Final answer:
The equilibrium constant for the reaction between acetic acid and ethanol can be determined using molar amounts at equilibrium. Based on initial molar ratios given, K can be approximated, but for the new scenario with 90g acetic acid and 60g ethanol, we lack sufficient data to confirm the provided options A-D.
Step-by-step explanation:
The equilibrium constant, K, for the esterification reaction between acetic acid and ethanol can be determined from the molar amounts of reactants and products at equilibrium. Given that 60g of acetic acid and 46g of ethanol react to yield 58.96g of ethyl ethanoate at equilibrium in a 1 dm3 vessel at 298 K, we can start by calculating the number of moles of each substance involved in the reaction to find the equilibrium concentrations.
Acetic acid has a molar mass of approximately 60.05 g/mol, which means the initial amount of acetic acid (60g) corresponds to 1 mol. Ethanol has a molar mass of 46 g/mol, so the initial amount (46g) also corresponds to 1 mol. Ethyl ethanoate has a molar mass of approximately 88 g/mol, so the amount at equilibrium (58.96g) corresponds to approximately 0.67 mol. Since the reaction consumed the same amount of acetic acid and ethanol, there would be 1 - 0.67 = 0.33 mol of each left unreacted at equilibrium.
The equilibrium constant K is calculated using the concentration of the products over the reactants raised to the power of their stoichiometric coefficients. Since the reaction vessel is 1 dm3, these values are also the molar concentrations. The reaction is 1:1:1:1 stoichiometry, so K would equal:
K = [ethyl ethanoate] / ([acetic acid][ethanol]) = 0.67 / (0.33 * 0.33) ≈ 6.10
However, to answer the question regarding how many grams of ethyl ethanoate would be formed if 90g of acid were reacted with 60g of ethanol, we need more information. If the reaction were to occur under the same conditions as the initial example, we would assume the same equilibrium constant applies. Taking into account the molar masses of acetic acid and ethanol, we could find the limiting reagent and determine how much ethyl ethanoate could theoretically be produced. Without knowing the precise reaction conditions or whether the amount of reagents used affects the equilibrium in this new scenario, calculating an exact yield would be speculative. Therefore based on the data provided within the question, none of the given options (A-D) can be accurately verified.