Cu(NO3)2 = O2 + Cu + NO2

Cu(NO_3)_2 copper(II) nitrate ⟶ O_2 oxygen + Cu copper + NO_2 nitrogen dioxide

Balance the chemical equation algebraically: Cu(NO_3)_2 ⟶ O_2 + Cu + NO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu(NO_3)_2 ⟶ c_2 O_2 + c_3 Cu + c_4 NO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, N and O: Cu: | c_1 = c_3 N: | 2 c_1 = c_4 O: | 6 c_1 = 2 c_2 + 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu(NO_3)_2 ⟶ O_2 + Cu + 2 NO_2

⟶ + +

copper(II) nitrate ⟶ oxygen + copper + nitrogen dioxide

Construct the equilibrium constant, K, expression for: Cu(NO_3)_2 ⟶ O_2 + Cu + NO_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 ⟶ O_2 + Cu + 2 NO_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 O_2 | 1 | 1 Cu | 1 | 1 NO_2 | 2 | 2 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) O_2 | 1 | 1 | [O2] Cu | 1 | 1 | [Cu] NO_2 | 2 | 2 | ([NO2])^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) [O2] [Cu] ([NO2])^2 = ([O2] [Cu] ([NO2])^2)/([Cu(NO3)2])

Construct the rate of reaction expression for: Cu(NO_3)_2 ⟶ O_2 + Cu + NO_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 ⟶ O_2 + Cu + 2 NO_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 O_2 | 1 | 1 Cu | 1 | 1 NO_2 | 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 Cu(NO_3)_2 | 1 | -1 | -(Δ[Cu(NO3)2])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(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[O2])/(Δt) = (Δ[Cu])/(Δt) = 1/2 (Δ[NO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) nitrate | oxygen | copper | nitrogen dioxide formula | Cu(NO_3)_2 | O_2 | Cu | NO_2 Hill formula | CuN_2O_6 | O_2 | Cu | NO_2 name | copper(II) nitrate | oxygen | copper | nitrogen dioxide IUPAC name | copper(II) nitrate | molecular oxygen | copper | Nitrogen dioxide

| copper(II) nitrate | oxygen | copper | nitrogen dioxide molar mass | 187.55 g/mol | 31.998 g/mol | 63.546 g/mol | 46.005 g/mol phase | | gas (at STP) | solid (at STP) | gas (at STP) melting point | | -218 °C | 1083 °C | -11 °C boiling point | | -183 °C | 2567 °C | 21 °C density | | 0.001429 g/cm^3 (at 0 °C) | 8.96 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) solubility in water | | | insoluble | reacts surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | | 4.02×10^-4 Pa s (at 25 °C) odor | | odorless | odorless |