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CO2 + Al(OH)3 = H2O + Al2(CO3)3

Input interpretation

CO_2 carbon dioxide + Al(OH)_3 aluminum hydroxide ⟶ H_2O water + Al2(CO3)3
CO_2 carbon dioxide + Al(OH)_3 aluminum hydroxide ⟶ H_2O water + Al2(CO3)3

Balanced equation

Balance the chemical equation algebraically: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 Al(OH)_3 ⟶ c_3 H_2O + c_4 Al2(CO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O, Al and H: C: | c_1 = 3 c_4 O: | 2 c_1 + 3 c_2 = c_3 + 9 c_4 Al: | c_2 = 2 c_4 H: | 3 c_2 = 2 c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)3
Balance the chemical equation algebraically: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO_2 + c_2 Al(OH)_3 ⟶ c_3 H_2O + c_4 Al2(CO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, O, Al and H: C: | c_1 = 3 c_4 O: | 2 c_1 + 3 c_2 = c_3 + 9 c_4 Al: | c_2 = 2 c_4 H: | 3 c_2 = 2 c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)3

Structures

+ ⟶ + Al2(CO3)3
+ ⟶ + Al2(CO3)3

Names

carbon dioxide + aluminum hydroxide ⟶ water + Al2(CO3)3
carbon dioxide + aluminum hydroxide ⟶ water + Al2(CO3)3

Equilibrium constant

Construct the equilibrium constant, K, expression for: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)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: 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)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 CO_2 | 3 | -3 Al(OH)_3 | 2 | -2 H_2O | 3 | 3 Al2(CO3)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 3 | -3 | ([CO2])^(-3) Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) H_2O | 3 | 3 | ([H2O])^3 Al2(CO3)3 | 1 | 1 | [Al2(CO3)3] 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 = ([CO2])^(-3) ([Al(OH)3])^(-2) ([H2O])^3 [Al2(CO3)3] = (([H2O])^3 [Al2(CO3)3])/(([CO2])^3 ([Al(OH)3])^2)
Construct the equilibrium constant, K, expression for: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)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: 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)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 CO_2 | 3 | -3 Al(OH)_3 | 2 | -2 H_2O | 3 | 3 Al2(CO3)3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO_2 | 3 | -3 | ([CO2])^(-3) Al(OH)_3 | 2 | -2 | ([Al(OH)3])^(-2) H_2O | 3 | 3 | ([H2O])^3 Al2(CO3)3 | 1 | 1 | [Al2(CO3)3] 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 = ([CO2])^(-3) ([Al(OH)3])^(-2) ([H2O])^3 [Al2(CO3)3] = (([H2O])^3 [Al2(CO3)3])/(([CO2])^3 ([Al(OH)3])^2)

Rate of reaction

Construct the rate of reaction expression for: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)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: 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)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 CO_2 | 3 | -3 Al(OH)_3 | 2 | -2 H_2O | 3 | 3 Al2(CO3)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 CO_2 | 3 | -3 | -1/3 (Δ[CO2])/(Δt) Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Al2(CO3)3 | 1 | 1 | (Δ[Al2(CO3)3])/(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 = -1/3 (Δ[CO2])/(Δt) = -1/2 (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Al2(CO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: CO_2 + Al(OH)_3 ⟶ H_2O + Al2(CO3)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: 3 CO_2 + 2 Al(OH)_3 ⟶ 3 H_2O + Al2(CO3)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 CO_2 | 3 | -3 Al(OH)_3 | 2 | -2 H_2O | 3 | 3 Al2(CO3)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 CO_2 | 3 | -3 | -1/3 (Δ[CO2])/(Δt) Al(OH)_3 | 2 | -2 | -1/2 (Δ[Al(OH)3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) Al2(CO3)3 | 1 | 1 | (Δ[Al2(CO3)3])/(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 = -1/3 (Δ[CO2])/(Δt) = -1/2 (Δ[Al(OH)3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[Al2(CO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| carbon dioxide | aluminum hydroxide | water | Al2(CO3)3 formula | CO_2 | Al(OH)_3 | H_2O | Al2(CO3)3 Hill formula | CO_2 | AlH_3O_3 | H_2O | C3Al2O9 name | carbon dioxide | aluminum hydroxide | water |
| carbon dioxide | aluminum hydroxide | water | Al2(CO3)3 formula | CO_2 | Al(OH)_3 | H_2O | Al2(CO3)3 Hill formula | CO_2 | AlH_3O_3 | H_2O | C3Al2O9 name | carbon dioxide | aluminum hydroxide | water |

Substance properties

| carbon dioxide | aluminum hydroxide | water | Al2(CO3)3 molar mass | 44.009 g/mol | 78.003 g/mol | 18.015 g/mol | 233.99 g/mol phase | gas (at STP) | | liquid (at STP) | melting point | -56.56 °C (at triple point) | | 0 °C | boiling point | -78.5 °C (at sublimation point) | | 99.9839 °C | density | 0.00184212 g/cm^3 (at 20 °C) | | 1 g/cm^3 | surface tension | | | 0.0728 N/m | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |
| carbon dioxide | aluminum hydroxide | water | Al2(CO3)3 molar mass | 44.009 g/mol | 78.003 g/mol | 18.015 g/mol | 233.99 g/mol phase | gas (at STP) | | liquid (at STP) | melting point | -56.56 °C (at triple point) | | 0 °C | boiling point | -78.5 °C (at sublimation point) | | 99.9839 °C | density | 0.00184212 g/cm^3 (at 20 °C) | | 1 g/cm^3 | surface tension | | | 0.0728 N/m | dynamic viscosity | 1.491×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |

Units

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