Cu(NO3)2 + Pb = Cu + Pb(NO3)2

Cu(NO_3)_2 (copper(II) nitrate) + Pb (lead) ⟶ Cu (copper) + Pb(NO_3)_2 (lead(II) nitrate)

Balance the chemical equation algebraically: Cu(NO_3)_2 + Pb ⟶ Cu + Pb(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu(NO_3)_2 + c_2 Pb ⟶ c_3 Cu + c_4 Pb(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, N, O and Pb: Cu: | c_1 = c_3 N: | 2 c_1 = 2 c_4 O: | 6 c_1 = 6 c_4 Pb: | 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_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(NO_3)_2 + Pb ⟶ Cu + Pb(NO_3)_2

+ ⟶ +

copper(II) nitrate + lead ⟶ copper + lead(II) nitrate

Construct the equilibrium constant, K, expression for: Cu(NO_3)_2 + Pb ⟶ Cu + Pb(NO_3)_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: Cu(NO_3)_2 + Pb ⟶ Cu + Pb(NO_3)_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(NO_3)_2 | 1 | -1 Pb | 1 | -1 Cu | 1 | 1 Pb(NO_3)_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(NO_3)_2 | 1 | -1 | ([Cu(NO3)2])^(-1) Pb | 1 | -1 | ([Pb])^(-1) Cu | 1 | 1 | [Cu] Pb(NO_3)_2 | 1 | 1 | [Pb(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(NO3)2])^(-1) ([Pb])^(-1) [Cu] [Pb(NO3)2] = ([Cu] [Pb(NO3)2])/([Cu(NO3)2] [Pb])

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

| copper(II) nitrate | lead | copper | lead(II) nitrate formula | Cu(NO_3)_2 | Pb | Cu | Pb(NO_3)_2 Hill formula | CuN_2O_6 | Pb | Cu | N_2O_6Pb name | copper(II) nitrate | lead | copper | lead(II) nitrate IUPAC name | copper(II) nitrate | lead | copper | plumbous dinitrate

| copper(II) nitrate | lead | copper | lead(II) nitrate molar mass | 187.55 g/mol | 207.2 g/mol | 63.546 g/mol | 331.2 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 327.4 °C | 1083 °C | 470 °C boiling point | | 1740 °C | 2567 °C | density | | 11.34 g/cm^3 | 8.96 g/cm^3 | solubility in water | | insoluble | insoluble | dynamic viscosity | | 0.00183 Pa s (at 38 °C) | | odor | | | odorless | odorless