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H2O + O2 + CO2 + Cu = Cu(OH)2 + CuCO3

Input interpretation

H_2O (water) + O_2 (oxygen) + CO_2 (carbon dioxide) + Cu (copper) ⟶ Cu(OH)_2 (copper hydroxide) + CuCO_3 (copper(II) carbonate)
H_2O (water) + O_2 (oxygen) + CO_2 (carbon dioxide) + Cu (copper) ⟶ Cu(OH)_2 (copper hydroxide) + CuCO_3 (copper(II) carbonate)

Balanced equation

Balance the chemical equation algebraically: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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 Cu(OH)_2 + c_6 CuCO_3 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 + 3 c_6 C: | c_3 = c_6 Cu: | c_4 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = 2 c_2 - 1 c_4 = 2 c_2 c_5 = 1 c_6 = 2 c_2 - 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3
Balance the chemical equation algebraically: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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 Cu(OH)_2 + c_6 CuCO_3 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 + 3 c_6 C: | c_3 = c_6 Cu: | c_4 = c_5 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = 2 c_2 - 1 c_4 = 2 c_2 c_5 = 1 c_6 = 2 c_2 - 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3

Structures

+ + + ⟶ +
+ + + ⟶ +

Names

water + oxygen + carbon dioxide + copper ⟶ copper hydroxide + copper(II) carbonate
water + oxygen + carbon dioxide + copper ⟶ copper hydroxide + copper(II) carbonate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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: H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3 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 | 1 | -1 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 2 | -2 Cu(OH)_2 | 1 | 1 CuCO_3 | 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 | 1 | -1 | ([H2O])^(-1) O_2 | 1 | -1 | ([O2])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) Cu | 2 | -2 | ([Cu])^(-2) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] CuCO_3 | 1 | 1 | [CuCO3] 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])^(-1) ([O2])^(-1) ([CO2])^(-1) ([Cu])^(-2) [Cu(OH)2] [CuCO3] = ([Cu(OH)2] [CuCO3])/([H2O] [O2] [CO2] ([Cu])^2)
Construct the equilibrium constant, K, expression for: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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: H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3 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 | 1 | -1 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 2 | -2 Cu(OH)_2 | 1 | 1 CuCO_3 | 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 | 1 | -1 | ([H2O])^(-1) O_2 | 1 | -1 | ([O2])^(-1) CO_2 | 1 | -1 | ([CO2])^(-1) Cu | 2 | -2 | ([Cu])^(-2) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] CuCO_3 | 1 | 1 | [CuCO3] 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])^(-1) ([O2])^(-1) ([CO2])^(-1) ([Cu])^(-2) [Cu(OH)2] [CuCO3] = ([Cu(OH)2] [CuCO3])/([H2O] [O2] [CO2] ([Cu])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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: H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3 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 | 1 | -1 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 2 | -2 Cu(OH)_2 | 1 | 1 CuCO_3 | 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 | 1 | -1 | -(Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) Cu | 2 | -2 | -1/2 (Δ[Cu])/(Δt) Cu(OH)_2 | 1 | 1 | (Δ[Cu(OH)2])/(Δt) CuCO_3 | 1 | 1 | (Δ[CuCO3])/(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[H2O])/(Δt) = -(Δ[O2])/(Δt) = -(Δ[CO2])/(Δt) = -1/2 (Δ[Cu])/(Δt) = (Δ[Cu(OH)2])/(Δt) = (Δ[CuCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + O_2 + CO_2 + Cu ⟶ Cu(OH)_2 + CuCO_3 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: H_2O + O_2 + CO_2 + 2 Cu ⟶ Cu(OH)_2 + CuCO_3 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 | 1 | -1 O_2 | 1 | -1 CO_2 | 1 | -1 Cu | 2 | -2 Cu(OH)_2 | 1 | 1 CuCO_3 | 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 | 1 | -1 | -(Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) CO_2 | 1 | -1 | -(Δ[CO2])/(Δt) Cu | 2 | -2 | -1/2 (Δ[Cu])/(Δt) Cu(OH)_2 | 1 | 1 | (Δ[Cu(OH)2])/(Δt) CuCO_3 | 1 | 1 | (Δ[CuCO3])/(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[H2O])/(Δt) = -(Δ[O2])/(Δt) = -(Δ[CO2])/(Δt) = -1/2 (Δ[Cu])/(Δt) = (Δ[Cu(OH)2])/(Δt) = (Δ[CuCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | oxygen | carbon dioxide | copper | copper hydroxide | copper(II) carbonate formula | H_2O | O_2 | CO_2 | Cu | Cu(OH)_2 | CuCO_3 Hill formula | H_2O | O_2 | CO_2 | Cu | CuH_2O_2 | CCuO_3 name | water | oxygen | carbon dioxide | copper | copper hydroxide | copper(II) carbonate IUPAC name | water | molecular oxygen | carbon dioxide | copper | copper dihydroxide | copper carbonate
| water | oxygen | carbon dioxide | copper | copper hydroxide | copper(II) carbonate formula | H_2O | O_2 | CO_2 | Cu | Cu(OH)_2 | CuCO_3 Hill formula | H_2O | O_2 | CO_2 | Cu | CuH_2O_2 | CCuO_3 name | water | oxygen | carbon dioxide | copper | copper hydroxide | copper(II) carbonate IUPAC name | water | molecular oxygen | carbon dioxide | copper | copper dihydroxide | copper carbonate

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