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Determine the equilibrium constant for the reaction of the complex ion formation between silver ion (Ag+) and ammonia (NH3) in a solution at 25°C, given that the concentration of Ag+ is 0.005 M and that of NH3 is 0.025 M. The balanced equation for the reaction is Ag+ + 2NH3 ⇋ [Ag(NH3)2]+.

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To determine the equilibrium constant  Kc  for the reaction, we need to know the equilibrium concentrations of all species involved. However, we are only given the initial concentrations of Ag+ and NH3. To find the equilibrium concentrations, we can set up an ICE  Initial, Change, Equilibrium  table and use the stoichiometry of the balanced equation.Initial concentrations:[Ag+] = 0.005 M[NH3] = 0.025 M[Ag NH3 2+] = 0 M  since the complex has not yet formed Change in concentrations:Let x be the change in concentration for Ag+ and Ag NH3 2+.Since the stoichiometry of NH3 is 2:1 with respect to Ag+, the change in concentration for NH3 will be 2x.Equilibrium concentrations:[Ag+] = 0.005 - x[NH3] = 0.025 - 2x[Ag NH3 2+] = xNow we can write the expression for the equilibrium constant  Kc :Kc = [Ag NH3 2+] /  [Ag+][NH3]^2 We need to find the value of x to determine the equilibrium concentrations and calculate Kc. To do this, we can use the solubility product constant  Ksp  for silver ion  Ag+ . The Ksp for silver ion is 1.77 x 10^-10.Ksp = [Ag+][NH3]^2Substitute the equilibrium concentrations into the Ksp expression:1.77 x 10^-10 =  0.005 - x  0.025 - 2x ^2This is a cubic equation, which can be difficult to solve analytically. However, we can make an assumption that x is very small compared to the initial concentrations, so we can approximate:1.77 x 10^-10   0.005  0.025 - 2x ^2Now, we can solve for x:1.77 x 10^-10   0.005  0.025 ^2x  5.64 x 10^-7Now that we have the value of x, we can find the equilibrium concentrations:[Ag+]  0.005 - 5.64 x 10^-7  0.005 M[NH3]  0.025 - 2 5.64 x 10^-7   0.025 M[Ag NH3 2+]  5.64 x 10^-7 MFinally, we can calculate the equilibrium constant  Kc :Kc = [Ag NH3 2+] /  [Ag+][NH3]^2 Kc =  5.64 x 10^-7  /   0.005  0.025 ^2 Kc  1.80 x 10^5The equilibrium constant for the reaction at 25C is approximately 1.80 x 10^5.

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