Calculating Standard Free Energy Change and Equilibrium Constant for a Redox Reaction Involving Nickel and Chromate Ions

Calculate number of moles of electrons transferred, the standard free energy change, and the value of the equilibrium constant for the following reaction, using the standard reduction potential values provided.3 Ni^2+ (aq) + 2 Cr(OH)3 (s) + 10 OH^- (aq) → 3 Ni (s) + 2 CrO4^2- (aq) + 8 H2O (l)Given: CrO4^2- (aq) + 4 H2O (l) + 3 e^- → Cr(OH)3 (s) + 5 OH^- (aq) E° = -0.13 VNi^2+ (aq) + 2 e^- → Ni (s) E° = -0.28 Va. Identify the half-reaction taking place at the anode and the half-reaction taking place at the cathode, based on the balanced redox equation provided.b. Identify the number of moles of e- transferred in the balanced redox equation.c. Calculate the standard free energy change.d. Calculate the value of the equilibrium constant.

a. Cathode: Ni^2+(aq)+2e^-=Ni(s)Anode: Cr(OH)3(s)+5OH^-(aq)=CrO4^2-(aq)+4H2O(l)+3e^-b. 6c. 87,000Jd. 5.62×10^-16

a. The half-reaction taking place at the anode is Ni^2+ (aq) + 2 e^- → Ni (s). The half-reaction taking place at the cathode is CrO4^2- (aq) + 4 H2O (l) + 3 e^- → Cr(OH)3 (s) + 5 OH^- (aq).

b. From the balanced redox equation, we can see that 6 moles of electrons are transferred, since the coefficient of electrons (e^-) is 6.

c. To calculate the standard free energy change (ΔG°) for the reaction, we first need to calculate the standard cell potential (E°cell) using the reduction potential values provided. The cell potential can be calculated using the following formula:

E°cell = E°cathode – E°anode

E°cell = (-0.13 V) – (-0.28 V)
E°cell = 0.15 V

The standard free energy change can be calculated using the following formula:

ΔG° = -nFE°cell

where n is the number of moles of electrons transferred, F is the Faraday constant (96,485 C/mol), and E°cell is the cell potential.

ΔG° = -(6 mol) x (96,485 C/mol) x (0.15 V)
ΔG° = -87,641 J/mol
ΔG° = -87.6 kJ/mol (rounded to one decimal place)

d. The equilibrium constant (K) can be calculated using the following formula:

ΔG° = -RT ln K

where R is the gas constant (8.314 J/mol∙K), T is the temperature in Kelvin (assumed to be 298 K), and ln is the natural logarithm.

K = e^(-ΔG°/RT)

K = e^(-(-87,641 J/mol) / (8.314 J/mol∙K x 298 K))
K = e^(111.1)
K = 1.13 x 10^48 (infinite with respect to practical purposes)

The value of the equilibrium constant is very large, indicating that the reaction strongly favors the products and that the position of equilibrium lies far to the right.

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