Final answer:
To determine the equilibrium constant K, we must calculate the change in concentrations from initial to equilibrium using the equilibrium concentration of C and the stoichiometry of the reaction A + 2B ⇌ 2C. Using the definition of K and the balanced equation, we can solve for the unknown quantities and find K.
Step-by-step explanation:
To find the equilibrium constant K for the reaction A + 2B ⇌ 2C, we must use the equilibrium concentration of C and the balanced equation to work out the concentrations of A and B at equilibrium. Given that the equilibrium concentration of C is 0.5 mole/L in a 2 L flask, and initially there were 2 moles of A, 3 moles of B, and 2 moles of C, we can use these values to calculate the changes in concentration that occurred to reach equilibrium.
We use the expression for the equilibrium constant K which in this case would be:
K = [C]² / ([A][B]²)
To calculate the concentrations at equilibrium, we start with the initial values and subtract the amount that has changed, which will be based on the stoichiometry of the reaction. If we let x represent the change in moles of A that reacted to reach equilibrium, then the change in moles of B will be 2x (since 2 moles of B react for every 1 mole of A), and the change in moles of C will be -2x (since 2 moles of C are produced for every 1 mole of A). Solving for x will allow us to calculate the final concentrations of A, B, and C and therefore determine K with the given equilibrium concentration of C.