CuSO4 + NH4OH = H2SO4 + [Cu(NH3)2](OH)2

CuSO_4 (copper(II) sulfate) + NH_4OH (ammonium hydroxide) ⟶ H_2SO_4 (sulfuric acid) + Cu(NH3)2(OH)2

Balance the chemical equation algebraically: CuSO_4 + NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(OH)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuSO_4 + c_2 NH_4OH ⟶ c_3 H_2SO_4 + c_4 Cu(NH3)2(OH)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O, S, H and N: Cu: | c_1 = c_4 O: | 4 c_1 + c_2 = 4 c_3 + 2 c_4 S: | c_1 = c_3 H: | 5 c_2 = 2 c_3 + 8 c_4 N: | c_2 = 2 c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CuSO_4 + 2 NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(OH)2

+ ⟶ + Cu(NH3)2(OH)2

copper(II) sulfate + ammonium hydroxide ⟶ sulfuric acid + Cu(NH3)2(OH)2

Construct the equilibrium constant, K, expression for: CuSO_4 + NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(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: CuSO_4 + 2 NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(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 CuSO_4 | 1 | -1 NH_4OH | 2 | -2 H_2SO_4 | 1 | 1 Cu(NH3)2(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 CuSO_4 | 1 | -1 | ([CuSO4])^(-1) NH_4OH | 2 | -2 | ([NH4OH])^(-2) H_2SO_4 | 1 | 1 | [H2SO4] Cu(NH3)2(OH)2 | 1 | 1 | [Cu(NH3)2(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 = ([CuSO4])^(-1) ([NH4OH])^(-2) [H2SO4] [Cu(NH3)2(OH)2] = ([H2SO4] [Cu(NH3)2(OH)2])/([CuSO4] ([NH4OH])^2)

Construct the rate of reaction expression for: CuSO_4 + NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(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: CuSO_4 + 2 NH_4OH ⟶ H_2SO_4 + Cu(NH3)2(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 CuSO_4 | 1 | -1 NH_4OH | 2 | -2 H_2SO_4 | 1 | 1 Cu(NH3)2(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 CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) NH_4OH | 2 | -2 | -1/2 (Δ[NH4OH])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) Cu(NH3)2(OH)2 | 1 | 1 | (Δ[Cu(NH3)2(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 = -(Δ[CuSO4])/(Δt) = -1/2 (Δ[NH4OH])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[Cu(NH3)2(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) sulfate | ammonium hydroxide | sulfuric acid | Cu(NH3)2(OH)2 formula | CuSO_4 | NH_4OH | H_2SO_4 | Cu(NH3)2(OH)2 Hill formula | CuO_4S | H_5NO | H_2O_4S | H8CuN2O2 name | copper(II) sulfate | ammonium hydroxide | sulfuric acid | IUPAC name | copper sulfate | ammonium hydroxide | sulfuric acid |

| copper(II) sulfate | ammonium hydroxide | sulfuric acid | Cu(NH3)2(OH)2 molar mass | 159.6 g/mol | 35.046 g/mol | 98.07 g/mol | 131.62 g/mol phase | solid (at STP) | aqueous (at STP) | liquid (at STP) | melting point | 200 °C | -57.5 °C | 10.371 °C | boiling point | | 36 °C | 279.6 °C | density | 3.603 g/cm^3 | 0.9 g/cm^3 | 1.8305 g/cm^3 | solubility in water | | very soluble | very soluble | surface tension | | | 0.0735 N/m | dynamic viscosity | | | 0.021 Pa s (at 25 °C) | odor | | | odorless |