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Calculate the minimum (least negative) cathode potential (versus SHE) needed to begin electroplating nickel from \(0.35 M \mathrm{Ni}^{2+}\) onto a piece of iron.

Short Answer

Expert verified
Answer: The minimum cathode potential needed is approximately -0.25 V.

Step by step solution

01

Find the standard reduction potentials of nickel and iron

First, we have to find the standard reduction potentials for nickel and iron. These values can be found in a standard reduction potential table. The standard half-cell potentials are as follows: Nickel: \(\mathrm{Ni^{2+}} + 2 \mathrm{e^-} \rightarrow \mathrm{Ni}; E^0_{Ni} = -0.25 V\) Iron: \(\mathrm{Fe^{2+}} + 2 \mathrm{e^-} \rightarrow \mathrm{Fe}; E^0_{Fe} = -0.44 V\)
02

Write the Nernst Equation for the nickel half-cell

The Nernst equation is used to calculate the cell potential under non-standard conditions. In this case, we have a non-standard concentration of \(\mathrm{Ni^{2+}}\). The Nernst equation for the nickel half-cell is given by: \(E_{Ni} = E^0_{Ni} - \cfrac{0.0592}{n} \log{(Q)}\) Here, \(E_{Ni}\) is the potential of nickel under nonstandard conditions, \(E^0_{Ni}\) is the standard potential of nickel, \(\cfrac{0.0592}{n}\) is a constant (where n is the number of electrons involved in the half-reaction, n = 2), and Q is the reaction quotient.
03

Calculate the reaction quotient (Q)

As the reaction involves only dissolved ions with no gases, we can find Q as follows: \(Q = \cfrac{[\mathrm{Ni}]}{[\mathrm{Ni^{2+}}]}\) Since there is no solid nickel initially, \([\mathrm{Ni}] = 0\). Thus, \(Q = 0\).
04

Substitute Q into the Nernst equation and solve for E_{Ni}

Now, we can substitute the value of Q (0) into the Nernst equation and solve for \(E_{Ni}\): \(E_{Ni} = E^0_{Ni} - \cfrac{0.0592}{2} \log{(0)}\) As we cannot take the logarithm of 0, we consider Q to be extremely small, allowing us to use the logarithm property: \(\log{(a)} = -\log{(\cfrac{1}{a})}\) \(E_{Ni} = E^0_{Ni} - \cfrac{0.0592}{2}(-\log{(\cfrac{1}{Q})})\) Since \(Q\) is extremely small, \(\cfrac{1}{Q}\) is considered to be large, and the logarithm term becomes large: \(E_{Ni} = E^0_{Ni} + \cfrac{0.0592}{2}(\log{(large)})\)
05

Determine the minimum cathode potential (versus SHE) needed

To start the electroplating process, the cathode potential must be more negative than the standard potential of the iron half-cell, so that the iron half-cell reduction becomes unfavorable. Therefore, the minimum cathode potential (versus SHE) needed is the potential of nickel when iron starts to reduce: \(E_{cathode} = E_{Ni} = E^0_{Ni} + \cfrac{0.0592}{2}(\log{(large)}) \approx E^0_{Ni} > E^0_{Fe}\) \(E_{cathode} \approx -0.25 V > -0.44 V\) Thus, the minimum cathode potential (versus SHE) needed to start electroplating nickel from the 0.35 M \(\mathrm{Ni^{2+}}\) solution onto a piece of iron is approximately -0.25 V.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cathode Potential
Cathode potential is an important concept when discussing electroplating. It refers to the potential at which reduction occurs at the cathode—or the negative electrode—of an electrochemical cell. In the context of electroplating, the cathode is the surface where metal ions (like nickel) gain electrons and form a solid metal coating on the substrate (like iron).

When calculating the cathode potential, especially for electroplating nickel from a nickel ion solution, it is crucial to determine the conditions under which nickel ions start to deposit on the cathode. This requires us to ensure the cathode potential is more negative than the metal ions being reduced. For nickel, it means adjusting the potential so that nickel (Ni) ions are reduced to solid nickel metal at the cathode. This forms the foundational step for effective nickel electroplating.
Nernst Equation
The Nernst equation is a core concept in electrochemistry for calculating the potential of an electrochemical cell under non-standard conditions. This is critical because in practical situations, like electroplating, the conditions usually deviate from the standard ones.

For nickel electroplating, the Nernst equation helps us find the potential at which nickel ions start depositing. It is expressed as: \[ E_{cell} = E^0 - \frac{RT}{nF} \ln Q \] where
  • \(E_{cell}\) is the cell potential.
  • \(E^0\) is the standard cell potential.
  • \(R\) is the universal gas constant.
  • \(T\) is the temperature in Kelvin.
  • \(n\) is the number of moles of electrons exchanged in the half-reaction.
  • \(F\) is the Faraday constant.
  • \(Q\) is the reaction quotient.

For nickel (with a common n of 2), and a concentration different from standard (like 0.35 M instead of 1 M), this equation helps adjust the theoretical standard potential to fit actual conditions, allowing us to anticipate the initiation of nickel deposition.
Standard Reduction Potential
Standard reduction potential provides the basic measurement for the tendency of a chemical species to acquire electrons and be reduced. Each metal has its own standard reduction potential, which is an essential reference for determining how one ion compares to another in terms of reactivity under standard conditions.

For nickel in the electroplating process, we use its standard reduction potential of \(-0.25\, V\) as a basis. This value indicates the propensity of nickel ions to gain electrons and form solid nickel at the electroplating cathode when conditions are standard. During electroplating, ensuring that the potential is more negative relative to other substances, such as iron (which has a \(-0.44\, V\) standard reduction potential), is vital.

This requirement ensures that during the electroplating process, nickel ions preferentially gain electrons over other possible ions, resulting in a desired nickel coat.
Nickel Electroplating
Nickel electroplating is a widespread technique used to apply a thin layer of nickel onto metal objects for various purposes, such as enhancing appearance, preventing corrosion, or increasing surface hardness. The process involves submerging the metal object in an electrolyte solution containing nickel ions and applying an electric current.

The object to be plated acts as the cathode, and nickel metal acts as the anode. Nickel ions (\(\mathrm{Ni^{2+}}\)) in the solution are reduced at the cathode, depositing as a thin metallic layer of nickel.
Key points about nickel electroplating include:
  • This process requires careful control of electrochemical conditions, ensuring nickel is preferentially deposited.
  • The cathode potential must be carefully maintained to allow for the efficient deposition of nickel without unwanted reactions.
  • Parameters like temperature, electrolyte concentration, and current density are all crucial for achieving a consistent and high-quality nickel coating.

Understanding these principles ensures successful outcomes in commercial applications and contributes to material durability and aesthetics.

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Most popular questions from this chapter

Methane can serve as the fuel for electric cars powered by fuel cells. Carbon dioxide is a product of the fuel cell reaction. All cars powered by internal combustion engines burning natural gas (mostly methane) produce \(\mathrm{CO}_{2}\). Why are electric vehicles powered by fuel cells likely to produce less \(\mathrm{CO}_{2}\) per mile?

The negative sign in Equation \(17.3\left(w_{\text {clec }}=-Q E_{\text {cell }}\right)\) seems to indicate that a voltaic cell with a positive cell potential does negative electrical work. How is this possible?

In a voltaic cell based on the \(\mathrm{Zn} / \mathrm{Cu}^{2+}\) cell reaction, $$ \mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Cu}(s)+\mathrm{Zn}^{2+}(a q) $$ there is exactly one mole of each reactant and product. A second cell based on the following cell reaction: $$ \mathrm{Cd}(s)+\mathrm{Cu}^{2+}(a q) \rightarrow \mathrm{Cu}(s)+\mathrm{Cd}^{2+}(a q) $$ also has exactly one mole of each reactant and product. Which of the following statements about these two cells is true? a. Their cell potentials are the same. b. The masses of their electrodes are the same. c. The quantities of electric charge that they can produce are the same. d. The quantities of electric energy that they can produce are the same.

From the table of standard reduction potentials in Appendix 6 a. Select an oxidizing agent that will oxidize \(\mathrm{Cr}(s)\) to \(\mathrm{Cr}^{3+}(a q)\) but not \(\mathrm{Cd}(s)\) to \(\mathrm{Cd}^{2+}(a q)\) b. Select a reducing agent that will reduce Br \(_{2}(\ell)\) to \(\mathrm{Br}^{-}(a q)\) but not \(\mathrm{I}_{2}(s)\) to \(1^{-}(a q).\)

Glucose Metabolism The standard potentials for the reduction of nicotinamide adenine dinuclcotide (NAD") and oxaloacetate (reactants in the multistep metabolism of glucose) are as follows: $$ \mathrm{NAD}^{+}(a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{NADH}(a q)+\mathrm{H}^{+}(a q) $$ Oxaloacetate \((a q)+2 \mathrm{H}^{+}(a q)+2 \mathrm{e}^{-} \rightarrow\) malate \((a q)\) \(E^{*}=-0.166 \mathrm{V}\) a. Calculate the standard potential for the following reaction: Oxaloacetate \((a q)+\mathrm{NADH}(a q)+\mathrm{H}^{+}(a q) \rightarrow\) malate( \(a q)+\mathrm{NAD}^{+}(a q)\) b. Calculate the equilibrium constant for the reaction at \(298 \mathrm{K}.\)

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