A graduate-level atmospheric chemistry model includes the following simplified set of…

CHEMISTRY · Multi-part · A Level · Chemistry · Chemical equilibria (Le Chatelier’s principle and Kc) · Chemical equilibria (Le Chatelier’s principle and Kc)

Problem

A graduate-level atmospheric chemistry model includes the following simplified set of equilibria at 298 K, with equilibrium constants expressed as base-10 logarithms: Reaction (A): O3(g)⇌O2(g)+12 O2(g)\text{O}_3(g) \rightleftharpoons \text{O}_2(g) + \tfrac{1}{2}\,\text{O}_2(g) log⁡10KA=29.4\log_{10} K_A = 29.4 Reaction (B): O(g)+O2(g)⇌O3(g)\text{O}(g) + \text{O}_2(g) \rightleftharpoons \text{O}_3(g) log⁡10KB=12.3\log_{10} K_B = 12.3 Reaction (C): 2 O(g)⇌O2(g)2\,\text{O}(g) \rightleftharpoons \text{O}_2(g) log⁡10KC=1.7\log_{10} K_C = 1.7 (Assume ideal-gas behavior.) (a) Write the balanced overall reaction obtained by adding Reactions (B) and (C) in such a way that O3(g)\text{O}_3(g) appears as a reactant and atomic oxygen does not appear in the net reaction. Show your work explicitly. (b) Derive an exact algebraic expression for log⁡10Koverall\log_{10} K_{\text{overall}} in terms of log⁡10KB\log_{10} K_B and log⁡10KC\log_{10} K_C that corresponds to the overall reaction from part (a). (c) Calculate the numerical value of KoverallK_{\text{overall}} (not its logarithm). Express your answer in scientific notation. (d) Using only the provided logarithmic equilibrium constants, verify mathematically whether Reaction (A) is thermodynamically consistent with the combination of Reactions (B) and (C). If any inconsistency is found, quantify its magnitude and suggest a plausible chemical or experimental explanation.

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