Al + H2CO3 = H2 + Al2(CO3)3

Al aluminum + H_2CO_3 carbonic acid ⟶ H_2 hydrogen + Al2(CO3)3

Balance the chemical equation algebraically: Al + H_2CO_3 ⟶ H_2 + Al2(CO3)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 H_2CO_3 ⟶ c_3 H_2 + c_4 Al2(CO3)3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, C, H and O: Al: | c_1 = 2 c_4 C: | c_2 = 3 c_4 H: | 2 c_2 = 2 c_3 O: | 3 c_2 = 9 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 H_2CO_3 ⟶ 3 H_2 + Al2(CO3)3

+ ⟶ + Al2(CO3)3

aluminum + carbonic acid ⟶ hydrogen + Al2(CO3)3

Construct the equilibrium constant, K, expression for: Al + H_2CO_3 ⟶ H_2 + 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: 2 Al + 3 H_2CO_3 ⟶ 3 H_2 + 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 Al | 2 | -2 H_2CO_3 | 3 | -3 H_2 | 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 Al | 2 | -2 | ([Al])^(-2) H_2CO_3 | 3 | -3 | ([H2CO3])^(-3) H_2 | 3 | 3 | ([H2])^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 = ([Al])^(-2) ([H2CO3])^(-3) ([H2])^3 [Al2(CO3)3] = (([H2])^3 [Al2(CO3)3])/(([Al])^2 ([H2CO3])^3)

Construct the rate of reaction expression for: Al + H_2CO_3 ⟶ H_2 + 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: 2 Al + 3 H_2CO_3 ⟶ 3 H_2 + 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 Al | 2 | -2 H_2CO_3 | 3 | -3 H_2 | 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 Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) H_2CO_3 | 3 | -3 | -1/3 (Δ[H2CO3])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(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 = -1/2 (Δ[Al])/(Δt) = -1/3 (Δ[H2CO3])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Al2(CO3)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | carbonic acid | hydrogen | Al2(CO3)3 formula | Al | H_2CO_3 | H_2 | Al2(CO3)3 Hill formula | Al | CH_2O_3 | H_2 | C3Al2O9 name | aluminum | carbonic acid | hydrogen | IUPAC name | aluminum | carbonic acid | molecular hydrogen |

| aluminum | carbonic acid | hydrogen | Al2(CO3)3 molar mass | 26.9815385 g/mol | 62.024 g/mol | 2.016 g/mol | 233.99 g/mol phase | solid (at STP) | | gas (at STP) | melting point | 660.4 °C | | -259.2 °C | boiling point | 2460 °C | | -252.8 °C | density | 2.7 g/cm^3 | | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | insoluble | | | surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |