2. Calculate the value of the equilibrium constant (Kc) for the reaction shown, if NO2(g) was found to be 95.54 % decomposed at 45.00 °C when its initial concentration was 5.725 mol/L. The initial concentration of the reaction products is 0 mol/L.
2NO2(g) = N2O4(g)
See your other post above.
To calculate the value of the equilibrium constant (Kc) for the reaction, we first need to determine the equilibrium concentrations of the reactants and products.
Given:
Initial concentration of NO2 (reactant) = 5.725 mol/L
Concentration of N2O4 (product) at equilibrium = 0 mol/L
Percent decomposition of NO2 = 95.54%
Temperature (T) = 45.00 °C
To find the equilibrium concentrations, we need to use the percent decomposition of NO2. The percent decomposition tells us how much of the initial reactant has decomposed at equilibrium.
Step 1: Calculate the amount of NO2 decomposed at equilibrium.
Percent decomposition = (Amount decomposed / Initial amount) * 100
Given:
Percent decomposition = 95.54%
Initial concentration of NO2 = 5.725 mol/L
Amount decomposed = (95.54 / 100) * 5.725 mol
Amount decomposed = 5.4709055 mol
Step 2: Calculate the equilibrium concentrations of NO2 and N2O4.
Since the decomposition reaction is 2NO2(g) = N2O4(g), we can assume that the amount of N2O4 formed is equal to half the amount of NO2 decomposed (based on the stoichiometry of the reaction).
Amount of N2O4 formed = 0.5 * amount of NO2 decomposed
Amount of N2O4 formed = 0.5 * 5.4709055 mol
Amount of N2O4 formed = 2.73545275 mol
The equilibrium concentration of NO2 = Initial concentration - amount decomposed
Equilibrium concentration of NO2 = 5.725 mol/L - 5.4709055 mol
Equilibrium concentration of NO2 = 0.2540945 mol/L
The equilibrium concentrations are:
[NO2]eq = 0.2540945 mol/L
[N2O4]eq = 2.73545275 mol/L
Step 3: Calculate the equilibrium constant (Kc).
The equilibrium constant (Kc) is obtained by dividing the product concentrations raised to their stoichiometric coefficients by the reactant concentrations raised to their stoichiometric coefficients.
Kc = ([N2O4]eq) / ([NO2]eq)^2
Substituting the values we calculated:
Kc = (2.73545275 mol/L) / (0.2540945 mol/L)^2
Kc = 43.03 mol/L
The value of the equilibrium constant (Kc) for the given reaction at 45.00 °C is 43.03 mol/L.