Question

In the electrolysis of a solution containing \(\mathrm{Ni}^{2+}(\mathrm{aq}),\) metallic \(\mathrm{Ni}(\mathrm{s})\) deposits on the cathode. Using a current of 0.150 A for 12.2 minutes, what mass of nickel will form?

Short answer

The mass of nickel deposited is 0.0913 grams.

Step-by-step solution

Find the Total Charge Passed

To find the total charge, use the formula: \( Q = I \times t \). Here, \( I = 0.150 \text{ A} \) and time \( t = 12.2 \text{ minutes} = 12.2 \times 60 \text{ seconds} \). Therefore, \( Q = 0.150 \times (12.2 \times 60) \text{ C} \). Calculate \( Q \).

Use Faraday's Law to Find Moles of Electrons

Faraday's Law states \( Q = nF \), where \( n \) is the moles of electrons, and \( F \) is Faraday's constant \( 96485 \text{ C/mol} \). Solve for \( n \): \( n = \frac{Q}{F} \). Use the charge \( Q \) calculated in the previous step.

Relate Moles of Electrons to Moles of Nickel

For \( \text{Ni}^{2+} \) ions depositing as \( \text{Ni} \), each metal ion requires 2 electrons (\( \text{Ni}^{2+} + 2e^- \rightarrow \text{Ni} \)). Therefore, moles of \( \text{Ni} \) formed is \( \frac{n}{2} \), where \( n \) is from Step 2.

Convert Moles of Nickel to Mass

Use the molar mass of nickel (58.69 g/mol) to convert moles of \( \text{Ni} \) to mass. Mass \( = \text{moles of Ni} \times 58.69 \text{ g/mol} \). Calculate this to find the mass of nickel deposited.

Key concepts

Nickel deposition

Electrolysis is a fascinating chemical process where electrical energy is used to drive a non-spontaneous chemical reaction. During the electrolysis of a nickel solution, nickel ions (\( \mathrm{Ni}^{2+}(\mathrm{aq})\)) are reduced and deposit as solid nickel (\( \mathrm{Ni}(\mathrm{s})\)) on the cathode.
This process is essential in fields such as electroplating, where a metal is deposited onto a surface. Nickel deposition is particularly useful in enhancing corrosion resistance and providing a decorative finish.
The cathode acts as the receiving end for the electrons, facilitating the reduction of nickel ions. As the current passes through the electrolytic cell, positively charged nickel ions migrate towards the negatively charged cathode and gain electrons to form solid nickel.
This transformation can be summarized by the equation: \( \mathrm{Ni}^{2+} + 2e^- \rightarrow \mathrm{Ni} \). By understanding the electrolysis process, we can calculate the amount of nickel deposited by examining the flow of electrical current and employing Faraday's laws.

Faraday's Law

Faraday's Law is a cornerstone of electrochemistry, defining the quantitative relationship between electric charge and chemical change. This law is instrumental in electrolysis, providing a precise way to relate the total charge passed through the system to the amount of substance that reacts or is deposited.
Faraday's Law is mathematically expressed as: \( Q = nF \), where

• \( Q \): total electric charge (in coulombs)
• \( n \): moles of electrons
• \( F \): Faraday's constant (\( 96485 \ \text{C/mol} \))

This relationship allows us to determine the amount of electron transfer occurring during electrolysis. In the context of nickel deposition, it lets us calculate the number of moles of electrons needed to deposit a specific amount of nickel.

Using Faraday's Law Calculations

Once the total charge \( Q \) is known, we can find the moles of electrons (\( n \)) using: \( n = \frac{Q}{F} \). This calculation gives us the means to figure out how much nickel will be deposited based on the electrical input, enabling precise predictions and control over the electroplating process.

Current and charge calculation

Current and charge calculations are vital for understanding and performing electrolysis processes. Current, measured in amperes (A), is the flow of electric charge per unit time and is crucial to determining the total charge that passes through an electrolytic solution.
Whenever you know the current and the time for which it flows, you can calculate the total charge using the formula: \( Q = I \times t \), where

• \( Q \) is the charge in coulombs (C)
• \( I \) is the current in amperes (A)
• \( t \) is the time in seconds (s)

For example, in the given exercise, a current of \( 0.150 \ \text{A} \) flowing for \( 12.2 \ \text{minutes} \) is equivalent to \( 12.2 \times 60 \text{ seconds} \). By inserting these values into the formula, we can calculate the total charge.
This charge is then used in Faraday's Law to determine the moles of electrons involved in the deposition process, which is a crucial step in quantifying how much nickel metal will be deposited.

Molar mass conversion

Converting moles to mass using molar mass is a straightforward yet essential step in chemistry, particularly in electrolysis. Once you've calculated the number of moles of a substance, converting that value into mass involves using the substance's molar mass.
The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol), and it acts as a bridge between the atomic world and the macroscopic laboratory scale. In the case of nickel, its molar mass is \( 58.69 \ \text{g/mol} \).
To convert moles of nickel to mass, you use the formula: Mass = Moles \( \times \) Molar Mass. After determining the moles of nickel formed during the electrolysis process, multiply it by nickel's molar mass to find the mass of nickel deposited.
This simple calculation allows scientists and engineers to accurately predict how much of a material is formed or needed in chemical processes, ensuring effective and efficient operation of industrial applications like electroplating.