Cu + AgNO3 = Ag + CuNO3

Cu (copper) + AgNO_3 (silver nitrate) ⟶ Ag (silver) + CuNO3

Balance the chemical equation algebraically: Cu + AgNO_3 ⟶ Ag + CuNO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 AgNO_3 ⟶ c_3 Ag + c_4 CuNO3 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 = c_4 Ag: | c_2 = c_3 N: | c_2 = c_4 O: | 3 c_2 = 3 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu + AgNO_3 ⟶ Ag + CuNO3

+ ⟶ + CuNO3

copper + silver nitrate ⟶ silver + CuNO3

Construct the equilibrium constant, K, expression for: Cu + AgNO_3 ⟶ Ag + CuNO3 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: Cu + AgNO_3 ⟶ Ag + CuNO3 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 | 1 | -1 AgNO_3 | 1 | -1 Ag | 1 | 1 CuNO3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) AgNO_3 | 1 | -1 | ([AgNO3])^(-1) Ag | 1 | 1 | [Ag] CuNO3 | 1 | 1 | [CuNO3] 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])^(-1) ([AgNO3])^(-1) [Ag] [CuNO3] = ([Ag] [CuNO3])/([Cu] [AgNO3])

Construct the rate of reaction expression for: Cu + AgNO_3 ⟶ Ag + CuNO3 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: Cu + AgNO_3 ⟶ Ag + CuNO3 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 | 1 | -1 AgNO_3 | 1 | -1 Ag | 1 | 1 CuNO3 | 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 | 1 | -1 | -(Δ[Cu])/(Δt) AgNO_3 | 1 | -1 | -(Δ[AgNO3])/(Δt) Ag | 1 | 1 | (Δ[Ag])/(Δt) CuNO3 | 1 | 1 | (Δ[CuNO3])/(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[Cu])/(Δt) = -(Δ[AgNO3])/(Δt) = (Δ[Ag])/(Δt) = (Δ[CuNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | silver nitrate | silver | CuNO3 formula | Cu | AgNO_3 | Ag | CuNO3 name | copper | silver nitrate | silver |

| copper | silver nitrate | silver | CuNO3 molar mass | 63.546 g/mol | 169.87 g/mol | 107.8682 g/mol | 125.55 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 | |