Question

Consider the reaction: Cu^2+ + 4NH3 ⇌ [Cu(NH3)4]^2+ If the initial concentration of Cu^2+ is 0.5 M and the initial concentration of NH3 is 2 M, what is the concentration of [Cu(NH3)4]^2+ at equilibrium if the concentration of NH3 is increased to 5 M? (Assume the volume of the solution remains constant and the temperature is kept constant.)

Answer 1

To solve this problem, we will use the reaction quotient  Q  and the equilibrium constant  K  for the reaction. First, we need to find the equilibrium constant  K  using the initial concentrations of Cu^2+ and NH3. We can write the expression for K as:K = [Cu NH3 4]^2+ /  [Cu^2+][NH3]^4 Let x be the change in concentration of Cu^2+ and NH3 at equilibrium. Then, the equilibrium concentrations will be:[Cu^2+] = 0.5 M - x[NH3] = 2 M - 4x[Cu NH3 4]^2+ = xNow, we can substitute these equilibrium concentrations into the K expression:K = x /   0.5 - x  2 - 4x ^4 Now, let's consider the new situation where the concentration of NH3 is increased to 5 M. We need to find the new equilibrium concentrations of the species. Let y be the change in concentration of Cu^2+ and NH3 at the new equilibrium. Then, the new equilibrium concentrations will be:[Cu^2+] = 0.5 M - y[NH3] = 5 M - 4y[Cu NH3 4]^2+ = ySince the temperature is constant, K remains the same. We can write the new equilibrium expression as:K = y /   0.5 - y  5 - 4y ^4 Now, we have two equations for K:x /   0.5 - x  2 - 4x ^4  = y /   0.5 - y  5 - 4y ^4 Since we are interested in finding the concentration of [Cu NH3 4]^2+ at the new equilibrium, we want to solve for y. However, this is a complex equation, and it is difficult to solve for y directly. Instead, we can use an approximation.Since the initial concentration of NH3 is much higher than that of Cu^2+, we can assume that the change in concentration of NH3  4x or 4y  is relatively small compared to the initial concentration of NH3. Therefore, we can approximate the equilibrium expressions as:K  x /  0.5 * 2^4  = y /  0.5 * 5^4 Now, we can solve for y:y = x *  0.5 * 5^4  /  0.5 * 2^4 Since we are given the initial concentrations, we can find x using the initial K expression:x = K *  0.5 * 2^4 Now, substitute x back into the equation for y:y =  K *  0.5 * 2^4   *  0.5 * 5^4  /  0.5 * 2^4 y = K *  0.5 * 5^4 The concentration of [Cu NH3 4]^2+ at the new equilibrium  y  depends on the value of K. Unfortunately, we cannot determine the exact value of K without more information. However, this equation shows the relationship between K and the concentration of [Cu NH3 4]^2+ at the new equilibrium.