Question

What mass of each of the following substances can be produced in 1.0 h with a current of 15 A? a. \(\mathrm{Co}\) from aqueous \(\mathrm{Co}^{2+}\) b. \(\mathrm{Hf}\) from aqueous \(\mathrm{Hf}^{4+}\) c. \(\mathrm{I}_{2}\) from aqueous \(\mathrm{KI}\) d. \(\mathrm{Cr}\) from molten \(\mathrm{CrO}_{3}\)

Short answer

With a current of 15 A in 1.0 h, we can calculate the mass of each substance produced as follows: a. Mass of Co = 31.31 g b. Mass of Hf = 43.94 g c. Mass of \(I_{2}\) = 63.41 g d. Mass of Cr = 10.26 g

Step-by-step solution

Identify the redox reactions

For each substance, we need to identify the redox reactions occurring during the electrolysis. a. \(\mathrm{Co^{2+}} + 2e^- \rightarrow \mathrm{Co}\) b. \(\mathrm{Hf^{4+}} + 4e^- \rightarrow \mathrm{Hf}\) c. For iodine, \(2I^-\rightarrow I_{2} +2e^-\) d. For chromium, \(Cr^{6+} + 6e^- \rightarrow Cr\)

Calculate the moles of electrons that can pass in 1 hour

Use the given time and current to find the number of moles of electrons passing through the circuit. We have time \(t = 1.0 hr = 3600 s\) and current \(I = 15 A\). We can use the given time and current to calculate the charge \(Q\) that passes through the system using the formula: \[Q = It\] Now we'll need to convert the charge to moles of electrons: We know that 1 mole of electrons has a charge of 1 Faraday \(F \approx 96485 \, C/mol\). To calculate the moles of electrons, we divide the calculated charge \(Q\) by Faraday's constant \(F\). Moles of electrons = \(\cfrac{Q}{F}\)

Determine the moles of each substance produced

Use the balanced redox reactions and the moles of electrons to determine the number of moles of each product formed. a. For cobalt, \(Moles \, of \, Co = \cfrac{1}{2} \cdot Moles \, of \, electrons\) b. For hafnium, \(Moles \, of \, Hf = \cfrac{1}{4}\cdot Moles\,of\,electrons\) c. For iodine, \(Moles \, of \, I_{2} = \cfrac{1}{2} \cdot Moles\,of\,electrons\) d. For chromium, \(Moles \, of \, Cr = \cfrac{1}{6} \cdot Moles\,of\,electrons\)

Calculate the mass of each substance produced

Multiply the moles of each substance produced by its molar mass to obtain the mass produced. a. Mass of Co = \(Moles \, of \, Co \cdot Molar \, mass \, of \, Co\) b. Mass of Hf = \(Moles \, of \, Hf \cdot Molar \, mass \, of \, Hf\) c. Mass of \(I_{2}\) = \(Moles \, of \, I_{2} \cdot Molar \, mass \, of \, I_{2}\) d. Mass of Cr = \(Moles \, of \, Cr\cdot Molar \, mass \, of \, Cr\) Following these steps, you can calculate the mass of each substance produced in 1.0 hour with a current of 15 A.

Key concepts

Redox Reactions

In the process of electrolysis, redox reactions are central to producing different substances. A redox (reduction-oxidation) reaction involves the transfer of electrons between species.

During electrolysis, electrical energy drives the transfer of electrons, allowing ions to gain or lose electrons and form different elements or compounds. For example, consider the reduction of cobalt ions:

• The reaction: \( \mathrm{Co^{2+}} + 2e^- \rightarrow \mathrm{Co} \) represents the cobalt ions gaining electrons to become metal cobalt.
• Oxidation happens when an ion loses electrons, like iodide ions forming iodine: \( 2I^-\rightarrow I_{2} + 2e^- \).

Each redox reaction requires a specific number of electrons to complete the transformation. Recognizing these reactions helps in determining how much of a substance can be produced during electrolysis.

Faraday's Constant

Faraday's constant is crucial in electrolysis calculations as it bridges the relationship between electric charge and moles of electrons. It represents the charge of one mole of electrons, approximately 96485 Coulombs per mole (\(C/mol\)).

This constant helps in converting the total charge passed through an electrolytic cell into the number of moles of electrons.

Understanding and correctly applying Faraday's constant allows accurate predictions of the amount of substance produced. It simplifies the calculations needed after determining how much charge has passed through the solution:

• Using formula: \( Q = It \)
• We divide \( Q \) by Faraday's constant to get moles of electrons. This step is essential in transitioning from electrical measurements to chemical quantities.

Moles of Electrons

The concept of moles of electrons is integral in linking the electric current supplied to the chemical reactions happening in electrolysis. In any electrolysis process, electrons are the moving charges that mediate reduction and oxidation reactions.

To determine the number of moles of electrons flowing through an electrolyte over a time period, the equation \( Q = It \) is used, where \(Q\) is the charge. Then, using Faraday's constant, convert this charge into moles of electrons:

• The number of moles of electrons = \( \cfrac{Q}{F} \)

This knowledge allows us to relate the electron flow to chemical transformations, using the stoichiometry from balanced equations (like reduction of \( \mathrm{Co^{2+}}\)). This is key in computing the amount of products formed.

Molar Mass

Molar mass is the mass of one mole of a given substance and is expressed in units of grams per mole (\(g/mol\)). It allows us to convert between moles and grams, which is crucial in calculating the mass of products formed during electrolysis.

To find the mass of a product, multiply the moles of the substance by its molar mass. For instance, if during electrolysis, you determine \(1\) mole of \( \mathrm{Co} \) is produced, and the molar mass of cobalt is \(58.93 \, g/mol\), the mass of cobalt can be calculated using:

• Mass = moles \( \times \) molar mass

This helps translate the theoretical yield of electrolytic reactions into measurable practical outcomes, allowing for precise mass estimations of substances produced.