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Al + BaCO3 = Al2O3 + BaO + Al4C3

Input interpretation

Al aluminum + BaCO_3 barium carbonate ⟶ Al_2O_3 aluminum oxide + BaO barium oxide + Al4C3
Al aluminum + BaCO_3 barium carbonate ⟶ Al_2O_3 aluminum oxide + BaO barium oxide + Al4C3

Balanced equation

Balance the chemical equation algebraically: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 BaCO_3 ⟶ c_3 Al_2O_3 + c_4 BaO + c_5 Al4C3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ba, C and O: Al: | c_1 = 2 c_3 + 4 c_5 Ba: | c_2 = c_4 C: | c_2 = 3 c_5 O: | 3 c_2 = 3 c_3 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3
Balance the chemical equation algebraically: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 BaCO_3 ⟶ c_3 Al_2O_3 + c_4 BaO + c_5 Al4C3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ba, C and O: Al: | c_1 = 2 c_3 + 4 c_5 Ba: | c_2 = c_4 C: | c_2 = 3 c_5 O: | 3 c_2 = 3 c_3 + 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3

Structures

+ ⟶ + + Al4C3
+ ⟶ + + Al4C3

Names

aluminum + barium carbonate ⟶ aluminum oxide + barium oxide + Al4C3
aluminum + barium carbonate ⟶ aluminum oxide + barium oxide + Al4C3

Equilibrium constant

Construct the equilibrium constant, K, expression for: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 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: 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3 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 | 8 | -8 BaCO_3 | 3 | -3 Al_2O_3 | 2 | 2 BaO | 3 | 3 Al4C3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 8 | -8 | ([Al])^(-8) BaCO_3 | 3 | -3 | ([BaCO3])^(-3) Al_2O_3 | 2 | 2 | ([Al2O3])^2 BaO | 3 | 3 | ([BaO])^3 Al4C3 | 1 | 1 | [Al4C3] 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])^(-8) ([BaCO3])^(-3) ([Al2O3])^2 ([BaO])^3 [Al4C3] = (([Al2O3])^2 ([BaO])^3 [Al4C3])/(([Al])^8 ([BaCO3])^3)
Construct the equilibrium constant, K, expression for: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 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: 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3 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 | 8 | -8 BaCO_3 | 3 | -3 Al_2O_3 | 2 | 2 BaO | 3 | 3 Al4C3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 8 | -8 | ([Al])^(-8) BaCO_3 | 3 | -3 | ([BaCO3])^(-3) Al_2O_3 | 2 | 2 | ([Al2O3])^2 BaO | 3 | 3 | ([BaO])^3 Al4C3 | 1 | 1 | [Al4C3] 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])^(-8) ([BaCO3])^(-3) ([Al2O3])^2 ([BaO])^3 [Al4C3] = (([Al2O3])^2 ([BaO])^3 [Al4C3])/(([Al])^8 ([BaCO3])^3)

Rate of reaction

Construct the rate of reaction expression for: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 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: 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3 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 | 8 | -8 BaCO_3 | 3 | -3 Al_2O_3 | 2 | 2 BaO | 3 | 3 Al4C3 | 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 | 8 | -8 | -1/8 (Δ[Al])/(Δt) BaCO_3 | 3 | -3 | -1/3 (Δ[BaCO3])/(Δt) Al_2O_3 | 2 | 2 | 1/2 (Δ[Al2O3])/(Δt) BaO | 3 | 3 | 1/3 (Δ[BaO])/(Δt) Al4C3 | 1 | 1 | (Δ[Al4C3])/(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 = -1/8 (Δ[Al])/(Δt) = -1/3 (Δ[BaCO3])/(Δt) = 1/2 (Δ[Al2O3])/(Δt) = 1/3 (Δ[BaO])/(Δt) = (Δ[Al4C3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Al + BaCO_3 ⟶ Al_2O_3 + BaO + Al4C3 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: 8 Al + 3 BaCO_3 ⟶ 2 Al_2O_3 + 3 BaO + Al4C3 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 | 8 | -8 BaCO_3 | 3 | -3 Al_2O_3 | 2 | 2 BaO | 3 | 3 Al4C3 | 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 | 8 | -8 | -1/8 (Δ[Al])/(Δt) BaCO_3 | 3 | -3 | -1/3 (Δ[BaCO3])/(Δt) Al_2O_3 | 2 | 2 | 1/2 (Δ[Al2O3])/(Δt) BaO | 3 | 3 | 1/3 (Δ[BaO])/(Δt) Al4C3 | 1 | 1 | (Δ[Al4C3])/(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 = -1/8 (Δ[Al])/(Δt) = -1/3 (Δ[BaCO3])/(Δt) = 1/2 (Δ[Al2O3])/(Δt) = 1/3 (Δ[BaO])/(Δt) = (Δ[Al4C3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| aluminum | barium carbonate | aluminum oxide | barium oxide | Al4C3 formula | Al | BaCO_3 | Al_2O_3 | BaO | Al4C3 Hill formula | Al | CBaO_3 | Al_2O_3 | BaO | C3Al4 name | aluminum | barium carbonate | aluminum oxide | barium oxide | IUPAC name | aluminum | barium(+2) cation carbonate | dialuminum;oxygen(2-) | oxobarium |
| aluminum | barium carbonate | aluminum oxide | barium oxide | Al4C3 formula | Al | BaCO_3 | Al_2O_3 | BaO | Al4C3 Hill formula | Al | CBaO_3 | Al_2O_3 | BaO | C3Al4 name | aluminum | barium carbonate | aluminum oxide | barium oxide | IUPAC name | aluminum | barium(+2) cation carbonate | dialuminum;oxygen(2-) | oxobarium |

Substance properties

| aluminum | barium carbonate | aluminum oxide | barium oxide | Al4C3 molar mass | 26.9815385 g/mol | 197.33 g/mol | 101.96 g/mol | 153.326 g/mol | 143.959 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 1350 °C | 2040 °C | 1920 °C | boiling point | 2460 °C | | | | density | 2.7 g/cm^3 | 3.89 g/cm^3 | | 5.72 g/cm^3 | solubility in water | insoluble | insoluble | | | surface tension | 0.817 N/m | | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | | odor | odorless | odorless | odorless | |
| aluminum | barium carbonate | aluminum oxide | barium oxide | Al4C3 molar mass | 26.9815385 g/mol | 197.33 g/mol | 101.96 g/mol | 153.326 g/mol | 143.959 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 660.4 °C | 1350 °C | 2040 °C | 1920 °C | boiling point | 2460 °C | | | | density | 2.7 g/cm^3 | 3.89 g/cm^3 | | 5.72 g/cm^3 | solubility in water | insoluble | insoluble | | | surface tension | 0.817 N/m | | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | | odor | odorless | odorless | odorless | |

Units

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