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Chapter 17: Problem 102

A factory wants to produce \(1.00 \times 10^{3} \mathrm{kg}\) barium from the electrolysis of molten barium chloride. What current must be applied for \(4.00 \mathrm{h}\) to accomplish this?

Short Answer

Expert verified
The current that must be applied for 4.00 hours to produce \(1.00 \times 10^3 \, \mathrm{kg}\) of barium from the electrolysis of molten barium chloride is approximately \(9.79 \times 10^4 \, \mathrm{A}\).

Step by step solution

01

Calculate the number of moles of barium to be produced

For barium, the molar mass (Ba) is approximately 137 g/mol. We're given the target production of barium is 1.00 x 10³ kg, so we need to first convert this mass to grams and then to moles: Mass of barium (g) = 1.00 x 10³ kg x (1000 g/kg) = 1.00 x 10⁶ g Now, convert the mass to moles: Moles = (Mass of barium) / (Molar mass of barium) Moles = \( \frac{1.00 \times 10^6 \, \mathrm{g}}{137 \, \mathrm{g/mol}} \approx 7.30 \times 10^3 \, \mathrm{mol} \)
02

Calculate the total charge required to produce the desired amount of barium

In electrolysis, two moles of electrons are required to produce one mole of barium (Ba²⁺ + 2e⁻ → Ba). From Faraday's law of electrolysis, 1 mole of electrons carries a charge, called a Faraday (F) which is approximately 96485 C/mol (Coulombs per mole). Total charge (C) = moles of barium x (moles of electrons per mole of barium) x Faraday's constant Total charge (C) = \( 7.30 \times 10^3 \, \mathrm{mol} \times 2 \, \mathrm{mol} \, \mathrm{e}^{-}/\mathrm{mol} \, \mathrm{Ba} \times 96485 \, \mathrm{C}/\mathrm{mol} \, \mathrm{e}^{-} \approx 1.41 \times 10^9 \, \mathrm{C} \)
03

Calculate the required current for the given time

We are given the total time required to produce 1.00 x 10³ kg of barium as 4.00 hours. To find the required current, first, we need to convert the time to seconds: Total time (s) = 4.00 hours x (3600 s/h) = 14400 s Now, from the formula: current (I) = total charge (C) / total time (s), we have: Current (I) = \( \frac{1.41 \times 10^9 \, \mathrm{C}}{14400 \, \mathrm{s}} \approx 9.79 \times 10^4 \, \mathrm{A} \) So, the current that must be applied for 4.00 hours to produce 1.00 x 10³ kg of barium from the electrolysis of molten barium chloride is approximately 9.79 x 10⁴ A.

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Most popular questions from this chapter

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