For a lead storage battery: (a) Sketch one cell that shows the anode, cathode, electrolyte, direction of electron and ion flow, and sign of the electrodes. (b) Write the anode, cathode, and overall cell reactions. (c) Calculate the equilibrium constant for the cell reaction (E° = 1.924 V). (d) What is the cell voltage when the cell reaction reaches equilibrium?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

검증된 단계별 안내

Step 1: Understand the components of a lead storage battery. The anode is made of lead (Pb), the cathode is lead dioxide (PbO2), and the electrolyte is sulfuric acid (H2SO4). Electrons flow from the anode to the cathode through an external circuit, while ions move through the electrolyte.

Step 2: Write the half-reactions for the anode and cathode. At the anode, lead is oxidized: \( \text{Pb} \rightarrow \text{Pb}^{2+} + 2\text{e}^- \). At the cathode, lead dioxide is reduced: \( \text{PbO}_2 + 4\text{H}^+ + 2\text{e}^- \rightarrow \text{Pb}^{2+} + 2\text{H}_2\text{O} \).

Step 3: Combine the half-reactions to write the overall cell reaction. Ensure that the electrons cancel out: \( \text{Pb} + \text{PbO}_2 + 4\text{H}^+ \rightarrow 2\text{Pb}^{2+} + 2\text{H}_2\text{O} \).

Step 4: Use the Nernst equation to calculate the equilibrium constant \( K \) for the cell reaction. The equation is \( E^\circ = \frac{RT}{nF} \ln K \), where \( E^\circ \) is the standard cell potential, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, \( n \) is the number of moles of electrons transferred, and \( F \) is Faraday's constant.

Step 5: Determine the cell voltage at equilibrium. At equilibrium, the cell voltage is zero because the forward and reverse reactions occur at the same rate, and there is no net electron flow.

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Electrochemical Cells

Electrochemical cells consist of two electrodes (anode and cathode) immersed in an electrolyte, facilitating redox reactions. The anode is where oxidation occurs, releasing electrons, while the cathode is where reduction takes place, accepting electrons. Understanding the flow of electrons and ions is crucial for analyzing the cell's operation and sketching its components accurately.

Cell Reactions and Standard Electrode Potentials

Cell reactions in electrochemical cells involve the transfer of electrons between the anode and cathode, which can be represented by half-reactions. The standard electrode potential (E°) quantifies the tendency of a species to gain electrons, influencing the overall cell reaction. Writing the anode and cathode reactions is essential for calculating the overall cell reaction and its equilibrium constant.

Equilibrium Constant and Cell Voltage

The equilibrium constant (K) for a cell reaction can be calculated using the Nernst equation, which relates the standard cell potential (E°) to the concentrations of reactants and products at equilibrium. At equilibrium, the cell voltage drops to zero, indicating no net reaction occurs. Understanding how to calculate K and interpret cell voltage is vital for predicting the behavior of the electrochemical cell under different conditions.