Problem 38 - Chemistry: An Atoms-Focused Approach

Question

The electrolyte in an electricity-generating device called a fuel cell consists of a mixture of \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) and \(\mathrm{K}_{2} \mathrm{CO}_{3}\) heated to \(650^{\circ} \mathrm{C} .\) At this temperature these ionic solids melt. Explain how the mixture of molten carbonates can conduct electricity.

Step-by-Step Solution

Answer

Question: Explain how a mixture of molten carbonates (Li₂CO₃ and K₂CO₃) can conduct electricity when heated to 650°C. Answer: A mixture of molten carbonates (Li₂CO₃ and K₂CO₃) conducts electricity when heated to 650°C because the ionic compounds melt and allow the ions (Li⁺, K⁺, and CO₃²⁻) to move freely. When an electric field is applied, the cations move toward the negatively charged electrode (cathode) and the anions move toward the positively charged electrode (anode), generating an electric current and enabling the conduction of electricity.

Step 1: Understand the components of the electrolyte

The electrolyte is a mixture of lithium carbonate (Li₂CO₃) and potassium carbonate (K₂CO₃). These are ionic compounds, meaning that they consist of positively charged cations (Li⁺ and K⁺) and negatively charged anions (CO₃²⁻). In the solid state, these ions are held together by strong electrostatic forces, forming a rigid ionic lattice.

Step 2: Explain the effect of heating on the ionic compounds

When the mixture is heated to 650°C, the ionic compounds melt, transitioning from the solid state to the liquid state. In the liquid state, the ions are able to move freely as the electrostatic forces holding the ions together in the lattice are overcome by the thermal energy.

Step 3: Define electrical conductivity and its relation to the ions

Electrical conductivity is the ability of a material to allow the movement of charged particles (like electrons or ions) under the influence of an electric field. In the case of molten carbonates, the charged particles are the ions (Li⁺, K⁺, and CO₃²⁻). In the molten state, these ions are free to move, and thus they can carry an electric charge through the electrolyte when an electric field is applied.

Step 4: Describe how the molten carbonate mixture conducts electricity

As mentioned earlier, the melting of the carbonates leads to the ions being free to move. When an electric field is applied to the molten carbonate mixture, the Li⁺ and K⁺ cations move toward the negatively charged electrode (cathode), while the CO₃²⁻ anions move toward the positively charged electrode (anode). This movement of ions generates an electric current, and therefore, the molten carbonate mixture is able to conduct electricity.

Key Concepts

Electrolyte

An electrolyte is a substance that produces an electrically conducting solution when dissolved in a polar solvent, such as water. A common example is salt dissolved in water. In the context of a fuel cell, electrolytes are crucial for conducting electricity. They facilitate the movement of ions between electrodes, which is essential for maintaining a steady electric current. In this exercise, the electrolyte consists of a mixture of lithium carbonate (

• Li₂CO₃
• Potassium carbonate (K₂CO₃)

These compounds are termed ionic because they consist of ions.
On heating, their solid structures melt, dissolving into a state where ions can move freely. This free movement is key for electric charge conduction. Without electrolytes, fuel cells wouldn't effectively produce electricity.

Ionic Compounds

Ionic compounds are made from ions, which are charged particles. These compounds form a crystal lattice, held together by strong electrostatic forces. This causes them to be hard and brittle in their solid state.
When out of this solid state, like when heated to high temperatures in a fuel cell, their structure breaks down allowing ions to become mobile. In our scenario:

• Lithium carbonate (Li₂CO₃)
• Potassium carbonate (K₂CO₃)

are ionic compounds. In the solid form, ions are locked in place. Upon melting, this restriction is lifted. This motion of ions from lattice to liquid state allows them to conduct electrical currents, as free ions can now move from one electrode to the other.

Electrical Conductivity

Electrical conductivity refers to a material's ability to conduct electric current. It denotes how easily electrons or ions can move through said material.
In the case of molten ionic compounds, such as the molten mixture of lithium and potassium carbonates, electrical conductivity changes dramatically from the solid to the liquid state.

• The solid state: ions are tightly held in a lattice, limiting movement and thus, conductivity.
• The liquid state: heat disrupts this lattice, allowing ions to move freely.

When an external electric field is applied, it initiates ion movement. This movement - Li⁺ and K⁺ ions towards the cathode, and CO₃²⁻ ions towards the anode - facilitates the flow of electrical current. This flow is vital for the working of devices like fuel cells, turning chemical energy into electrical energy efficiently.