Problem 39 - Chemistry: An Atoms-Focused Approach

Question

Nickel-Sodium Batteries Researchers in England are developing a battery for electric vehicles based on the reaction between \(\mathrm{NiCl}_{2}(s)\) and \(\mathrm{Na}(\mathrm{s}):\) $$ 2 \mathrm{Na}(s)+\mathrm{NiCl}_{2}(s) \rightarrow \mathrm{Ni}(s)+2 \mathrm{NaCl}(s) $$ The cells in the battery produce \(2.58 \mathrm{V}\) a. Assign oxidation numbers to each element in the nickel and sodium compounds. b. How many electrons are transferred in the overall reaction? c. What is the value of \(\Delta G_{\text {cen }} ?\)

Step-by-Step Solution

Answer

Based on the given electrochemical reaction involving sodium and nickel chloride, calculate the Gibbs free energy change (ΔGcen) in the reaction. Solution: 1. Determine the oxidation numbers of each element in the reactants. 2. Identify the redox reaction taking place. 3. Determine the number of electrons transferred in the redox reaction. 4. Calculate ΔGcen using the given voltage and the number of transferred electrons. Using these steps, we find that ΔGcen for this electrochemical reaction is approximately -497,739 J/mol.

Step 1: Determine the Oxidation Numbers

To start, we need to determine the oxidation numbers of each element in the given reactants. In the equation \(2\mathrm{Na}(s)+\mathrm{NiCl}_{2}(s) \rightarrow \mathrm{Ni}(s)+2\mathrm{NaCl}(s)\), the oxidation numbers for each species are as follows: Na: The oxidation number of a pure metal, such as sodium, is 0. NiCl₂: In a compound, the sum of the oxidation numbers equals the overall charge. The overall charge of a neutral molecule (no net charge) is 0. Chlorine has an oxidation number of -1, and since there are two chlorine atoms in the molecule, the oxidation number of nickel is +2. Ni: The oxidation number of pure nickel is 0. NaCl: Sodium has an oxidation number of +1, and Chlorine has an oxidation number of -1.

Step 2: Identify the Redox Reaction

Now that the oxidation numbers have been determined, we can identify the redox reaction taking place. Sodium is going from an oxidation number of 0 to +1, which means it's losing one electron. This is called an oxidation reaction. $$ \mathrm{Na}(s) \rightarrow \mathrm{Na}^{+}(s)+\mathrm{e}^{-} $$ Nickel is going from an oxidation number of +2 to 0, which means it's gaining two electrons. This is called a reduction reaction. $$ \mathrm{Ni}^{2+}(s)+2\mathrm{e}^{-} \rightarrow \mathrm{Ni}(s) $$

Step 3: Determine Electron Transfer

Two moles of sodium atoms are involved in the reaction, and for each mole, one electron is transferred. In this overall electrochemical reaction, two sodium atoms will each lose one electron to form two sodium ions. $$ 2\mathrm{Na}(s) \rightarrow 2\mathrm{Na}^{+}(s)+2\mathrm{e}^{-} $$ On the other hand, nickel(II) ions will gain two of these electrons to form metallic nickel. $$ \mathrm{Ni}^{2+}(s)+2\mathrm{e}^{-} \rightarrow \mathrm{Ni}(s) $$ This means that in the overall redox reaction, a total of 2 (2x1) electrons are transferred.

Step 4: Calculate ΔGcen

Given the number of electrons transferred (n) and the voltage (E) produced by the battery, we can calculate ΔGcen using the following equation: $$ \Delta G_{\text{cen}} = -nFE $$ In this case, n = 2, F (Faraday's constant) = 96,485 C/mol, and E = 2.58 V. Plugging these values into the equation, we get: $$ \Delta G_{\text{cen}} = -2(96,485\ \mathrm{C/mol})(2.58\ \mathrm{V}) $$ $$ \Delta G_{\text{cen}} = -497,\!739\ \mathrm{J/mol} $$ Thus, the Gibbs free energy change (ΔGcen) for this electrochemical reaction is approximately -497,739 J/mol.

Key Concepts

Oxidation Numbers

Oxidation numbers are a key concept in redox reactions. They help us understand how electrons are being transferred between atoms in a reaction. In the given reaction involving sodium (Na) and nickel chloride (NiCl₂), each element begins with a specific oxidation state. For pure sodium, the oxidation number is 0 because it is in its elemental form. Similarly, pure nickel has an oxidation number of 0. In \( \mathrm{NiCl}_2 \), nickel carries an oxidation number of +2 because each of the two chloride ions has an oxidation number of -1, and the compound is overall neutral. When sodium transforms into sodium chloride (NaCl), sodium's oxidation number changes to +1, while chlorine remains at -1. Tracking these changes helps identify the oxidation and reduction processes within the reaction, highlighting the movement of electrons between the reactants and products. When sodium's oxidation number increases, it loses electrons. Nickel's decrease in oxidation number indicates it gains electrons.

Electron Transfer

Electron transfer is the fundamental aspect of redox reactions. During the reaction between sodium and nickel chloride, sodium atoms lose electrons, and nickel ions gain them. This movement of electrons is crucial for completing the redox reaction.In this particular reaction:

• Sodium (\(\mathrm{Na(s)}\)) transitions from an oxidation number of 0 to +1, indicating that each sodium atom loses one electron.
• Nickel (\(\mathrm{Ni}^{2+}(s)\)), initially carrying a +2 charge, gains two electrons to become neutral nickel metal (\(\mathrm{Ni(s)}\)).

To balance the electron transfer, two moles of sodium donate a total of two electrons, which are then accepted by one mole of \(\mathrm{Ni}^{2+}\) ions. This complete transfer of 2 electrons showcases the intrinsic link between electron flow and chemical changes in a redox reaction.

Gibbs Free Energy

Gibbs Free Energy (\(\Delta G_{\text{cen}}\)) is a vital concept in understanding the energetics of redox reactions. It provides the measure of the maximum amount of work that can be extracted from the electrochemical process, such as in a battery.The change in Gibbs Free Energy for the reaction is calculated using the equation: \[\Delta G_{\text{cen}} = -nFE\]where:

• \( n \) is the number of moles of electrons transferred, which is 2 in this reaction.
• \( F \) is Faraday's constant, equivalent to 96,485 C/mol.
• \( E \) is the electromotive force, or cell potential, here equal to 2.58 V.

Substituting these values into the formula provides:\[\Delta G_{\text{cen}} = -2 \times 96,485\ \text{C/mol} \times 2.58\ \text{V} = -497,739\ \text{J/mol}\]Thus, this negative value indicates that the reaction proceeds spontaneously, releasing energy that can be harnessed for electrical work, central to the functioning of nickel-sodium batteries.