be used to measure the potential of the $$Fe$$ electrode. 

Note: Hydrogen electrodes are always shown on the left in diagrams.

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Half cell equations:

​$$2H^++2e^-\rightarrow H_2$$

$$E^\theta(H_2)=0.00 \ V$$

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​$$Fe\rightarrow Fe^{2+}+2e^-$$

$$E^\theta(Fe)=-0.42\ V$$​​

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Cell potential

The difference in voltage $$V$$ between the half cells is referred to as the cell potential or the electromotive force (EMF), written as $$E_{cell}$$. The cell potential shows the flow of electrons and can be calculated using this equation:

$$Cell\ potential=Reduction\ potential-Oxidation\ potential$$

​$$E_{cell}=(E^\theta_{reduction}-E^\theta_{oxidation})$$​​

Example

​$$Mg+\frac{1}{2}O_2\rightarrow MgO$$​​

​$$Mg\rightarrow Mg^{2+}+2e^-\ E^\theta=-1.75\ V$$

$$\frac{1}{2}O_2 +2e^-\rightarrow O^{2-}\ E^\theta=+0.89\ V$$

Magnesium has been oxidised as it has lost electrons and increased in oxidation number whereas oxygen has been reduced as it has gain electrons and decreased in oxidation number. 

Therefore, you can work out the $$E_{cell}$$: 

$$E_{cell}=(E^\theta_{reduction}-E^\theta_{oxidation})$$

$$E_{cell}=+0.89-(-1.75)$$​​

$$E_{cell}=+0.89+1.75$$

$$E_{cell}=+2.64\ V$$

The cell potential is $$\underline{+2.64\ V}$$.

Note: All cell potentials will be positive as the negative oxidation potential is subtracted from the positive reduction potential.