Q.Using the standard reduction potentials $E^{\circ}(\text{Cu}^{2+}/\text{Cu}) = +0.34\ \text{V}$ and $E^{\circ}(\text{Zn}^{2+}/\text{Zn}) = -0.76\ \text{V}$, calculate the standard EMF, $E^{\circ}_{cell}$, of the Daniell cell.

Electrode potential is governed jointly by the identity of the metal, the temperature, and the concentration of the ions in solution around the electrode (Nernst equation).

The electrode potential of a metal electrode M dipped in a solution of its own ions $M^{n+}$ is given by the Nernst equation:

$E_{M^{n+}/M} = E^\ominus_{M^{n+}/M} - \dfrac{0.059}{n}\log\dfrac{1}{[M^{n+}]} \quad \text{(at 298 K)}$

• Nature of the metal: $E^\ominus$ (the standard electrode potential) is an intrinsic property of the metal — different metals have very different tendencies to lose or gain electrons, so $E^\ominus$ differs from metal to metal.
• Concentration of the solution: the log term shows the potential varies with the ion concentration $[M^{n+}]$ around the electrode.
• Temperature: both $E^\ominus$ itself and the $0.059/n$ (really $RT/nF$) factor are temperature-dependent, so electrode potential changes with temperature.

All three factors together determine the actual (non-standard) electrode potential.

A negative standard reduction potential means the species is easier to oxidise (a weaker oxidising agent) than the reference $H^+/H_2$ couple.

Meaning of the sign

Standard electrode potentials are measured relative to the Standard Hydrogen Electrode (SHE), $E^0_{H^+/H_2}=0.00\ V$, for the reduction half-reaction $2H^++2e^-\rightarrow H_2$.

For zinc, $E^0_{Zn^{2+}/Zn}=-0.76\ V$ refers to $Zn^{2+}+2e^-\rightarrow Zn$. A negative value means this reduction is less favourable (occurs with a lower tendency) than the reduction of $H^+$ to $H_2$. Equivalently, the reverse (oxidation) reaction,

$Zn\rightarrow Zn^{2+}+2e^-$

is more favourable than the oxidation of $H_2$ to $H^+$. So metallic zinc is oxidised in preference to hydrogen — Zn is a stronger reducing agent than $H_2$, and $Zn^{2+}$ is a weaker oxidising agent than $H^+$.

This is exactly why zinc, sitting above hydrogen in the electrochemical (activity) series, displaces $H_2$ from dilute acids: $Zn+2H^+\rightarrow Zn^{2+}+H_2$.

By international convention, the standard hydrogen electrode is assigned an electrode potential of exactly 0 V so it can serve as the reference against which all other electrode potentials are measured.

Since the absolute potential of a single electrode cannot be measured directly (only the potential difference between two electrodes, i.e. a full cell, can be measured), chemists needed a universal reference point. The Standard Hydrogen Electrode (SHE) — Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M) — was chosen as this reference and its standard reduction potential was arbitrarily fixed at 0.00 V at 298 K. All other standard electrode potentials (like Zn²⁺/Zn = −0.76 V or Cu²⁺/Cu = +0.34 V) are reported relative to this SHE.

The standard hydrogen electrode is the universal reference electrode, and its electrode potential is arbitrarily fixed at exactly zero volts at all temperatures.

The standard hydrogen electrode (SHE) consists of a platinum electrode coated with platinum black, dipped in a 1 M H⁺ solution, with H2 gas bubbled at 1 bar pressure and 298 K.

$2H^{+}(aq, 1M) + 2e^{-} \rightleftharpoons H_2(g, 1\ bar)$

Since absolute electrode potentials cannot be measured, the SHE is assigned a reference value of 0.00 V by international convention, and all other standard electrode potentials are measured relative to it.

By convention, the Standard Hydrogen Electrode (SHE) is assigned a standard electrode potential of exactly $0.0\ \text{V}$.

Since absolute electrode potentials cannot be measured directly, the SHE — a platinum electrode in contact with $\text{H}_2$ gas at 1 bar, dipped in a 1 M $\text{H}^+$ solution at 298 K — is chosen as the reference electrode against which all other standard electrode potentials are measured. It is arbitrarily assigned $E^\circ = 0.0\ \text{V}$.

A single electrode's absolute potential cannot be measured directly; it is obtained by constructing a cell of the $Mg$ electrode against the standard hydrogen electrode (SHE), whose potential is arbitrarily fixed at exactly $0$ volts.

It is impossible to measure the potential of a single (isolated) electrode because any measurement necessarily needs a complete circuit, i.e. a second electrode. Therefore, standard electrode potentials are always measured relative to a reference electrode — the Standard Hydrogen Electrode (SHE), $Pt, H_2(1\ bar)|H^+(1\ M)$, whose standard reduction potential is, by convention, assigned the value $0.00\ V$ at all temperatures.

Method: A galvanic cell is set up by combining the $Mg^{2+}(aq, 1\ M)|Mg(s)$ electrode with the SHE:

$Mg(s)|Mg^{2+}(1\ M)\ ||\ H^+(1\ M)|H_2(1\ bar), Pt(s)$

Magnesium, being more reactive (a stronger reducing agent) than hydrogen, acts as the anode (oxidation), while the SHE acts as the cathode (reduction). The emf of this cell is measured using a potentiometer under standard conditions ($298\ K$, $1\ M$ concentration, $1\ bar$ pressure). Since $E^\circ_{SHE} = 0$, the measured cell emf directly equals the standard reduction potential of the $Mg^{2+}/Mg$ electrode:

$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode} = 0 - E^\circ_{Mg^{2+}/Mg}$

Experimentally this gives $E^\circ_{Mg^{2+}/Mg} = -2.37\ V$.

Platinum is a common inert electrode.

Electrode potential measures how strongly a metal electrode tends to get oxidised or reduced relative to a reference (the standard hydrogen electrode).

When a metal electrode is dipped into a solution of its own ions, an equilibrium is set up at the metal–solution interface, and a potential difference develops between the metal and the solution due to the tendency of the metal to lose electrons (oxidation, giving reduction/oxidation potential) or of the ions to gain electrons (reduction). This tendency, measured relative to the standard hydrogen electrode (taken as 0 V), is called the electrode potential of that electrode.

Standard electrode potential is the reduction potential of a half-cell measured under standard-state conditions (1M, 1 atm, 298K), relative to the standard hydrogen electrode, which is arbitrarily assigned 0V.

Since the potential of a single electrode cannot be measured in isolation, it is always measured relative to a reference electrode — the standard hydrogen electrode (SHE), whose reduction potential is, by convention, taken as exactly 0.00 V under standard conditions. The standard electrode potential of any other electrode, E°, is then defined as the potential difference (EMF) developed by a cell consisting of that electrode (with its ion at 1M concentration, or gas at 1 atm pressure, at 298 K) coupled to the SHE. If the electrode has a greater tendency to be reduced than H$^+$/H$_2$, its E° is positive; if it has a lesser tendency (i.e. it more readily gets oxidised), its E° is negative.

A platinum electrode conducts electrons between the external circuit and the non-conducting $Cl_2$/$Cl^-$ couple without itself reacting, exactly as in the standard hydrogen electrode.

Since gaseous $Cl_2$ cannot itself conduct electrons to/from an external circuit, an inert, chemically unreactive but electronically conducting metal (platinum, platinised platinum) is used as the physical electrode. Chlorine gas is bubbled over the platinum surface, which is also in contact with the solution containing $Cl^-$ ions. Electron transfer for the half-reaction $Cl_2 + 2e^- \rightleftharpoons 2Cl^-$ then occurs at the platinum metal surface — the platinum simply provides a conducting surface for electron exchange and does not itself get oxidised or reduced (the same principle used in the standard hydrogen electrode).

The Standard Hydrogen Electrode (SHE) is the reference electrode, and its potential is fixed at 0 V by convention.

All electrode potentials in electrochemistry are relative values — they are measured against a chosen reference electrode. The Standard Hydrogen Electrode (SHE), consisting of platinum foil coated with platinum black, dipped in 1 M H⁺ solution, with H₂ gas bubbled at 1 bar pressure and 298 K, is internationally agreed as this reference.

By convention, the standard reduction potential of the SHE is arbitrarily assigned the value 0.00 V at all temperatures:

$2H^+(aq) + 2e^- \rightarrow H_2(g), \quad E^\circ = 0.00\ V$

Every other electrode's standard potential is then measured by pairing it with SHE and measuring the cell EMF — a positive value means the electrode is a better reducing agent for H⁺ than H₂ is, and vice versa.