An iron plate of 0.559 m² surface area is to be chrome plated using a chromic acid-sulfuric acid plating bath. The anode and cathode half-equations are: Cathode: Cr₂O₇^2-+ 14 H⁺ + 12 e- → 2 Cr + 7 H₂O E° = 0.320 V
Anode: 2 H₂O → O₂ + 4 H+ + 4 e- E° = 1.229 V
Determine the minimum energy needed to produce a plating 0.115 mm thick on the iron plate. The density of chromium is 7.19 g/cm3.

Question

Quizplus · Accepted Answer

To determine the energy required to produce the desired plating, we need to calculate the amount of charge required, and then use the equation: ΔG = nFΔE, where n is the number of moles of electrons transferred, F is Faraday's constant (96485 C/mol e-), and ΔE is the cell potential.

First, we need to calculate the number of moles of electrons transferred in the reaction. From the cathode half-equation, we see that 12 electrons are transferred for every 2 moles of chromium plated:

2 Cr + 7 H2O + 14 e- = 2 Cr(OH)3 + 14 H+

So, for 1 mole of chromium plated, 6 moles of electrons are transferred. The mass of chromium plated can be calculated using the density and the surface area of the iron plate:

mass = density x volume = density x thickness x surface area

mass = 7.19 g/cm3 x (0.115 mm / 10 mm/cm) x 0.559 m2 = 0.0454 g

The number of moles of chromium plated is:

moles = mass / molar mass = 0.0454 g / 52 g/mol = 0.000872 mol

Therefore, the number of moles of electrons transferred is:

n = 6 x 0.000872 mol = 0.00523 mol e-

The cell potential can be calculated by subtracting the anode potential from the cathode potential:

ΔE = E°cathode - E°anode

ΔE = 0.320 V - 1.229 V = -0.909 V

Note that the negative sign indicates that the reaction is not spontaneous as written. However, we can still use the equation ΔG = nFΔE to calculate the energy required, since it is the total change in free energy that is important.

ΔG = nFΔE = (0.00523 mol e-) x (96485 C/mol e-) x (-0.909 V) = 487.6 C·V

To convert C·V to joules, we use the conversion factor 1 C·V = 1 J:

ΔG = 487.6 J = 0.4876 kJ

Therefore, the minimum energy required to produce the desired plating is 0.4876 kJ. However, this is only the minimum energy required assuming 100% efficiency of the plating process. In practice, the actual energy required will be higher due to losses from resistance in the plating bath and other sources. Choice D, 4.68 × 1013 kJ, is the closest option to the calculated value.

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