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Intext Questions · 2.1

Q.How would you determine the standard electrode potential of the system Mg2+∣MgMg^{2+}|Mg?

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The standard electrode potential of Mg2+∣MgMg^{2+}|Mg cannot be measured directly because Mg reacts with water. We determine it indirectly by constructing a cell with a known reference electrode (like SHE), measuring the cell potential, and then using the Nernst equation to correct for non-standard conditions — the final value is −2.36 V-2.36\ \text{V}.

The standard electrode potential of a system like Mg2+∣MgMg^{2+}|Mg is defined as the potential of the half-cell Mg2+(aq,1 M)∣Mg(s)Mg^{2+}(aq, 1\ \text{M}) | Mg(s) measured against the Standard Hydrogen Electrode (SHE) at 298 K. But here’s the catch: magnesium metal is so reactive that it displaces hydrogen from water even in neutral solutions. If you dip a magnesium rod into a 1 M Mg2+Mg^{2+} solution, you’ll see bubbles of hydrogen gas — the Mg is actually reacting with water, not sitting quietly at equilibrium. That makes a direct measurement impossible.

So how do we get the value? We use a clever indirect method: construct a cell where the Mg half-cell is combined with a reference electrode whose potential is known, measure the cell potential under carefully controlled conditions, and then back-calculate the Mg potential.

Let’s walk through the actual experimental procedure step by step.

  1. Choose a reference electrode that doesn’t interfere. The Standard Hydrogen Electrode (SHE) is the universal reference, but it’s impractical for routine lab work. Instead, we often use a calomel electrode (saturated calomel electrode, SCE) or a silver-silver chloride electrode — these have stable, well-known potentials. For this explanation, let’s assume we use the SHE as the reference, since that’s the definition.

  2. Set up the cell carefully. We cannot simply put Mg metal in a 1 M Mg2+Mg^{2+} solution and connect it to the SHE, because the Mg will react with water. Instead, we use a non-aqueous solvent or a very carefully deoxygenated aqueous solution, and we work quickly. In practice, the measurement is done in a solution of MgSO4MgSO_4 or MgCl2MgCl_2 at exactly 1 M concentration, with the Mg electrode freshly polished and the solution thoroughly purged of dissolved oxygen. The cell is:

Pt, H2(g,1 atm)∣H+(aq,1 M)∣∣Mg2+(aq,1 M)∣Mg(s)\text{Pt, H}_2(g, 1\ \text{atm}) | H^+(aq, 1\ \text{M}) || Mg^{2+}(aq, 1\ \text{M}) | Mg(s)

  1. Measure the cell potential. A voltmeter (or potentiometer) connected between the two electrodes gives the electromotive force (emf) of the cell. Because the Mg electrode is more negative than the SHE, the measured cell potential will be positive if we connect the SHE as the cathode and Mg as the anode. Let’s say we measure Ecell=2.36 VE_{\text{cell}} = 2.36\ \text{V} at 298 K.

  2. Apply the cell potential equation. For a cell written as:

Anode (oxidation): Mg(s)→Mg2+(aq)+2e−\text{Anode (oxidation): } Mg(s) \rightarrow Mg^{2+}(aq) + 2e^-

Cathode (reduction): 2H+(aq)+2e−→H2(g)\text{Cathode (reduction): } 2H^+(aq) + 2e^- \rightarrow H_2(g)

The overall cell reaction is:

Mg(s)+2H+(aq)→Mg2+(aq)+H2(g)Mg(s) + 2H^+(aq) \rightarrow Mg^{2+}(aq) + H_2(g)

The cell potential is the difference between the cathode and anode potentials:

Ecell=Ecathode−EanodeE_{\text{cell}} = E_{\text{cathode}} - E_{\text{anode}}

Here, Ecathode=EH+/H2∘=0 VE_{\text{cathode}} = E^\circ_{H^+/H_2} = 0\ \text{V} (by definition), and Eanode=EMg2+/Mg∘E_{\text{anode}} = E^\circ_{Mg^{2+}/Mg} (the value we want). So:

2.36 V=0 V−EMg2+/Mg∘2.36\ \text{V} = 0\ \text{V} - E^\circ_{Mg^{2+}/Mg}

Therefore:

EMg2+/Mg∘=−2.36 VE^\circ_{Mg^{2+}/Mg} = -2.36\ \text{V}

Watch out

A common mistake is to forget the sign convention. The measured cell potential is positive when the SHE is the cathode, meaning the Mg electrode is the anode (oxidation occurs there). The standard reduction potential of Mg is therefore negative. If you reverse the cell, you’d get a negative reading — but the standard reduction potential is always defined for the reduction reaction Mg2++2e−→MgMg^{2+} + 2e^- \rightarrow Mg.

  1. Is it really that simple? In practice, the measurement isn’t done at exactly 1 M concentrations because of the reactivity issue. Instead, we measure the cell potential at a known, lower concentration of Mg2+Mg^{2+} (say 10−3 M10^{-3}\ \text{M}) and then use the Nernst equation to extrapolate to standard conditions. The Nernst equation for the Mg half-cell is:

EMg2+/Mg=EMg2+/Mg∘+0.0592log⁡[Mg2+]E_{Mg^{2+}/Mg} = E^\circ_{Mg^{2+}/Mg} + \frac{0.059}{2} \log [Mg^{2+}]

(at 298 K, using base-10 log). If we measure the cell potential at [Mg2+]=10−3 M[Mg^{2+}] = 10^{-3}\ \text{M}, we get a different EcellE_{\text{cell}}, and we solve for EMg2+/Mg∘E^\circ_{Mg^{2+}/Mg}.

Tip

The factor 0.059n\frac{0.059}{n} comes from 2.303RTF\frac{2.303RT}{F}. At 298 K, 2.303RT/F≈0.05916 V2.303RT/F \approx 0.05916\ \text{V}. For Mg, n=2n=2, so the slope is about 0.0296 V0.0296\ \text{V} per decade of concentration change.

  1. Confirm with multiple concentrations. To be rigorous, we measure EcellE_{\text{cell}} at several different Mg2+Mg^{2+} concentrations, plot EcellE_{\text{cell}} vs. log⁡[Mg2+]\log[Mg^{2+}], and extrapolate to log⁡[Mg2+]=0\log[Mg^{2+}] = 0 (i.e., 1 M). The intercept gives EMg2+/Mg∘E^\circ_{Mg^{2+}/Mg} directly. This also checks that the system obeys the Nernst equation (the slope should be 0.0296 V0.0296\ \text{V}), confirming that the electrode is behaving reversibly.

Ecell=Ecathode∘−(EMg2+/Mg∘+0.0592log⁡[Mg2+])E_{\text{cell}} = E^\circ_{\text{cathode}} - \left( E^\circ_{Mg^{2+}/Mg} + \frac{0.059}{2} \log[Mg^{2+}] \right)

At 298 K, with SHE as cathode (E∘=0E^\circ = 0), this simplifies to:

Ecell=−EMg2+/Mg∘−0.0592log⁡[Mg2+]E_{\text{cell}} = -E^\circ_{Mg^{2+}/Mg} - \frac{0.059}{2} \log[Mg^{2+}]

  1. The accepted value. Through such careful experiments, the standard electrode potential of the Mg2+∣MgMg^{2+}|Mg system is determined to be −2.36 V-2.36\ \text{V} (vs. SHE). This large negative value reflects magnesium’s strong tendency to lose electrons — it’s a powerful reducing agent.
Important

The standard electrode potential is an intensive property: it doesn’t depend on how much Mg or Mg2+Mg^{2+} you have. It’s a measure of the thermodynamic tendency for the reduction reaction Mg2++2e−→MgMg^{2+} + 2e^- \rightarrow Mg to occur. The more negative the value, the stronger the reducing agent.

✓Final answer

The standard electrode potential of Mg2+∣MgMg^{2+}|Mg is determined indirectly by measuring the cell potential against a reference electrode (like SHE) and applying the Nernst equation, yielding −2.36 V\boxed{-2.36\ \text{V}}.

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