R09 Electrode-concentration cells

Illustration R9 shows an electrochemical cell consisting of two hydrogen electrodes as half-cells, only differing in the concentration of hydrochloric acid: 0.1 mol/L in the half-cell on the left and 1 mol/L in the half-cell on the right. Hydrogen is passed over both platinum electrodes at a pressure of 1 atmosphere (1013 hPa) and the temperature is 25°C. The right-hand electrode is therefore a standard hydrogen electrode and = 0 V . The pH of the left-hand half-cell is 1 (Concentration of H⁺ = 0.1 mol/L). The half-reaction equation for both half-cells is:

Which is a 2 electron reaction with an expression for Q_c of :

The voltmeter detects a potential difference between the two half-cells. This can only result from the difference in concentration, since all other factors are identical The actual reduction potential for the left-hand, non-standard half-cell reaction can be determined using the Nernst equation:

This value indicates that the left-hand half-cell is a stronger reducing agent than the right-hand standard half-cell. The lower the concentration of hydrogen ions in the left-hand half-cell , i.e. the higher the pH, the more negative the potential of the left-hand half-cell. The potential for this cell, E_cell, is the difference between the reduction potential of the cathode (right-hand half-cell) E_C and the reduction potential of the anode (left-hand half-cell), E_A:

This can be seen to have a positive value numerically equal to the value for E_A calculated using the Nernst equation. The cell convention is to assign a positive value of E_cell to an electrochemical cell-reaction when the reaction is written down in the direction of self-sustaining change. A negative value for is required for a self-sustaining (spontaneous) reaction and since = -nFE_cell it is clear that if E_cell is positive is negative.
The fact that the potential difference between two otherwise identical cells varies with pH is used in a potentiometric pH meter, despite the fact that the hydrogen electrode is not well suited for routine pH measurement since it is a source of gaseous hydrogen and is sensitive to various poisons that inhibit the activity of the platinised surface of the electrode. This potential difference can also be used to calculate an unknown concentration of a solution using the same electrochemical cell as shown in illustration R9.