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Chapter 17: Problem 133

An aqueous solution of an unknown salt of ruthenium is electrolyzed by a current of 2.50 A passing for 50.0 min. If 2.618 g Ru is produced at the cathode, what is the charge on the ruthenium ions in solution?

Short Answer

Expert verified
The charge on the ruthenium ions in the unknown salt solution is approximately +3.

Step by step solution

01

Calculate the total charge passed during electrolysis

First, we will need to calculate the total charge transferred during the electrolysis process. The formula we will use is: Total charge (Q) = Current (I) × Time (t) The current is given as 2.50 A, and the time is given as 50.0 minutes. Convert the time to seconds before proceeding: Time (t) = 50.0 min × (60 s / 1 min) = 3000 s Now, calculate the total charge: Q = I × t = 2.50 A × 3000 s = 7500 C
02

Determine the Faraday constant

The Faraday constant (F) represents the amount of charge per mole of electrons. It is a constant value equal to approximately 96485 C/mol e-, and we will use this value in our calculations: F = 96485 C/mol e-
03

Calculate the moles of electrons transferred

With the total charge and the Faraday constant, we can now calculate the moles of electrons transferred during the electrolysis: Moles of electrons transferred = Total charge / Faraday constant = Q / F Moles of electrons = 7500 C / 96485 C/mol e- ≈ 0.0777 mol e-
04

Calculate moles of ruthenium produced

Since we know the mass of ruthenium produced at the cathode (2.618 g), we can determine the moles of ruthenium produced by using its molar mass (Mm(Ru) ≈ 101.07 g/mol): Moles of Ru = Mass of Ru / Mm(Ru) Moles of Ru = 2.618 g / 101.07 g/mol ≈ 0.0259 mol Ru
05

Determine the charge on the ruthenium ions

To find the charge on the ruthenium ions, we will divide the moles of electrons transferred by the moles of ruthenium produced during the electrolysis process, and round the closest integer: Charge on Ru ions (z) ≈ (Moles of e- / Moles of Ru) z ≈ (0.0777 mol e- / 0.0259 mol Ru) ≈ 3 Therefore, the charge on the ruthenium ions in the unknown salt solution is approximately +3.

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Most popular questions from this chapter

Calculate \(\mathscr{E}^{\circ}\) values for the following cells. Which reactions are spontaneous as written (under standard conditions)? Balance the equations. Standard reduction potentials are found in Table \(17-1\) a. \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{I}^{-}(a q) \longrightarrow \mathrm{I}_{2}(a q)+\mathrm{Mn}^{2+}(a q)\) b. \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{F}^{-}(a q) \longrightarrow \mathrm{F}_{2}(g)+\mathrm{Mn}^{2+}(a q)\)

Sketch the galvanic cells based on the following half-reactions. Show the direction of electron flow, show the direction of ion migration through the salt bridge, and identify the cathode and anode. Give the overall balanced equation, and determine \(\mathscr{E}^{\circ}\) for the galvanic cells. Assume that all concentrations are \(1.0 M\) and that all partial pressures are 1.0 atm. a. \(\mathrm{Cl}_{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Cl}^{-} \quad \mathscr{E}^{\circ}=1.36 \mathrm{V}\) \(\mathrm{Br}_{2}+2 \mathrm{e}^{-} \rightarrow 2 \mathrm{Br}^{-} \quad \mathscr{E}^{\circ}=1.09 \mathrm{V}\) b. \(\mathrm{MnO}_{4}^{-}+8 \mathrm{H}^{+}+5 \mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O} \quad \mathscr{E}^{\circ}=1.51 \mathrm{V}\) \(\mathrm{IO}_{4}^{-}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} \rightarrow \mathrm{IO}_{3}^{-}+\mathrm{H}_{2} \mathrm{O} \quad \quad \mathscr{E}^{\circ}=1.60 \mathrm{V}\)

In the electrolysis of a sodium chloride solution, what volume of \(\mathrm{H}_{2}(g)\) is produced in the same time it takes to produce \(257 \mathrm{L}\) \(\mathrm{Cl}_{2}(g),\) with both volumes measured at \(50 .^{\circ} \mathrm{C}\) and 2.50 atm?

Sketch the galvanic cells based on the following overall reactions. Show the direction of electron flow, the direction of ion migration through the salt bridge, and identify the cathode and anode. Give the overall balanced equation. Assume that all concentrations are \(1.0 \mathrm{M}\) and that all partial pressures are 1.0 atm. a. \(\mathrm{IO}_{3}^{-}(a q)+\mathrm{Fe}^{2+}(a q) \rightleftharpoons \mathrm{Fe}^{3+}(a q)+\mathrm{I}_{2}(a q)\) b. \(\mathrm{Zn}(s)+\mathrm{Ag}^{+}(a q) \rightleftharpoons \mathrm{Zn}^{2+}(a q)+\mathrm{Ag}(s)\)

Electrolysis of an alkaline earth metal chloride using a current of 5.00 A for 748 s deposits 0.471 g of metal at the cathode. What is the identity of the alkaline earth metal chloride?
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