How would you determine the standard electrode potential of the system Mg²⁺ | Mg?
To determine the standard electrode potential of Mg²⁺ | Mg, we need to construct a cell using the standard hydrogen electrode (SHE) as the reference half-cell (anode) and the Mg²⁺ | Mg half-cell as the cathode.
The cell is represented as: Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M) || Mg²⁺(aq, 1 M) | Mg. The concentration of Mg²⁺ ions in the solution should be unity (1 M).
The emf of this cell is measured at 298 K. Since the standard electrode potential of SHE is taken as zero (E⁰_L = 0), the measured emf directly gives the standard electrode potential of the Mg²⁺ | Mg system. This follows from the relation: E⁰ = E⁰_R - E⁰_L = E⁰_R - 0 = E⁰_R.
Explanation
The textbook context explains that at 298 K, when a cell is constructed with SHE as the anode (reference half-cell) and another half-cell as the cathode, the measured emf gives the reduction potential of that half-cell. When concentrations of all species are unity, this equals the standard electrode potential. The example of Cu²⁺ | Cu determination (0.34 V) illustrates this principle. Since E⁰_L for SHE is zero, the formula E⁰ = E⁰_R - E⁰_L simplifies to E⁰ = E⁰_R, making the measured emf directly equal to the standard electrode potential of the Mg²⁺ | Mg system.
Solution Steps
Step 1: Construct a cell with SHE as anode and Mg²⁺ | Mg half-cell as cathode
Step 2: Maintain unity concentration (1 M) of Mg²⁺ ions in solution
Step 3: Measure the emf of the cell at 298 K
Step 4: The measured emf equals the standard electrode potential of Mg²⁺ | Mg since E⁰(SHE) = 0