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Chapter 20: Problem 25

What mass of barium is produced when molten \(\mathrm{BaCl}_{2}\) is electrolyzed by a current of \(2.50 \times 10^{5} \mathrm{A}\) for 6.00 \(\mathrm{h} ?\)

Short Answer

Expert verified
The mass of barium produced when molten BaCl2 is electrolyzed by a current of \(2.50 \times 10^{5} A\) for 6.00 hours is \(3.84 \times 10^6\) grams.

Step by step solution

01

Calculate the amount of charge passed during the electrolysis

To find the charge passed during electrolysis, we use the formula: Charge (Q) = Current (I) × Time (t) Given that the current, I = 2.50 x 10^5 A and time, t = 6 h, we need to convert the time to seconds (1 h = 3600 s). t = 6 h × 3600 s/h = 21,600 s Now, we can calculate the charge: Q = (2.50 x 10^5 A) × (21,600 s) = 5.40 x 10^9 C
02

Find the moles of electrons during the electrolysis process

For this step, we will use Faraday's constant (F = 96,485 C/mol of electrons). Number of moles of electrons = Charge (Q) / Faraday's constant (F) Moles of electrons = (5.40 x 10^9 C) / (96,485 C/mol) = 5.60 x 10^4 mol
03

Convert moles of electrons to moles of barium

The balanced chemical equation for the reduction of BaCl2 is: \(Ba^{2+} + 2e^- \rightarrow Ba\) This means that 2 moles of electrons are needed for the reduction of 1 mole of Ba^2+ ions into 1 mole of barium. Now, to convert moles of electrons to moles of barium, we will use the stoichiometry of the reaction: Moles of barium = (Moles of electrons)(1 mol Ba / 2 mol electrons) Moles of barium = (5.60 x 10^4 mol)(1 mol Ba / 2 mol electrons) = 2.80 x 10^4 mol
04

Calculate the mass of barium produced

Finally, to find the mass of barium produced, we will multiply the moles of barium by the molar mass of barium (Mm = 137.33 g/mol): Mass of barium = (Moles of barium)(Molar mass of barium) Mass of barium = (2.80 x 10^4 mol)(137.33 g/mol) = 3.84 x 10^6 g Hence, the mass of barium produced in this process is 3.84 x 10^6 grams.

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Most popular questions from this chapter

Which of the following statement(s) is(are) true? a. The alkali metals are found in the earth’s crust in the form of pure elements. b. Gallium has one of the highest melting points known for metals. c. When calcium metal reacts with water, one of the products is \(\mathrm{H}_{2}(g) .\) d. When AlCl \(_{3}\) is dissolved in water, it produces an acidic solution. e. Lithium reacts in the presence of excess oxygen gas to form lithium superoxide.

Describe the bonding in \(\mathrm{SO}_{2}\) and \(\mathrm{SO}_{3}\) using the localized electron model (hybrid orbital theory). How would the molecular orbital model describe the \(\pi\) bonding in these two compounds?

Use bond energies to estimate the maximum wavelength of light that will cause the reaction $$ \mathrm{O}_{3} \stackrel{\mathrm{h}}{\longrightarrow} \mathrm{O}_{2}+\mathrm{O} $$

Electrolysis of an alkaline earth metal chloride using a current of 5.00 \(\mathrm{A}\) for 748 seconds deposits 0.471 \(\mathrm{g}\) of metal at an electrode. Is the metal deposited at the cathode or the anode of the electrolytic cell? What is produced at the other electrode? What is the identity of the alkaline earth metal?

How can the paramagnetism of \(\mathrm{O}_{2}\) be explained using the molecular orbital model?
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