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The Gibbs free energy is given below. Use it to determine the equilibrium constant of the reaction under standard conditions. Pb2+ (aq) + Mg(s) = Pb(s) + Mg²+ (aq) AG=-432 kJ

The Gibbs free energy is given below. Use it to determine the equilibrium constant of the reaction under standard conditions. Pb2+ (aq) + Mg(s) = Pb(s) + Mg²+ (aq) AG=-432 kJ

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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### Determination of the Equilibrium Constant Using Gibbs Free Energy #### Problem Statement Utilize the provided Gibbs free energy data to determine the equilibrium constant of the following reaction under standard conditions: \[ \text{Pb}^{2+} (\text{aq}) + \text{Mg} (\text{s}) \rightarrow \text{Pb} (\text{s}) + \text{Mg}^{2+} (\text{aq}) \] The Gibbs free energy change (\( \Delta G^\circ \)) for the reaction is given as: \[ \Delta G^\circ = -432 \, \text{kJ} \] #### Calculation To find the equilibrium constant \( K \), we use the relationship between the Gibbs free energy change and the equilibrium constant at standard conditions, given by the equation: \[ \Delta G^\circ = -RT \ln K \] Where: - \( R \) is the universal gas constant (\( R = 8.314 \, \text{J/mol} \cdot \text{K} \)) - \( T \) is the temperature in Kelvin (assumed to be 298 K unless otherwise specified) - \( \Delta G^\circ \) is the standard Gibbs free energy change Solve for \( K \): \[ K = e^{-\Delta G^\circ / RT} \] Substituting the given values: \[ \Delta G^\circ = -432,000 \, \text{J} \] \[ K = e^{\frac{432,000}{8.314 \times 298}} \] #### Input Instructions 1. Calculate the coefficient in scientific notation. 2. Determine the exponent in scientific notation. 3. Enter either a \( + \) or \( - \) sign and the magnitude accordingly. #### Input Fields - **Coefficient (green box):** Enter the coefficient from your scientific notation calculation. - **Exponent (yellow box):** Enter the exponent from your scientific notation calculation. Press **Enter** to submit your answer. --- This explanation provides the contextual background needed to understand the calculations and steps required to determine the equilibrium constant using the Gibbs free energy change. Ensure you double-check your calculations for accuracy.
Transcribed Image Text:### Determination of the Equilibrium Constant Using Gibbs Free Energy #### Problem Statement Utilize the provided Gibbs free energy data to determine the equilibrium constant of the following reaction under standard conditions: \[ \text{Pb}^{2+} (\text{aq}) + \text{Mg} (\text{s}) \rightarrow \text{Pb} (\text{s}) + \text{Mg}^{2+} (\text{aq}) \] The Gibbs free energy change (\( \Delta G^\circ \)) for the reaction is given as: \[ \Delta G^\circ = -432 \, \text{kJ} \] #### Calculation To find the equilibrium constant \( K \), we use the relationship between the Gibbs free energy change and the equilibrium constant at standard conditions, given by the equation: \[ \Delta G^\circ = -RT \ln K \] Where: - \( R \) is the universal gas constant (\( R = 8.314 \, \text{J/mol} \cdot \text{K} \)) - \( T \) is the temperature in Kelvin (assumed to be 298 K unless otherwise specified) - \( \Delta G^\circ \) is the standard Gibbs free energy change Solve for \( K \): \[ K = e^{-\Delta G^\circ / RT} \] Substituting the given values: \[ \Delta G^\circ = -432,000 \, \text{J} \] \[ K = e^{\frac{432,000}{8.314 \times 298}} \] #### Input Instructions 1. Calculate the coefficient in scientific notation. 2. Determine the exponent in scientific notation. 3. Enter either a \( + \) or \( - \) sign and the magnitude accordingly. #### Input Fields - **Coefficient (green box):** Enter the coefficient from your scientific notation calculation. - **Exponent (yellow box):** Enter the exponent from your scientific notation calculation. Press **Enter** to submit your answer. --- This explanation provides the contextual background needed to understand the calculations and steps required to determine the equilibrium constant using the Gibbs free energy change. Ensure you double-check your calculations for accuracy.
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