NH3 + Cu(OH)2 = [Cu(NH3)4](OH)2

NH_3 ammonia + Cu(OH)_2 copper hydroxide ⟶ Cu(NH3)4(OH)2

Balance the chemical equation algebraically: NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 Cu(OH)_2 ⟶ c_3 Cu(NH3)4(OH)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, Cu and O: H: | 3 c_1 + 2 c_2 = 14 c_3 N: | c_1 = 4 c_3 Cu: | c_2 = c_3 O: | 2 c_2 = 2 c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2

+ ⟶ Cu(NH3)4(OH)2

ammonia + copper hydroxide ⟶ Cu(NH3)4(OH)2

Construct the equilibrium constant, K, expression for: NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 4 NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i NH_3 | 4 | -4 Cu(OH)_2 | 1 | -1 Cu(NH3)4(OH)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 4 | -4 | ([NH3])^(-4) Cu(OH)_2 | 1 | -1 | ([Cu(OH)2])^(-1) Cu(NH3)4(OH)2 | 1 | 1 | [Cu(NH3)4(OH)2] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([NH3])^(-4) ([Cu(OH)2])^(-1) [Cu(NH3)4(OH)2] = ([Cu(NH3)4(OH)2])/(([NH3])^4 [Cu(OH)2])

Construct the rate of reaction expression for: NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 4 NH_3 + Cu(OH)_2 ⟶ Cu(NH3)4(OH)2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i NH_3 | 4 | -4 Cu(OH)_2 | 1 | -1 Cu(NH3)4(OH)2 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term NH_3 | 4 | -4 | -1/4 (Δ[NH3])/(Δt) Cu(OH)_2 | 1 | -1 | -(Δ[Cu(OH)2])/(Δt) Cu(NH3)4(OH)2 | 1 | 1 | (Δ[Cu(NH3)4(OH)2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/4 (Δ[NH3])/(Δt) = -(Δ[Cu(OH)2])/(Δt) = (Δ[Cu(NH3)4(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | copper hydroxide | Cu(NH3)4(OH)2 formula | NH_3 | Cu(OH)_2 | Cu(NH3)4(OH)2 Hill formula | H_3N | CuH_2O_2 | H14CuN4O2 name | ammonia | copper hydroxide | IUPAC name | ammonia | copper dihydroxide |

| ammonia | copper hydroxide | Cu(NH3)4(OH)2 molar mass | 17.031 g/mol | 97.56 g/mol | 165.68 g/mol phase | gas (at STP) | | melting point | -77.73 °C | | boiling point | -33.33 °C | | density | 6.96×10^-4 g/cm^3 (at 25 °C) | | surface tension | 0.0234 N/m | | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | |