Question

A solution containing \(\mathrm{Pt}^{4+}\) is electrolyzed with a current of 4.00 \(\mathrm{A} .\) How long will it take to plate out 99\(\%\) of the platinum in 0.50 \(\mathrm{L}\) of a \(0.010-M\) solution of \(\mathrm{Pt}^{4+} ?\)

Short answer

It will take approximately 132.8 hours to plate out 99% of the platinum present in the 0.50 L of a 0.010-M solution of \(Pt^{4+}\) electrolyzed with a current of 4.00 A.

Step-by-step solution

Calculate the number of moles of Pt

First, we need to determine the total number of moles of \(\mathrm{Pt}^{4+}\) ions present in the solution. We are given that the solution is 0.50 L in volume and has a concentration of 0.010 M. Therefore, the number of moles can be calculated using the equation: moles = volume × concentration moles of Pt = (\(0.50\,\mathrm{L}\)) × (\(0.010\,\mathrm{M}\)) moles of Pt = \(0.005\,\mathrm{mol}\)

Calculate the moles of Pt to be plated out

Next, we need to calculate the number of moles of Pt that we want to plate out, which is given as 99% of the total moles. moles of Pt to be plated out = (0.99) × (0.005 mol) moles of Pt to be plated out = \(0.00495\,\mathrm{mol}\)

Calculate the amount of charge needed

Now, we need to calculate the amount of charge required to plate out the desired amount of Pt. Since we are dealing with a \(\mathrm{Pt}^{4+}\) ion, we know that 4 moles of electrons are needed for each mole of Pt. Thus, the amount of charge required can be calculated using Faraday's constant (F), where F = \(96,485\,\mathrm{\dfrac{C}{mol e^{-}}\): Charge (C) = moles of Pt × 4 × F Charge (C) = (0.00495 mol) × 4 × (96,485 \(\dfrac{\mathrm{C}}{\mathrm{mol\,e^{-}}\)) Charge (C) = \(1,911,538\,\mathrm{C}\)

Calculate the time required

Finally, to determine the time required to plate out 99% of the Pt, we will use the current value given in the problem. The current is the amount of charge being transferred per unit of time, which in this case is 4.00 A. Therefore, we can use the following equation to find the time required: time (s) = \(\dfrac{\text{Charge (C)}}{\text{Current (A)}}\) time (s) = \(\dfrac{1,911,538\,\mathrm{C}}{4.00\,\mathrm{A}}\) time (s) = \(477,885\,\mathrm{s}\) Now, we can convert the time in seconds to minutes or hours for a more practical understanding: time (min) = \(\dfrac{477,885\,\mathrm{s}}{60\,\mathrm{s/min}}\) = \(7,965\,\mathrm{min}\) time (hr) = \(\dfrac{7,965\,\mathrm{min}}{60\,\mathrm{min/h}}\) ≈ \(132.8\,\mathrm{h}\) So, it will take approximately 132.8 hours to plate out 99% of the platinum present in the solution.

Key concepts

Redox Reactions

Redox reactions are a fundamental part of electrochemistry. In these reactions, oxidation and reduction occur simultaneously.
The term "redox" comes from the two processes involved: reduction, where a substance gains electrons, and oxidation, where it loses electrons. In the context of electrolysis, such as plating out platinum, the platinum ions in solution undergo reduction.

• The ion \( ext{Pt}^{4+}\) in solution gains electrons (is reduced) to form solid platinum.
• As Pt undergoes reduction, electrons are supplied to the electrode, enabling the metal to deposit out of the solution.

This reaction can be represented by the half-equation:
\[ ext{Pt}^{4+} + 4e^- \rightarrow ext{Pt}(s) \]
Understanding redox reactions helps in predicting the flow of electrons and the changes in oxidation states during electrolysis.

Faraday's Laws of Electrolysis

Faraday's laws lay the foundation for understanding the quantitative aspects of electrolysis. The laws comprise two fundamental principles:

• First Law: The amount of substance altered at an electrode during electrolysis is directly proportional to the quantity of electricity that passes through the circuit.
  This is represented by the formula: \( ext{mass deposited} (m) \propto ext{Q}\), where Q is the charge (in coulombs).
• Second Law: The amounts of different substances deposited by the same quantity of electricity are proportional to their equivalent weights.
  Combining both, Faraday's constant (F \(= 96,485\ \text{C/mol e}^-\)) is used to determine the charge needed for depositing a specific amount of a substance.

Faraday's laws are essential in calculating how much material is deposited or dissolved during electrolysis. They help relate the molecules and ions involved to the electric current and time.

Mole Concept

The mole concept plays a crucial role in connecting the microscopic scales of chemical reactions to real-world quantities. A mole is a counting unit, like a "dozen," but used for atoms, molecules, and ions.
One mole equates to Avogadro’s number (approximately \(6.022 \, x \, 10^{23}\)).
In the exercise, determining the moles of \(\text{Pt}^{4+}\) involves calculating the total amount in moles based on the concentration and the volume of the solution.

• The formula used is \(\text{moles} = \text{concentration} \times \text{volume}\).

This mole calculation is a stepping stone to further calculations involving charge and time required for electrolysis. Understanding how to translate chemical concentrations to mole quantities allows chemistry to lever practical experimental setups.

Current and Charge Calculations

Current is central to the process of electrolysis. Measured in amperes (A), it represents the flow of electricity or charge over time.
During electrolysis, the relationship between current, charge, and time is articulated by the formula:

• \(\text{Current} (I) = \dfrac{\text{Charge} (Q)}{\text{Time} (t)}\)\.

In our problem, the current facilitates the transfer of electrons needed for reducing \(\text{Pt}^{4+}\).
By rearranging the above formula, one can solve for time if the current and charge are known:

• \(\text{Time} (t) = \dfrac{\text{Charge} (Q)}{\text{Current} (I)}\).

Calculating the charge involves leveraging Faraday's constant to translate between moles of electrons and coulombs. By using these calculations, you can determine how long it will take for the desired amount of a substance to be electrolyzed at a given constant current.