Question

An aqueous solution of a platinum salt is electrolyzed at a current of \(2.50 \mathrm{~A}\) for \(2.00 \mathrm{~h}\). As a result, \(9.09 \mathrm{~g}\) of metallic Pt is formed at the cathode. Calculate the charge on the Pt ions in this solution.

Short answer

The charge on the Pt ions is \(+2\).

Step-by-step solution

Calculate Total Charge Passed

To calculate the total charge passed through the solution, use the formula: \[ Q = I \cdot t \], where \( Q \) is the total charge, \( I \) is the current, and \( t \) is the time in seconds. Convert hours to seconds: \( 2.00 \text{ h} = 7200 \text{ s} \). Then: \[ Q = 2.50 \text{ A} \times 7200 \text{ s} = 18000 \text{ C} \].

Calculate Moles of Pt Formed

First find the molar mass of Pt, which is approximately \( 195.08 \text{ g/mol} \). Calculate the moles of Pt formed using the mass given: \[ \text{moles of Pt} = \frac{9.09 \text{ g}}{195.08 \text{ g/mol}} \approx 0.0466 \text{ mol} \].

Determine the Charge per Mole of Pt

Use Faraday's constant \( F = 96485 \text{ C/mol} \) to find the charge that would correspond to the formation of a certain amount of moles if the charge on Pt is unknown. Assume \( n \) moles of electrons are required for one mole of Pt, so: \[ 18000 \text{ C} = n \times 0.0466 \text{ mol} \times 96485 \text{ C/mol} \].

Solve for the Charge on Pt Ions

Solve the equation from Step 3 for \( n \): \[ n = \frac{18000 \text{ C}}{0.0466 \text{ mol} \times 96485 \text{ C/mol}} \approx 2.00 \]. Thus, the charge on the Pt ions is \(+2\).

Key concepts

Faraday's constant

In electrochemistry, Faraday's constant is a key concept. It is essential for calculating the amount of substance that can be produced or consumed during electrolysis. Faraday's constant represents the charge of one mole of electrons and is denoted by the symbol \( F \).

Its value is approximately 96485 Coulombs per mole. This constant is crucial because it connects the amount of electrical charge passed through a solution to the amount of chemical substance produced. For example, if you were to pass a charge of 96485 C through a solution, one mole of electrons would be involved in the reaction, potentially resulting in the production or consumption of one mole of ions or molecules.

When solving electrochemical problems, Faraday's constant allows us to translate between the electrical world (charge in Coulombs) and the chemical world (moles of substance). This connection helps us understand how electrical energy is converted into chemical energy and vice versa.

Platinum ion charge

The charge of platinum ions in a solution is vital for determining the type of electrochemical reaction occurring during electrolysis. In the case of platinum (Pt), it can have different oxidation states, such as \(+2\) or \(+4\).

When calculating the charge on the Pt ions in an electrolysis process, understanding the number of electrons transferred is essential. Typically, the ion charge is equivalent to the number of electrons that must be transferred for the ion to be fully reduced or oxidized.

If two electrons are transferred per Pt ion, then the charge is \(+2\). This information is derived from the amount of charge passed during the electrolysis and the moles of Pt formed. By analyzing the stoichiometry of the reaction, you determine how many charges, or electrons, are associated with each ion, helping to identify its state in the solution.

Electrolysis calculations

Electrolysis calculations involve determining the amount of charged particles required and the resulting chemical change. These calculations are essential for describing how the transfer of electrons results in the production of a chemical substance.

In electrolysis, the total charge \( Q \) passed through the solution is calculated by multiplying current \( I \) in Amperes by time \( t \) in seconds, using the formula \( Q = I \times t \). This tells us how much electrical energy has been used to drive the electrochemical reaction.

Knowing the total charge is key to figuring out how many moles of a substance have been produced. We apply Faraday's constant to connect electrical quantities with chemical amounts. We use the formula \( n = \frac{Q}{F} \), where \( n \) is moles of electrons, \( Q \) is the total charge, and \( F \) is Faraday's constant. The result relates the charged passed to the physical quantity of substance changed, helping us understand the efficiency and completeness of the electrolysis process.

Mole concept

The mole concept is foundational in chemistry, providing a way to quantify the amount of substance. A "mole" corresponds to Avogadro's number \(6.022 \times 10^{23}\) of particles, be it atoms, ions, or molecules. This simplifies working with vast quantities of small particles such as platinum atoms in electrolysis.

In our electrolysis example, the problem involves calculating the number of moles of platinum formed from a given mass. Using the molar mass of platinum, found on the periodic table, you convert mass to moles with the formula:

• \[ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The mole concept allows us to use mass measurements to understand chemical reactions on the atomic scale. This concept is crucial when determining how many atoms or ions participate in or result from a chemical process. It bridges the macroscopic world of grams and liters with the microscopic realm of atoms and molecules.