Problem 75 - Chemistry The Molecular Science

Question

Calculate how long it would take to electroplate a metal surface with \(0.500 \mathrm{~g}\) nickel metal from a solution of \(\mathrm{Ni}^{2+}\) with a current of \(4.00 \mathrm{~A}\).

Step-by-Step Solution

Answer

It takes approximately 6.85 minutes to electroplate 0.500 g of nickel.

Step 1: Write the relevant electrochemical equation

The relevant electrochemical equation for nickel electroplating is the reduction of nickel ions: \(\text{Ni}^{2+} + 2e^- \rightarrow \text{Ni}\). This equation shows that 2 moles of electrons are required to reduce 1 mole of \(\text{Ni}^{2+}\) to nickel metal.

Step 2: Determine the moles of nickel

Calculate the number of moles of nickel using the formula: \[\text{Moles of Ni} = \frac{\text{Mass of Ni}}{\text{Molar Mass of Ni}}\]. The molar mass of nickel is approximately \(58.69 \, \text{g/mol}\). Thus, \[\text{Moles of Ni} = \frac{0.500 \text{ g}}{58.69 \text{ g/mol}} = 0.00852 \text{ mol}.\]

Step 3: Calculate the moles of electrons needed

From the electrochemical equation, 2 moles of electrons are needed to deposit 1 mole of nickel. Therefore, calculate the moles of electrons required to deposit 0.00852 mol of nickel: \[\text{Moles of } e^- = 2 \times 0.00852 = 0.01704 \text{ mol}.\]

Step 4: Calculate the total charge needed

To find the total charge needed, use the formula: \[\text{Total Charge } (C) = \text{Moles of e}^- \times F\], where \(F\) (Faraday's constant) is approximately \(96485 \text{ C/mol}\). Thus, \[\text{Total Charge} = 0.01704 \times 96485 = 1644.28 \text{ C}.\]

Step 5: Calculate the time required

Use the formula \[t = \frac{Q}{I}\], where \(Q\) is the total charge, and \(I\) is the current (4.00 A). Thus, \[t = \frac{1644.28}{4.00} = 411.07 \text{ s}.\] Finally, convert the time from seconds to minutes: \(\frac{411.07}{60} \approx 6.85 \text{ minutes}.\)

Key Concepts

Nickel Reduction

Nickel reduction is a crucial process in electroplating. Electroplating involves depositing a thin layer of metal onto a surface. In nickel reduction, nickel ions (\(\text{Ni}^{2+}\)) from a solution are converted to nickel metal. This transformation occurs with the help of electrons. This is represented by the electrochemical equation:

• \(\text{Ni}^{2+} + 2e^- \rightarrow \text{Ni}\)

This equation shows that two electrons are needed to reduce one nickel ion to nickel metal. In practical applications, this reduction is achieved by applying an electric current. The electric current provides the necessary electrons.

Faraday's Constant

Faraday's constant is a key element in electrochemistry. It is defined as the amount of electric charge per mole of electrons.Faraday's constant is approximately 96,485 coulombs per mole (C/mol). This constant allows us to link the amount of substance deposited or dissolved in an electrochemical reaction with the quantity of electricity used.In electroplating, it helps determine how many moles of electrons are required to deposit a metal. When calculating the total charge in a reaction, we multiply the moles of electrons by Faraday's constant:

• \( \text{Total charge} = \text{moles of } e^- \times F \)

Electrochemical Equation

An electrochemical equation represents the overall reaction in electrochemical cells. For nickel electroplating, the electrochemical equation is:

• \( \text{Ni}^{2+} + 2e^- \rightarrow \text{Ni} \)

This equation is essential because it tells us how many moles of electrons are needed to induce a certain reaction. In this case, two moles of electrons will reduce one mole of nickel ions to nickel metal. Understanding this equation is vital because it forms the basis for calculating how much electricity is required to perform the necessary plating.

Molar Mass Calculation

Calculating molar mass is a basic skill in chemistry. The molar mass of an element is the mass of one mole of its atoms, usually expressed in grams per mole (g/mol).For nickel, the molar mass is approximately 58.69 g/mol. Knowing the molar mass allows us to convert mass into moles, facilitating calculations in electrochemical equations.The formula to calculate moles from mass is:

• \(\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\)

This conversion is crucial in electroplating calculations, as it lets us know the exact number of moles of the metal involved in the reaction.