### Calculating the Equilibrium Constant for the Hydrogenation of Acetylene#### Problem DescriptionCalculate the equilibrium constant, \( K \), at 25.0 °C for the hydrogenation of acetylene to ethane, using the thermodynamic information provided in the table.#### Chemical ReactionThe balanced chemical equation for the hydrogenation of acetylene (C₂H₂) to ethane (C₂H₆) is as follows:\[ \text{C}_2\text{H}_2 (g) + 2 \text{H}_2 (g) \rightleftharpoons \text{C}_2\text{H}_6 (g) \]#### Required FormulaThe equilibrium constant \( K \) can be calculated from the standard Gibbs free energy change \( \Delta G^\circ \) using the formula:\[ \Delta G^\circ = -RT \ln K \]Where:- \( R \) is the gas constant, 8.314 J/(mol·K)- \( T \) is the temperature in Kelvin (298.15 K for 25.0 °C)#### Thermodynamic DataThe following table provides the standard Gibbs free energy of formation \( \Delta G_f^\circ \) for each compound involved in the reaction:| Compound | \( \Delta G_f^\circ \) (kJ · mol⁻¹) ||----------------|--------------------------------------|| CH₃Cl(g) | 48.50 || CH₄(g) | -50.72 || C₂H₂(g) | 209.2 || C₂H₆(g) | -32.82 || Cl₂(g) | 0.00 || H₂(g) | 0.00 || H₂O(l) | -237.13 || HCl(g) | -95.30 || HNO₃(aq) | -111.25 || NO(g) | 86.55 || NO₂(g) | 51.31 |#### Steps to Calculate \( \Delta G^\circ \) for the Reaction1. **Identify Products and Reactants:** - Products: C₂H₆(g) - Reactants: C₂H₂(g),

∆rG° = free energy of formation of products - free energy of formation of reactants∆rG° = - RTlnK T…

Calculate the equilibrium constant, K, at 25.0 °C for each of the reactions. Use the thermodynamic information provided in the table. The hydrogenation of acetylene to ethane. C,H,(g) +2H,(g) →C,H(g) K = x10 TOOLS Compound CH₂Cl(g) CH₂(g) C₂H₂(g) C₂H6 (g) Cl₂(g) H₂(g) H₂O(1) HCl(g) HNO₂ (aq) NO(g) NO₂ (g) AG; (kJ. mol-¹) 48.50 -50.72 209.2 -32.82 0.00 0.00 -237.13 -95.30 -111.25 86.55 51.31

Calculate the equilibrium constant, K, at 25.0 °C for each of the reactions. Use the thermodynamic information provided in the table. The hydrogenation of acetylene to ethane. C,H,(g) +2H,(g) →C,H(g) K = x10 TOOLS Compound CH₂Cl(g) CH₂(g) C₂H₂(g) C₂H6 (g) Cl₂(g) H₂(g) H₂O(1) HCl(g) HNO₂ (aq) NO(g) NO₂ (g) AG; (kJ. mol-¹) 48.50 -50.72 209.2 -32.82 0.00 0.00 -237.13 -95.30 -111.25 86.55 51.31

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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