Answer:
0.61 V
Step-by-step explanation:
a. The two metals in this voltaic cell are cadmium (Cd) and copper (Cu). Cadmium is oxidized (loses electrons) and copper is reduced (gains electrons).
b. Half-reactions:
Cathode: Cu2+(aq) + 2e- → Cu(s)
Anode: Cd(s) → Cd2+(aq) + 2e-
Overall reaction: Cd(s) + Cu2+(aq) → Cd2+(aq) + Cu(s)
c. The anode is where oxidation occurs, so the anode is the cadmium electrode. The cathode is where reduction occurs, so the cathode is the copper electrode.
d. Standard cell potential (Eᵒcell) can be calculated using the standard reduction potentials (Eᵒred) for each half-reaction.
Eᵒcell = Eᵒred(cathode) - Eᵒred(anode)
Eᵒred(Cu2+(aq) + 2e- → Cu(s)) = +0.34 V (from tables)
Eᵒred(Cd(s) → Cd2+(aq) + 2e-) = -0.40 V (from tables)
Eᵒcell = +0.34 V - (-0.40 V) = +0.74 V
e. The standard free energy change (ΔG°) can be calculated from the standard cell potential (Eᵒcell) using the following equation:
ΔG° = -nFEᵒcell
where n is the number of electrons transferred in the balanced equation (2), and F is the Faraday constant (96,485 C/mol).
ΔG° = -2 x 96,485 C/mol x 0.74 V = -141,800 J/mol = -141.8 kJ/mol
f. The cell diagram for this voltaic cell is:
Cd(s) | Cd(NO3)2 (0.10 M) || Cu(NO3)2 (0.20 M) | Cu(s)
g. The Nernst equation can be used to calculate the cell potential (E) under non-standard conditions, where the concentrations of the species involved are not at their standard state. The Nernst equation is:
E = Eᵒcell - (RT/nF) x ln(Q)
where R is the gas constant (8.314 J/mol-K), T is the temperature in Kelvin, n is the number of electrons transferred (2), F is the Faraday constant (96,485 C/mol), and Q is the reaction quotient, which is the ratio of the concentrations of the products over the concentrations of the reactants raised to their stoichiometric coefficients.
At non-standard conditions, the concentrations of the species involved are:
[Cd2+] = 0.10 M
[Cu2+] = 0.20 M
The reaction quotient (Q) is:
Q = ([Cd2+]/[Cu2+])^2 = (0.10 M / 0.20 M)^2 = 0.25
Plugging in the values:
E = 0.74 V - (8.314 J/mol-K x 298 K / (2 x 96,485 C/mol)) x ln(0.25) = 0.61 V
Therefore, the cell potential at non-standard conditions is 0.61 V.