H2O + O2 + CO2 + Cu = H2O2 + CuCO2

H_2O water + O_2 oxygen + CO_2 carbon dioxide + Cu copper ⟶ H_2O_2 hydrogen peroxide + CuCO2

Balance the chemical equation algebraically: H_2O + O_2 + CO_2 + Cu ⟶ H_2O_2 + CuCO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 CO_2 + c_4 Cu ⟶ c_5 H_2O_2 + c_6 CuCO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C and Cu: H: | 2 c_1 = 2 c_5 O: | c_1 + 2 c_2 + 2 c_3 = 2 c_5 + 2 c_6 C: | c_3 = c_6 Cu: | c_4 = c_6 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 = 2 c_2 = 1 c_4 = c_3 c_5 = 2 c_6 = c_3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_3 = 1 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + CO_2 + Cu ⟶ 2 H_2O_2 + CuCO2

+ + + ⟶ + CuCO2

water + oxygen + carbon dioxide + copper ⟶ hydrogen peroxide + CuCO2

Construct the equilibrium constant, K, expression for: H_2O + O_2 + CO_2 + Cu ⟶ H_2O_2 + CuCO2 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: 2 H_2O + O_2 + CO_2 + Cu ⟶ 2 H_2O_2 + CuCO2 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 H_2O | 2 | -2 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 1 | -1 H_2O_2 | 2 | 2 CuCO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) Cu | 1 | -1 | ([Cu])^(-1) H_2O_2 | 2 | 2 | ([H2O2])^2 CuCO2 | 1 | 1 | [CuCO2] 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 = ([H2O])^(-2) ([O2])^(-1) ([CO2])^(-1) ([Cu])^(-1) ([H2O2])^2 [CuCO2] = (([H2O2])^2 [CuCO2])/(([H2O])^2 [O2] [CO2] [Cu])

Construct the rate of reaction expression for: H_2O + O_2 + CO_2 + Cu ⟶ H_2O_2 + CuCO2 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: 2 H_2O + O_2 + CO_2 + Cu ⟶ 2 H_2O_2 + CuCO2 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 H_2O | 2 | -2 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 1 | -1 H_2O_2 | 2 | 2 CuCO2 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) Cu | 1 | -1 | -(Δ[Cu])/(Δt) H_2O_2 | 2 | 2 | 1/2 (Δ[H2O2])/(Δt) CuCO2 | 1 | 1 | (Δ[CuCO2])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[O2])/(Δt) = -(Δ[CO2])/(Δt) = -(Δ[Cu])/(Δt) = 1/2 (Δ[H2O2])/(Δt) = (Δ[CuCO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | carbon dioxide | copper | hydrogen peroxide | CuCO2 formula | H_2O | O_2 | CO_2 | Cu | H_2O_2 | CuCO2 Hill formula | H_2O | O_2 | CO_2 | Cu | H_2O_2 | CCuO2 name | water | oxygen | carbon dioxide | copper | hydrogen peroxide | IUPAC name | water | molecular oxygen | carbon dioxide | copper | hydrogen peroxide |

| water | oxygen | carbon dioxide | copper | hydrogen peroxide | CuCO2 molar mass | 18.015 g/mol | 31.998 g/mol | 44.009 g/mol | 63.546 g/mol | 34.014 g/mol | 107.55 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) | melting point | 0 °C | -218 °C | -56.56 °C (at triple point) | 1083 °C | -0.43 °C | boiling point | 99.9839 °C | -183 °C | -78.5 °C (at sublimation point) | 2567 °C | 150.2 °C | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.00184212 g/cm^3 (at 20 °C) | 8.96 g/cm^3 | 1.44 g/cm^3 | solubility in water | | | | insoluble | miscible | surface tension | 0.0728 N/m | 0.01347 N/m | | | 0.0804 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | | 0.001249 Pa s (at 20 °C) | odor | odorless | odorless | odorless | odorless | |