Question

A galvanic cell at a temperature of

25.0°C

is powered by the following redox reaction:

→+2Cr+3aq3Cas+2Crs3Ca+2aq

Suppose the cell is prepared with

7.11

M

Cr+3

in one half-cell and

2.55

M

Ca+2

in the other.

Calculate the cell voltage under these conditions. Round your answer to

3

significant digits.

Answer 1

To calculate the cell voltage under the given conditions, we can use the Nernst equation, which relates the cell potential to the concentrations of the reactants and products in the half-cells. The Nernst equation is given by:

Ecell = E°cell - (RT / nF) * ln(Q)

where: Ecell = Cell potential (in volts) E°cell = Standard cell potential (in volts) R = Gas constant (8.314 J/(mol·K)) T = Temperature (in Kelvin) n = Number of electrons transferred in the balanced redox reaction F = Faraday constant (96,485 C/mol) ln = Natural logarithm Q = Reaction quotient

Given data: Temperature (T) = 25.0°C = 298.15 K Concentration of Cr3+ in one half-cell = 7.11 M Concentration of Ca2+ in the other half-cell = 2.55 M Balanced redox reaction: 2 Cr3+ (aq) + 3 Ca(s) → 2 Cr(s) + 3 Ca2+ (aq)

First, we need to find the value of the reaction quotient (Q) using the concentrations of the reactants and products in the cell:

Q = [Ca2+]^3 / [Cr3+]^2 Q = (2.55)^3 / (7.11)^2 Q ≈ 0.164 (rounded to three decimal places)

Next, we need to find the standard cell potential (E°cell) for the given redox reaction. The standard cell potential can be found from standard reduction potentials (E°red) for the half-reactions involved in the cell reaction. Look up the standard reduction potentials for Cr3+ and Ca2+:

E°red (Cr3+/Cr) = -0.74 V E°red (Ca2+/Ca) = -2.76 V

Now, calculate the standard cell potential (E°cell):

E°cell = E°red (cathode) - E°red (anode) E°cell = (0 V - (-2.76 V)) E°cell = 2.76 V

Finally, calculate the cell voltage (Ecell) using the Nernst equation:

Ecell = 2.76 V - [(8.314 J/(mol·K) * 298.15 K) / (6 * 96,485 C/mol)] * ln(0.164) Ecell ≈ 2.76 V - (2491.49 / 577.71) * (-1.804) Ecell ≈ 2.76 V - (-7.283) Ecell ≈ 9.043 V

The cell voltage under these conditions is approximately 9.043 volts, rounded to three significant digits.

Answer 2

To calculate the cell voltage for the galvanic cell, we can use the Nernst equation, which relates the cell potential to the concentrations of the species involved in the redox reaction and the temperature.

The Nernst equation is given by:

Ecell = E°cell - (RT / nF) * ln(Q)

where: Ecell is the cell potential (voltage) under the given conditions. E°cell is the standard cell potential at standard conditions (standard temperature and concentration). R is the ideal gas constant (8.314 J/(mol·K)). T is the temperature in Kelvin (25.0°C = 298.15 K). n is the number of electrons transferred in the redox reaction (for this reaction, n = 3). F is the Faraday constant (96,485 C/mol). ln(Q) is the natural logarithm of the reaction quotient Q.

First, we need to find the reaction quotient Q. Since the reaction is: Cr+3(aq) + 3e- → Cr(s) Ca(s) → Ca+2(aq) + 2e-

The reaction quotient Q can be expressed as follows:

Q = ([Cr+3] / [Ca+2]^2)

Given the concentrations: [Cr+3] = 7.11 M [Ca+2] = 2.55 M

Q = (7.11 M) / (2.55 M)^2 ≈ 1.109

Next, we need the standard cell potential E°cell for the redox reaction. Since it is not given, we can look up the standard reduction potentials for the half-reactions involved and calculate the standard cell potential:

E°cell = E°(Cr+3/Cr) - E°(Ca/Ca+2)

From standard reduction potential tables: E°(Cr+3/Cr) = -0.74 V E°(Ca/Ca+2) = -2.87 V

E°cell = (-0.74 V) - (-2.87 V) = 2.13 V

Now, we can calculate the cell potential (Ecell) using the Nernst equation:

Ecell = 2.13 V - ((8.314 J/(mol·K) * 298.15 K) / (3 * 96,485 C/mol)) * ln(1.109)

Ecell ≈ 2.13 V - (2071.05 / 289,455) * ln(1.109)

Ecell ≈ 2.13 V - 0.01475 * ln(1.109)

Ecell ≈ 2.13 V - 0.01475 * 0.10427

Ecell ≈ 2.13 V - 0.00154

Ecell ≈ 2.128 V

The cell voltage under these conditions is approximately 2.128 volts (rounded to 3 significant digits).