The standard EMF of a galvanic cell can be calculated from — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Understand the Definition of Standard EMF ($E^\circ_{\text{cell}}$) The standard electromotive force (EMF) or standard cell potential ($E^\circ_{\text{cell}}$) of a galvanic (voltaic) cell represents the maximum potential difference between the cathode and the anode under standard state conditions. By standard IUPAC convention, the standard cell potential is calculated using the standard reduction potentials ($E^\circ$) of the two constituent half-cells: $$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$$ Where: * $E^\circ_{\text{cathode}}$ is the standard reduction potential of the reduction half-cell (the cathode, written on the right in a cell diagram). * $E^\circ_{\text{anode}}$ is the standard reduction potential of the oxidation half-cell (the anode, written on the left in a cell diagram). Step 2 - Analyze Standard State Conditions By definition, standard state conditions dictate: 1. The activity of all dissolved solute species (ions) is exactly $1.0\text{ M}$ (or unit activity). 2. The partial pressure of any gaseous reactant or product is exactly $1\text{ bar}$ (or $1\text{ atm}$). 3. The temperature is typically maintained at a constant reference point of $25^\circ\text{C}$ ($298.15\text{ K}$). Because all concentration-dependent terms in the Nernst equation become zero under these standard conditions ($\log(1) = 0$), the actual cell potential ($E_{\text{cell}}$) is exactly equal to the standard cell potential ($E^\circ_{\text{cell}}$): $$E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln(1) = E^\circ_{\text{cell}}$$ Step 3 - Evaluate and Explain the Options * **Option (A) is incorrect:** The size (or surface area) of the electrodes has no effect on the standard EMF ($E^\circ_{\text{cell}}$). While a larger electrode area can deliver more electric current (higher amperage) or decrease internal resistance, electrode potential is an **intensive property**. An intensive property does not depend on the size, volume, or quantity of the substance present. * **Option (B) is incorrect:** The pH of the solution represents the concentration of hydrogen ions ($[\ce{H^+}] = 10^{-\text{pH}}$). The actual cell potential ($E_{\text{cell}}$) depends on concentrations (including pH if hydrogen ions are involved in the cell reaction) according to the Nernst equation. However, the *standard* EMF ($E^\circ_{\text{cell}}$) is defined strictly at standard concentrations where $[\ce{H^+}] = 1.0\text{ M}$ (which corresponds to $\text{pH} = 0$). Hence, $E^\circ_{\text{cell}}$ is a constant at a given temperature and is completely independent of the actual operating pH of the solution. * **Option (C) is incorrect:** Similar to Option (A), the amount of metal present in the anode or cathode does not affect the cell potential. Potential difference is a thermodynamic property (related to $\Delta G^\circ = -nFE^\circ$), which represents work done per unit charge, making it independent of the total mass of the active metal. * **Option (D) is correct:** The standard cell potential depends solely on the chemical nature of the half-cells and is calculated directly from their standard reduction potentials ($E^\circ_{\text{cathode}}$ and $E^\circ_{\text{anode}}$). $$\text{Correct Option: } \boxed{\text{D}}$$