AgNO3 + Cu(OH)2 = Cu(NO3)2 + AgOH

AgNO_3 silver nitrate + Cu(OH)_2 copper hydroxide ⟶ Cu(NO_3)_2 copper(II) nitrate + AgOH

Balance the chemical equation algebraically: AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + AgOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 AgNO_3 + c_2 Cu(OH)_2 ⟶ c_3 Cu(NO_3)_2 + c_4 AgOH Set the number of atoms in the reactants equal to the number of atoms in the products for Ag, N, O, Cu and H: Ag: | c_1 = c_4 N: | c_1 = 2 c_3 O: | 3 c_1 + 2 c_2 = 6 c_3 + c_4 Cu: | c_2 = c_3 H: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + 2 AgOH

+ ⟶ + AgOH

silver nitrate + copper hydroxide ⟶ copper(II) nitrate + AgOH

Construct the equilibrium constant, K, expression for: AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + AgOH 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: 2 AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + 2 AgOH 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 AgNO_3 | 2 | -2 Cu(OH)_2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 AgOH | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression AgNO_3 | 2 | -2 | ([AgNO3])^(-2) Cu(OH)_2 | 1 | -1 | ([Cu(OH)2])^(-1) Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] AgOH | 2 | 2 | ([AgOH])^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 = ([AgNO3])^(-2) ([Cu(OH)2])^(-1) [Cu(NO3)2] ([AgOH])^2 = ([Cu(NO3)2] ([AgOH])^2)/(([AgNO3])^2 [Cu(OH)2])

Construct the rate of reaction expression for: AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + AgOH 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: 2 AgNO_3 + Cu(OH)_2 ⟶ Cu(NO_3)_2 + 2 AgOH 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 AgNO_3 | 2 | -2 Cu(OH)_2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 AgOH | 2 | 2 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 AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) Cu(OH)_2 | 1 | -1 | -(Δ[Cu(OH)2])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) AgOH | 2 | 2 | 1/2 (Δ[AgOH])/(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 = -1/2 (Δ[AgNO3])/(Δt) = -(Δ[Cu(OH)2])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[AgOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| silver nitrate | copper hydroxide | copper(II) nitrate | AgOH formula | AgNO_3 | Cu(OH)_2 | Cu(NO_3)_2 | AgOH Hill formula | AgNO_3 | CuH_2O_2 | CuN_2O_6 | HAgO name | silver nitrate | copper hydroxide | copper(II) nitrate | IUPAC name | silver nitrate | copper dihydroxide | copper(II) nitrate |

| silver nitrate | copper hydroxide | copper(II) nitrate | AgOH molar mass | 169.87 g/mol | 97.56 g/mol | 187.55 g/mol | 124.875 g/mol phase | solid (at STP) | | | melting point | 212 °C | | | solubility in water | soluble | | | odor | odorless | | |