12. An electrochemical cell (galvanic cell) is designed by coupling a Zn electrode with a standard hydrogen electrode (SHE). Given, [tex]E_{\text{Zn}^2+/ \text{Zn}} = -0.76 \text{ V}[/tex]
### i) Draw the galvanic cell To draw the galvanic cell, we can provide a detailed description since a physical drawing isn't feasible in this format. A galvanic cell involves two half-cells connected by a salt bridge or a porous membrane. In this case, the galvanic cell consists of a zinc electrode and a standard hydrogen electrode (SHE).
Description of the galvanic cell: - Anode: Zinc electrode (Zn) - Anode reaction (oxidation): Zn → Zn²⁺ + 2e⁻ - Cathode: Standard Hydrogen Electrode (SHE) - Cathode reaction (reduction): 2H⁺ + 2e⁻ → H₂ - Salt bridge: To complete the circuit
The overall cell is described as: ``` Zn electrode | Zn²⁺ (solution) || H⁺ (solution) | Standard Hydrogen Electrode (SHE) ```
### ii) Write down the complete cell reaction To find the overall cell reaction, we combine the oxidation reaction at the anode and the reduction reaction at the cathode.
Adding these two half-reactions together, the electrons cancel out: [tex]\[ \text{Zn} + 2\text{H}^+ \rightarrow \text{Zn}^{2+} + \text{H}_2 \][/tex]
So, the complete cell reaction is: [tex]\[ \text{Zn} + 2\text{H}^+ \rightarrow \text{Zn}^{2+} + \text{H}_2 \][/tex]
### iii) Calculate the emf of the cell To calculate the electromotive force (emf) of the cell, we use the standard electrode potentials for the two half-cells.
Given standard reduction potentials: - For the zinc electrode ([tex]\( \text{Zn}^{2+}/\text{Zn} \)[/tex]): [tex]\( E^\circ = -0.76 \text{ V} \)[/tex] - For the standard hydrogen electrode ([tex]\(\text{SHE}\)[/tex]): [tex]\( E^\circ = 0.00 \text{ V} \)[/tex]
The emf of the cell is calculated using the formula: [tex]\[ \text{EMF of the cell} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \][/tex]
Here: - The cathode is the SHE: [tex]\( E^\circ_{\text{cathode}} = 0.00 \text{ V} \)[/tex] - The anode is the Zn: [tex]\( E^\circ_{\text{anode}} = -0.76 \text{ V} \)[/tex]
Thus: [tex]\[ \text{EMF of the cell} = 0.00 \text{ V} - (-0.76 \text{ V}) = 0.76 \text{ V} \][/tex]
