Final answer:
To find the percentage of COF2 decomposed, use the equilibrium concentration of CF4 and the stoichiometry of the reaction. Equilibrium concentrations of COF2 and CO2 can be calculated using the given Kc value, which allows the computation of the percentage decomposed based on the change in COF2 concentration.
Step-by-step explanation:
To calculate the percentage of COF2 decomposed at equilibrium, we can use the given equilibrium concentration of CF4 and the balanced chemical equation 2 COF2 (g) ⇌ CO2 (g) + CF4 (g) with Kc = 2.00 at 1000 °C.
At equilibrium, we are told [CF4] = 0.266 M. According to the stoichiometry of the balanced equation, 1 mole of CF4 is produced for every 2 moles of COF2 decomposed. Thus, [COF2] decreased by 2 * [CF4] = 2 * 0.266 M = 0.532 M at equilibrium.
If we let the initial concentration of COF2 be [COF2]initial, then at equilibrium, [COF2] would be [COF2]initial - 0.532 M. Because CF4 is produced, we can use the Kc expression: Kc = ([CO2][CF4])/([COF2]^2) = 2.00. We know [CF4] and Kc, and we are solving for the equilibrium concentration of COF2.
Assuming [COF2]initial is large compared to the change (which is reasonable given that we are looking at percentage decomposition), then the equilibrium concentration [COF2] is approximately [COF2]initial - 0.532 M. Therefore, the percentage decomposed is (0.532 M / [COF2]initial) * 100%.
Since [COF2] and [CO2] are in a 2:1 ratio with CF4, and [COF2] at equilibrium equals 0.532 M less than its initial concentration, whichever that may have been, [CO2] = 0.266 M. Therefore, Kc = (0.266 * 0.266) / (2 * 0.266)².
Given that Kc value is 2.00, we can solve for [COF2]initial, find the final concentration at equilibrium, and ultimately calculate the percentage decomposed.