Equilibrium Concentrations Calculation at 430°C
How can we calculate the equilibrium concentrations of each gas at 430 °C based on the provided data?
The equilibrium concentrations of each gas at 430 °C can be calculated using the provided equilibrium constant (Kc) and the initial concentrations of the reactants. Given the equilibrium equation H2(g) + I2(g) ⇌ 2HI(g) and the equilibrium constant Kc = 54.3 at 430 °C, we can set up an ICE (Initial-Change-Equilibrium) table to calculate the equilibrium concentrations. Let's denote the initial concentrations of H2, I2, and HI as [H2]₀, [I2]₀, and [HI]₀, respectively. Based on the given information, we have [H2]₀ = 0.543 M, [I2]₀ = 0.306 M, and [HI]₀ = 0.866 M. In the ICE table, we start with the initial concentrations and then determine the changes in concentration (x) based on the stoichiometry of the reaction. Since the stoichiometric coefficients are 1:1:2 for H2, I2, and HI, the change in concentration for H2 and I2 is -x, while the change for HI is +2x. At equilibrium, we add the initial concentration and the change in concentration to obtain the equilibrium concentrations. Therefore, the equilibrium concentrations are [H2] = [H2]₀ - x, [I2] = [I2]₀ - x, and [HI] = [HI]₀ + 2x. To solve for x, we can set up an expression using the equilibrium constant Kc and substitute the equilibrium concentrations into it. In this case, Kc = ([HI]²) / ([H2] * [I2]) = 54.3. Once we solve for x, we can substitute the value back into the expressions for the equilibrium concentrations to obtain the final values at 430 °C.