Problem 82 - Introductory Chemistry Atoms First

Question

Recharging a battery means forcing a spontaneous redox reaction to run backwards - in the nonspontaneous direction - once all the reactants have been used up. In Practice Problem \(10.24\), you considered a battery made from lead and copper. (a) Write the spontaneous redox reaction for this battery. (b) Write the recharging reaction for this battery.

Step-by-Step Solution

Answer

(a) The spontaneous redox reaction for the battery is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\) (b) The recharging reaction for the battery is: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\)

Step 1: Identify half-reactions for lead and copper

For a battery made from lead and copper, we need to identify the half-reactions for both the metals involved. Lead reacts as follows: \(Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\) And copper reacts as: \(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\)

Step 2: Combine half-reactions to find the spontaneous redox reaction

Now, we need to combine both half-reactions to find the overall redox reaction for the battery. Balance the number of electrons in both half-reactions by multiplying the entire copper reaction by 2, so the electrons balance out. Then, add both half-reactions: \(Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\) \(2(Cu^{2+}(aq) + 2e^- \rightarrow Cu(s))\) The balanced redox reaction is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\)

Step 3: Write the recharging reaction for the battery

Finally, the recharging reaction for the battery can be found by reversing the spontaneous redox reaction we've found in Step 2: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\) So, the answers are: (a) The spontaneous redox reaction for the battery is: \(Pb^{2+}(aq) + 2Cu(s) \rightarrow Pb(s) + 2Cu^{2+}(aq)\) (b) The recharging reaction for the battery is: \(Pb(s) + 2Cu^{2+}(aq) \rightarrow Pb^{2+}(aq) + 2Cu(s)\)

Key Concepts

Spontaneous Reactions

In the world of chemistry, spontaneous reactions are processes that occur naturally without external intervention. These reactions happen because the energy favorably flows from one form to another, usually releasing energy in the form of heat or electricity. In the case of our battery made from lead and copper, the spontaneous redox reaction combines the movement of electrons between these two metals.

A spontaneous reaction is always accompanied by a negative free energy change, which indicates that it releases energy. In our specific scenario, the balanced spontaneous reaction can be identified as:

• Lead ions \(Pb^{2+}(aq)\) react with solid copper \(Cu(s)\)
• This reaction forms solid lead \(Pb(s)\) and copper ions \(Cu^{2+}(aq)\)

This favorable exchange of electrons is the essence of a working battery, allowing it to produce electricity.

Half-Reactions

Half-reactions are a convenient way to break down redox reactions into two parts: oxidation and reduction. In our exercise, we focus on the separate transformations happening to lead and copper during the battery's discharge and recharging phases.

The concept is pretty simple:

• Oxidation (loss of electrons) and reduction (gain of electrons) occur simultaneously
• For lead: \[Pb^{2+}(aq) + 2e^- \rightarrow Pb(s)\]
• For copper: \[Cu^{2+}(aq) + 2e^- \rightarrow Cu(s)\]

Each half-reaction highlights the change in electron density around the specific elements and allows chemists to see exactly what happens during electron transfer processes. To find the overall redox reaction, simply combine these half-reactions and ensure the electrons lost and gained balance out, illustrating the complete chemical process.

Battery Recharging

When a battery is drained of its reactive components, it enters a phase where the spontaneous reaction ceases. To recharge it, you have to reverse the redox reactions that occurred during the discharging phase. This is because to recharge it, energy must be inputted back into the system, allowing it to push electrons in the reverse direction.

In the context of the lead and copper battery exercise, the recharging reaction is simply the reverse of the discharging reaction:

• Lead solid \(Pb(s)\) and copper ions \(2Cu^{2+}(aq)\) reconvert to lead ions \(Pb^{2+}(aq)\) and solid copper \(2Cu(s)\)

By plugging the charger, external energy is delivered to the battery, reversing the chemical reactions. This builds up the original reactants and resets the battery, enabling it to release energy again in future uses.

Electrochemistry

Electrochemistry is a branch of chemistry that studies the relationship between electricity and identifiable chemical changes. In our discussion about batteries, it provides the backbone knowledge to how reactions convert chemical energy into electrical energy and vice-versa.

Here are some key ideas:

• Redox reactions are central, involving electron transfer
• Spontaneous redox in batteries produces current
• Non-spontaneous reactions, as seen during recharging, require external energy

Electrochemistry at its core helps us understand how batteries work, and more importantly, how they can be recharged to continue providing energy. It's a fascinating field, as it bridges the two worlds of chemistry and electronics, making everyday technologies possible.