Cu + AgNO3 = Ag + Cu9(NO3)2

Cu copper + AgNO_3 silver nitrate ⟶ Ag silver + Cu9(NO3)2

Balance the chemical equation algebraically: Cu + AgNO_3 ⟶ Ag + Cu9(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 AgNO_3 ⟶ c_3 Ag + c_4 Cu9(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Ag, N and O: Cu: | c_1 = 9 c_4 Ag: | c_2 = c_3 N: | c_2 = 2 c_4 O: | 3 c_2 = 6 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 9 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 Cu + 2 AgNO_3 ⟶ 2 Ag + Cu9(NO3)2

+ ⟶ + Cu9(NO3)2

copper + silver nitrate ⟶ silver + Cu9(NO3)2

Construct the equilibrium constant, K, expression for: Cu + AgNO_3 ⟶ Ag + Cu9(NO3)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: 9 Cu + 2 AgNO_3 ⟶ 2 Ag + Cu9(NO3)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 Cu | 9 | -9 AgNO_3 | 2 | -2 Ag | 2 | 2 Cu9(NO3)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 9 | -9 | ([Cu])^(-9) AgNO_3 | 2 | -2 | ([AgNO3])^(-2) Ag | 2 | 2 | ([Ag])^2 Cu9(NO3)2 | 1 | 1 | [Cu9(NO3)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 = ([Cu])^(-9) ([AgNO3])^(-2) ([Ag])^2 [Cu9(NO3)2] = (([Ag])^2 [Cu9(NO3)2])/(([Cu])^9 ([AgNO3])^2)

Construct the rate of reaction expression for: Cu + AgNO_3 ⟶ Ag + Cu9(NO3)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: 9 Cu + 2 AgNO_3 ⟶ 2 Ag + Cu9(NO3)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 Cu | 9 | -9 AgNO_3 | 2 | -2 Ag | 2 | 2 Cu9(NO3)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 Cu | 9 | -9 | -1/9 (Δ[Cu])/(Δt) AgNO_3 | 2 | -2 | -1/2 (Δ[AgNO3])/(Δt) Ag | 2 | 2 | 1/2 (Δ[Ag])/(Δt) Cu9(NO3)2 | 1 | 1 | (Δ[Cu9(NO3)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 = -1/9 (Δ[Cu])/(Δt) = -1/2 (Δ[AgNO3])/(Δt) = 1/2 (Δ[Ag])/(Δt) = (Δ[Cu9(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | silver nitrate | silver | Cu9(NO3)2 formula | Cu | AgNO_3 | Ag | Cu9(NO3)2 Hill formula | Cu | AgNO_3 | Ag | Cu9N2O6 name | copper | silver nitrate | silver |

| copper | silver nitrate | silver | Cu9(NO3)2 molar mass | 63.546 g/mol | 169.87 g/mol | 107.8682 g/mol | 695.92 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 1083 °C | 212 °C | 960 °C | boiling point | 2567 °C | | 2212 °C | density | 8.96 g/cm^3 | | 10.49 g/cm^3 | solubility in water | insoluble | soluble | insoluble | odor | odorless | odorless | |