To find the values for E°cell, Ecell, ΔG°rxn, and ΔGrxn for the given galvanic cell, you can follow these steps:
Step 1: Write the balanced equation for the cell reaction. The cell reaction for the given galvanic cell can be written as follows: Zn(s) + 2Ag+(aq) → Zn2+(aq) + 2Ag(s)
Step 2: Determine the standard cell potential, E°cell. E°cell is the potential difference between the two electrodes of the galvanic cell under standard conditions. Look up the standard reduction potentials for the half-reactions involved in the cell reaction.
The standard reduction potentials for the half-reactions are as follows: Zn2+(aq) + 2e- → Zn(s): E° = -0.76 V (reduction potential) Ag+(aq) + e- → Ag(s): E° = +0.80 V (reduction potential)
To determine the standard cell potential, E°cell, use the equation: E°cell = E°(cathode) - E°(anode) E°cell = (+0.80 V) - (-0.76 V) E°cell = +1.56 V
Step 3: Calculate the cell potential, Ecell. The cell potential, Ecell, can be determined by considering the concentrations of the species involved in the cell reaction.
Ecell = E°cell - (0.0592 V/n) log(Q) where Q is the reaction quotient calculated from the concentrations of the species in the cell reaction.
Given concentrations: [Zn2+] = 0.045 M [Ag+] = 3.8 x 10^-5 M
The reaction quotient, Q, can be calculated using the Nernst equation: Q = ([Zn2+]/[Ag+])^n where n is the stoichiometric coefficient in the balanced cell reaction. In this case, n = 2.
Q = (0.045 M / 3.8 x 10^-5 M)^2 = 148.76
Substituting the values into the equation for Ecell: Ecell = E°cell - (0.0592 V/2) log(Q) Ecell = 1.56 V - (0.0296 V) log(148.76)
Step 4: Calculate ΔG°rxn. ΔG°rxn, the standard Gibbs free energy change, can be calculated using the equation: ΔG°rxn = -nF E°cell where n is the number of moles of electrons transferred in the balanced cell reaction, and F is Faraday's constant (96,485 C/mol).
In this case, n = 2 (as per the balanced equation). ΔG°rxn = -2 * 96,485 C/mol * 1.56 V
Step 5: Calculate ΔGrxn. ΔGrxn, the Gibbs free energy change, can be calculated using the equation: ΔGrxn = ΔG°rxn + RT ln(Q) where R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and ln(Q) is the natural logarithm of the reaction quotient.
Substitute the appropriate values into the equation to calculate ΔGrxn.
Please note that the calculations in Step 3, Step 4, and Step 5 require the temperature to be specified.