Given the equilibrium constants for the equilibria, H₂O(l) H₃O⁺(aq) ; K = 2CH₃COOH(aq) + 2H₂O(l) 2CH₃COO−(aq) + 2H₃O⁺(aq) ; K = determine K_c for the following equilibrium.
CH₃COOH(aq) + NH₃(aq) CH₃COO−(aq) + NH₄⁺(aq)

Question

Given the equilibrium constants for the equilibria, H₂O(l)

Given the equilibrium constants for the equilibria, H<sub>2</sub>O(l) H<sub>3</sub>O<sup>+</sup>(aq) ; K = 2CH<sub>3</sub>COOH(aq) + 2H<sub>2</sub>O(l) 2CH<sub>3</sub>COO−(aq) + 2H<sub>3</sub>O<sup>+</sup>(aq) ; K = determine K<sub>c</sub> for the following equilibrium. CH<sub>3</sub>COOH(aq) + NH<sub>3</sub>(aq) CH<sub>3</sub>COO−(aq) + NH<sub>4</sub><sup>+</sup>(aq) A) 3.08 × 10<sup>4</sup> B) 3.25 × 10<sup>-5</sup> C) 9.96 × 10<sup>-15</sup> D) 1.00 × 10<sup>14</sup> E) 1.75 × 10<sup>-5</sup>

H₃O⁺(aq) ; K =

2CH₃COOH(aq) + 2H₂O(l)

2CH₃COO−(aq) + 2H₃O⁺(aq) ; K =

determine K_c for the following equilibrium.
CH₃COOH(aq) + NH₃(aq)

CH₃COO−(aq) + NH₄⁺(aq)

Quizplus · Accepted Answer

To find K_c, we can use the fact that the overall reaction is the sum of the two given reactions, with the NH₃ cancelling out. Thus, we have: CH₃COOH(aq) + 2H₂O(l) ⇌ 2CH₃COO−(aq) + 2H₃O⁺(aq) Taking the equilibrium constant of this reaction gives: K_c = ([CH₃COO−]2 / [H₂O]2) / ([CH₃COOH][H₂O]11eac9a9_4ba4_d199_acc3_b9788c60d29d_TB7480_11) We can substitute the equilibrium concentrations of the species based on stoichiometry and the given equilibrium constants. This gives: K_c = ((2x)2 / (x)2) / (x)(1-x)(11eac9a9_4ba4_aa87_acc3_ef986166cfa9_TB7480_11) where x = [CH₃COOH] at equilibrium Simplifying, we get: K_c = 4 / (1-x)(11eac9a9_4ba4_aa87_acc3_ef986166cfa9_TB7480_11) Since the equilibrium constant for the second reaction is much larger than the equilibrium constant for the first reaction, we can assume that most of the CH₃COOH will be converted to CH₃COO−, and thus x will be small compared to 1. Therefore, (1-x) ≈ 1, and we can approximate: K_c ≈ 4 / (11eac9a9_4ba4_aa87_acc3_ef986166cfa9_TB7480_11) Plugging in the given equilibrium constant, we get: K_c = 3.08 × 10⁴.

Given the Equilibrium Constants for the Equilibria, H2O(l) H3O+(aq);

Given the Equilibrium Constants for the Equilibria, H₂O(l) H₃O⁺(aq);