Question

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

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

Step-by-step solution

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

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-

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-

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

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.

Key concepts

Ruthenium

Ruthenium is a chemical element that belongs to the platinum group of metals. It is represented by the symbol Ru and has the atomic number 44. It’s one of those metals that you probably don't hear much about because it’s not as common as some other precious metals.
However, ruthenium is used in a variety of applications due to its unique properties. It's often incorporated into electrical contacts and multiple resistant coatings because it's very durable. But what's really interesting about ruthenium is its role in electrochemistry.
In electrolysis, ruthenium can exist in several oxidation states. This means it can form ions with different charges when dissolved in a solution, making it key in determining the outcome of certain electrochemical reactions. For instance, if ruthenium ions are reduced at the cathode during electrolysis, the specific charge on these ions will affect exactly how much solid metal is deposited.

Faraday constant

The Faraday constant is a very significant figure in electrochemistry, especially when it comes to understanding electrolysis. It is named after the scientist Michael Faraday, and it represents the amount of electric charge carried by one mole of electrons. This value is approximately 96485 coulombs per mole of electrons (C/mol e-).
The Faraday constant is crucial for calculations involving converting between electric charge and amount of chemical change, such as when determining how much of a substance has been transformed in an electrochemical cell. It helps us link the flow of electricity to the chemical reactions it induces.

• This constant allows one to calculate the amount of substance altered in electrolysis by measuring the total charge transferred.
• In practice, you can think of it as a bridge that connects electricity (in amperes or coulombs) with observable chemical changes (like moles of a substance).

By using the Faraday constant, we can predict how much metal can be deposited at an electrode during electrolysis, or calculate the charge of ions participating in the reaction.

Electrolysis

Electrolysis is a fascinating process used across various fields to drive chemical reactions using electricity. Simply put, it's a way to use an electric current to achieve a chemical reaction that would not normally happen on its own. In the context of ruthenium and other metals, electrolysis can help extract or deposit a metal in the form of solid.
Here’s how it generally works during an electrolysis experiment:

• A solution containing metal ions, such as ruthenium ions, is placed in an electrochemical cell.
• When an electric current is passed through the solution, ions move towards the electrodes.
• Ruthenium ions will migrate to the cathode (negatively charged electrode) where they gain electrons and transform into solid ruthenium metal.

Using this method, electrochemists can control the amount of metal deposited by adjusting variables like current and time. It's a powerful technique for purifying metals or separating substances within a solution.

Moles of electrons

In electrochemistry, understanding the concept of moles of electrons is fundamental to understanding how vast quantities of atoms interact. A mole is simply a really big number that we use to count particles (like electrons) because they're so tiny and there are so many of them.
The unit "moles of electrons" helps us relate the amount of electricity used in electrolysis to the amount of chemical change occurring. The relationship can be calculated easily using the Faraday constant.
For example, say we have a total charge that passes through a solution calculated from the current and time of electrolysis. By dividing this charge by the Faraday constant, we can find out how many moles of electrons were involved in the reaction.

• Calculating moles of electrons is essential in obtaining precise results for the amount of substances produced or consumed in electrochemical reactions.
• This calculation helps in determining the stoichiometry of electrochemical reactions, and in identifying the charge on ions produced in electrolysis.

Understanding the flow and quantity of electrons in a reaction helps clarify the entire process of electrolysis and how different ions transform.