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Chapter 18: Problem 100

A factory wants to produce \(1.00 \times 10^{3}\) 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
A current of 9.750 × 10⁴ A must be applied for 4.00 h to produce 1.00 × 10³ kg of barium from the electrolysis of molten barium chloride (BaCl2).

Step by step solution

01

Determine the molar mass of barium

From the periodic table, we know that the molar mass of barium (Ba) is 137.33 g/mol.
02

Convert the mass of barium into moles

Next, we will find the number of moles of barium (Ba) present in 1000 kg using the following formula: Number of moles (n) = mass (m) / molar mass (M) n(Ba) = \( \frac{1.00 \times 10^3 \, \mathrm{kg}}{137.33 \, \mathrm{g/mol}} \) Before solving, we need to convert kg to g: 1.00 × 10³ kg = 1.00 × 10³ × 10³ g = 1.00 × 10⁶ g Now, we can calculate the number of moles: n(Ba) = \( \frac{1.00 \times 10^6 \, \mathrm{g}}{137.33 \, \mathrm{g/mol}} \) = 7.280 × 10³ mol
03

Calculate the total charge needed

To find the total charge (Q) needed, we will use Faraday's law of electrolysis: Q = n × F × z where: - n: number of moles - F: Faraday's constant (96,485 C/mol) - z: Charge number (for Ba, z = 2 e-) Q = (7.280 × 10³ mol) × (96,485 C/mol) × (2 e-) = 1.404 × 10⁹ C
04

Convert the time to seconds

The given time is 4.00 h. We need to convert this time to seconds: 4.00 h = 4.00 × 60 min/h × 60 s/min = 1.440 × 10⁴ s
05

Calculate the current needed

Lastly, we calculate the current (I) needed using the formula: Current (I) = \( \frac{Charge (Q)}{time (t)} \) I = \( \frac{1.404 \times 10^9 \, \mathrm{C}}{1.440 \times 10^4 \, \mathrm{s}} \) = 9.750 × 10⁴ A Thus, a current of 9.750 × 10⁴ A must be applied for 4.00 h to produce 1.00 × 10³ kg of barium from the electrolysis of molten barium chloride (BaCl2).

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