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 \(0.010 \mathrm{M}\) solution of \(\mathrm{Pt}^{4+}\) ?

Short answer

The time required to plate out \(99 \%\) of the platinum in the \(0.50 \mathrm{~L}\) of \(0.010 \mathrm{M}\) solution of \(\mathrm{Pt}^{4+}\) is approximately \(477.71 \mathrm{s}\).

Step-by-step solution

Calculate the moles and mass of the platinum

First, we need to find the number of moles (\(n\)) of \(\mathrm{Pt}^{4+}\) ions in the solution. We can use the formula: $$n = C \times V$$ We can then find the mass of the platinum using the formula: $$m = n \times M$$

Calculate the charge required for the electrolysis process

Next, we need to calculate the charge required to plate out \(99 \%\) of the platinum. We can use Faraday's law of electrolysis: $$Q = n \times F \times z$$ Here, \(z\) represents the charge number of the \(\mathrm{Pt}^{4+}\) ions, which is \(4\).

Calculate the time required for the electrolysis process

Finally, we can use the current (\(I\)) to find the time required for the electrolysis process. We can use the formula: $$t = \frac{Q}{I}$$ Now, let's plug in the values and find the time required.

Calculations

1. Calculate the moles and mass of the platinum $$n = (0.010 \mathrm{M})(0.50 \mathrm{~L}) = 0.005 \mathrm{mol}$$ $$m = (0.005 \mathrm{mol})(195.08 \mathrm{g/mol}) = 0.976 \mathrm{g}$$ 2. Calculate the charge required for the electrolysis process Since we want to plate \(99 \%\) of the platinum, we'll use \(0.99m\) to calculate the charge required. $$Q = (0.005 \mathrm{mol})(96485 \mathrm{C/mol})(4) = 1930.14 \times 0.99 = 1910.84 \mathrm{C}$$ 3. Calculate the time required for the electrolysis process $$t = \frac{1910.84 \mathrm{C}}{4.00 \mathrm{~ A}} = 477.71 \mathrm{s}$$ The time required to plate out \(99 \%\) of the platinum in the \(0.50 \mathrm{~L}\) of \(0.010 \mathrm{M}\) solution of \(\mathrm{Pt}^{4+}\) is approximately \(477.71 \mathrm{s}\).

Key concepts

Faraday's Law of Electrolysis

Faraday's Law of electrolysis is a fundamental principle that helps calculate the amount of substance deposited or dissolved during electrolysis. When an electric current passes through an electrolyte, it can induce chemical reactions that separate elements or compounds. The amount of substance transformed at each electrode is directly proportional to the amount of electrical charge that flows through the circuit. This law is expressed with the formula:

• \[ Q = n \times F \times z \]

In this equation, \( Q \) is the total electric charge measured in coulombs (C), \( n \) represents the number of moles of electrons exchanged, \( F \) is Faraday's constant (approximately 96485 C/mol), and \( z \) is the charge number of the ion involved in the reaction. Understanding Faraday’s Law is crucial since it connects the world of chemistry with the measurable currents and charges in electrical circuits.
This principle allows us to calculate how much material is deposited from an electrolyte solution during the electrolysis process.

Charge Calculation

The charge calculation is a key step in determining how much electric charge is required to achieve a chemical transformation in an electrolysis process. In the given exercise, you need to determine the charge needed to deposit 99% of the platinum from a solution. Using Faraday's Law of Electrolysis, the formula is:

• \[ Q = n \times F \times z \]

Here’s the breakdown:

• **Number of Moles (\( n \))**: First, find the number of moles of Pt ions in the solution. This involves using the molarity and volume of the solution.
• **Faraday's Constant (\( F \))**: Utilized to convert moles of electrons into the respective coulombs.
• **Charge Number (\( z \))**: Represents the number of electrons swapped per ion, which is 4 for \( \mathrm{Pt}^{4+} \).

By plugging these values into the formula, you can find the total charge required to electrolyze the given platinum solution until 99% of the platinum metals are plated out.

Current Calculation

Current is the rate of flow of electric charge and is measured in amperes (A). In electrolysis, understanding the current helps determine how fast a chemical reaction will occur. The current affects how quickly the platinum will plate out from the electrolyte solution.

• **Formula**: The current (I) value is often given directly in electrolysis problems.
• **Example in given problem**: It was provided that a current of 4.00 A passes through the solution. This means 4 coulombs of charge go through the solution every second.
• The relationship between charge, time, and current is fixed by the basic rule: \[ Q = I \times t \] Where \( Q \) is the charge in coulombs, \( I \) is the current in amperes, and \( t \) is time in seconds.

Using these values, you can adjust the time accordingly to get the necessary charge deposited based on the process parameters you set.

Time of Electrolysis

Calculating the time of electrolysis is an essential step in understanding the duration needed to achieve a particular degree of electroplating or electrolysis. Once you know the electrical current and the total charge required, you can determine the time through:

• **Formula**: This uses the relationship \[ t = \frac{Q}{I} \], where \( t \) is the time in seconds, \( Q \) is the total charge, and \( I \) is the current.
• **Given Problem**: Using the calculated charge of 1910.84 C and the provided current of 4.00 A, the time required to plate out the platinum is calculated as:
• \[ t = \frac{1910.84 \, \mathrm{C}}{4.00 \, \mathrm{A}} \approx 477.71 \, \mathrm{s} \]

Breaking down these calculations allows you to understand how factors such as current and charge influence how long the electrolysis process takes to achieve a specific result. This elementary process is crucial for designing systems that require precise timing based on electrical input.