To calculate the equilibrium constant K for the formation of the complex ion Cu NH3 42+, we need to use the spectroscopic data provided. The spectroscopic data should include the absorbance A of the solution at a specific wavelength, which can be used to determine the concentration of the complex ion formed.First, let's write the balanced chemical equation for the formation of the complex ion:Cu2+ + 4NH3 Cu NH3 42+Now, let's assume that x moles of Cu NH3 42+ are formed at equilibrium. The change in concentration for each species can be represented as follows:Cu2+: 0.02 - xNH3: 0.5 - 4xCu NH3 42+: xNext, we need to use the Beer-Lambert Law to relate the absorbance A to the concentration of the complex ion formed. The Beer-Lambert Law is given by:A = * l * cwhere A is the absorbance, is the molar absorptivity, l is the path length, and c is the concentration of the complex ion.Using the spectroscopic data provided, we can determine the concentration of the complex ion x at equilibrium. Once we have the concentration of the complex ion, we can calculate the equilibrium constant K using the expression:K = [Cu NH3 42+] / [Cu2+] * [NH3]^4 Substitute the concentrations of the species at equilibrium:K = x / 0.02 - x * 0.5 - 4x ^4 Now, solve for K using the calculated concentration of the complex ion x from the spectroscopic data. This will give you the equilibrium constant for the formation of the complex ion Cu NH3 42+ in the given solution at room temperature.