Pb + Cu(NO3)24 = Cu + Pb(NO3)2

Pb lead + Cu(NO3)24 ⟶ Cu copper + Pb(NO_3)_2 lead(II) nitrate

Balance the chemical equation algebraically: Pb + Cu(NO3)24 ⟶ Cu + Pb(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Pb + c_2 Cu(NO3)24 ⟶ 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 Pb, Cu, N and O: Pb: | c_1 = c_4 Cu: | c_2 = c_3 N: | 24 c_2 = 2 c_4 O: | 72 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 1 c_3 = 1 c_4 = 12 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 Pb + Cu(NO3)24 ⟶ Cu + 12 Pb(NO_3)_2

+ Cu(NO3)24 ⟶ +

lead + Cu(NO3)24 ⟶ copper + lead(II) nitrate

Construct the equilibrium constant, K, expression for: Pb + Cu(NO3)24 ⟶ 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: 12 Pb + Cu(NO3)24 ⟶ Cu + 12 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 Pb | 12 | -12 Cu(NO3)24 | 1 | -1 Cu | 1 | 1 Pb(NO_3)_2 | 12 | 12 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Pb | 12 | -12 | ([Pb])^(-12) Cu(NO3)24 | 1 | -1 | ([Cu(NO3)24])^(-1) Cu | 1 | 1 | [Cu] Pb(NO_3)_2 | 12 | 12 | ([Pb(NO3)2])^12 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 = ([Pb])^(-12) ([Cu(NO3)24])^(-1) [Cu] ([Pb(NO3)2])^12 = ([Cu] ([Pb(NO3)2])^12)/(([Pb])^12 [Cu(NO3)24])

Construct the rate of reaction expression for: Pb + Cu(NO3)24 ⟶ 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: 12 Pb + Cu(NO3)24 ⟶ Cu + 12 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 Pb | 12 | -12 Cu(NO3)24 | 1 | -1 Cu | 1 | 1 Pb(NO_3)_2 | 12 | 12 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 Pb | 12 | -12 | -1/12 (Δ[Pb])/(Δt) Cu(NO3)24 | 1 | -1 | -(Δ[Cu(NO3)24])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) Pb(NO_3)_2 | 12 | 12 | 1/12 (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 = -1/12 (Δ[Pb])/(Δt) = -(Δ[Cu(NO3)24])/(Δt) = (Δ[Cu])/(Δt) = 1/12 (Δ[Pb(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| lead | Cu(NO3)24 | copper | lead(II) nitrate formula | Pb | Cu(NO3)24 | Cu | Pb(NO_3)_2 Hill formula | Pb | CuN24O72 | Cu | N_2O_6Pb name | lead | | copper | lead(II) nitrate IUPAC name | lead | | copper | plumbous dinitrate

| lead | Cu(NO3)24 | copper | lead(II) nitrate molar mass | 207.2 g/mol | 1551.6 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