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What is the Gibbs free energy for the reaction below at standard conditions? 3Pb(s) + 2Cr3+ (aq) = 3Pb²+ (aq) + 2Cr(s) K 1.30 x 10-61 = AG° = [?] kJ

What is the Gibbs free energy for the reaction below at standard conditions? 3Pb(s) + 2Cr3+ (aq) = 3Pb²+ (aq) + 2Cr(s) K 1.30 x 10-61 = AG° = [?] 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
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### Gibbs Free Energy Calculation for a Chemical Reaction #### Problem Statement: Determine the Gibbs free energy change (ΔG°) for the reaction below under standard conditions: \[ \text{3Pb(s) + 2Cr}^{3+}\text{(aq)} \rightarrow \text{3Pb}^{2+}\text{(aq) + 2Cr(s)} \] Given the equilibrium constant (K) for this reaction: \[ K = 1.30 \times 10^{-61} \] #### Required Calculation: \[ \Delta G° = \text{[?]} \, \text{kJ} \] #### Instructions: To find ΔG°: 1. Enter either a "+" or "-" sign and the magnitude of your answer in the provided text box. 2. Make sure your answer is in kilojoules (kJ). #### Input Section: - **Free Energy, kJ:** [_________________] - <Enter> #### Explanation of the Reaction: The given reaction involves solid lead (Pb) reacting with aqueous chromium ions (\( \text{Cr}^{3+} \)) to form aqueous lead ions (\( \text{Pb}^{2+} \)) and solid chromium (Cr). #### Explanation of the Gibbs Free Energy (ΔG°): Gibbs free energy is a thermodynamic quantity that helps to predict whether a reaction will occur spontaneously at constant temperature and pressure. It is related to the equilibrium constant (K) by the following equation: \[ \Delta G° = -RT \ln K \] where: - \( R \) is the gas constant (8.314 J/mol·K), - \( T \) is the temperature in Kelvin (usually 298 K for standard conditions), - \( \ln \) is the natural logarithm function. This equation illustrates that if the equilibrium constant (K) is very small, the natural logarithm of K will be negative, making \( \Delta G° \) positive, implying that the reaction is non-spontaneous under standard conditions. Users need to calculate the Gibbs free energy using the provided K value and enter the correct numerical value with the appropriate sign in the input box. **Note:** Ensure all units are correct and consistent throughout calculations.
Transcribed Image Text:### Gibbs Free Energy Calculation for a Chemical Reaction #### Problem Statement: Determine the Gibbs free energy change (ΔG°) for the reaction below under standard conditions: \[ \text{3Pb(s) + 2Cr}^{3+}\text{(aq)} \rightarrow \text{3Pb}^{2+}\text{(aq) + 2Cr(s)} \] Given the equilibrium constant (K) for this reaction: \[ K = 1.30 \times 10^{-61} \] #### Required Calculation: \[ \Delta G° = \text{[?]} \, \text{kJ} \] #### Instructions: To find ΔG°: 1. Enter either a "+" or "-" sign and the magnitude of your answer in the provided text box. 2. Make sure your answer is in kilojoules (kJ). #### Input Section: - **Free Energy, kJ:** [_________________] - <Enter> #### Explanation of the Reaction: The given reaction involves solid lead (Pb) reacting with aqueous chromium ions (\( \text{Cr}^{3+} \)) to form aqueous lead ions (\( \text{Pb}^{2+} \)) and solid chromium (Cr). #### Explanation of the Gibbs Free Energy (ΔG°): Gibbs free energy is a thermodynamic quantity that helps to predict whether a reaction will occur spontaneously at constant temperature and pressure. It is related to the equilibrium constant (K) by the following equation: \[ \Delta G° = -RT \ln K \] where: - \( R \) is the gas constant (8.314 J/mol·K), - \( T \) is the temperature in Kelvin (usually 298 K for standard conditions), - \( \ln \) is the natural logarithm function. This equation illustrates that if the equilibrium constant (K) is very small, the natural logarithm of K will be negative, making \( \Delta G° \) positive, implying that the reaction is non-spontaneous under standard conditions. Users need to calculate the Gibbs free energy using the provided K value and enter the correct numerical value with the appropriate sign in the input box. **Note:** Ensure all units are correct and consistent throughout calculations.
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