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H2O + Al(NO3)3 = O2 + H2 + HNO3 + Al + Al(OH)3

Input interpretation

H_2O water + Al(NO_3)_3 aluminum nitrate ⟶ O_2 oxygen + H_2 hydrogen + HNO_3 nitric acid + Al aluminum + Al(OH)_3 aluminum hydroxide
H_2O water + Al(NO_3)_3 aluminum nitrate ⟶ O_2 oxygen + H_2 hydrogen + HNO_3 nitric acid + Al aluminum + Al(OH)_3 aluminum hydroxide

Balanced equation

Balance the chemical equation algebraically: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al(NO_3)_3 ⟶ c_3 O_2 + c_4 H_2 + c_5 HNO_3 + c_6 Al + c_7 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al and N: H: | 2 c_1 = 2 c_4 + c_5 + 3 c_7 O: | c_1 + 9 c_2 = 2 c_3 + 3 c_5 + 3 c_7 Al: | c_2 = c_6 + c_7 N: | 3 c_2 = c_5 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_7 = 1 and solve the system of equations for the remaining coefficients: c_3 = c_1/2 - 3/2 c_4 = -3/2 + c_1 - (3 c_2)/2 c_5 = 3 c_2 c_6 = c_2 - 1 c_7 = 1 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 11 and c_2 = 5 and solve for the remaining coefficients: c_1 = 11 c_2 = 5 c_3 = 4 c_4 = 2 c_5 = 15 c_6 = 4 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_3
Balance the chemical equation algebraically: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al(NO_3)_3 ⟶ c_3 O_2 + c_4 H_2 + c_5 HNO_3 + c_6 Al + c_7 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al and N: H: | 2 c_1 = 2 c_4 + c_5 + 3 c_7 O: | c_1 + 9 c_2 = 2 c_3 + 3 c_5 + 3 c_7 Al: | c_2 = c_6 + c_7 N: | 3 c_2 = c_5 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_7 = 1 and solve the system of equations for the remaining coefficients: c_3 = c_1/2 - 3/2 c_4 = -3/2 + c_1 - (3 c_2)/2 c_5 = 3 c_2 c_6 = c_2 - 1 c_7 = 1 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 11 and c_2 = 5 and solve for the remaining coefficients: c_1 = 11 c_2 = 5 c_3 = 4 c_4 = 2 c_5 = 15 c_6 = 4 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_3

Structures

+ ⟶ + + + +
+ ⟶ + + + +

Names

water + aluminum nitrate ⟶ oxygen + hydrogen + nitric acid + aluminum + aluminum hydroxide
water + aluminum nitrate ⟶ oxygen + hydrogen + nitric acid + aluminum + aluminum hydroxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_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: 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_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 | 11 | -11 Al(NO_3)_3 | 5 | -5 O_2 | 4 | 4 H_2 | 2 | 2 HNO_3 | 15 | 15 Al | 4 | 4 Al(OH)_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 | 11 | -11 | ([H2O])^(-11) Al(NO_3)_3 | 5 | -5 | ([Al(NO3)3])^(-5) O_2 | 4 | 4 | ([O2])^4 H_2 | 2 | 2 | ([H2])^2 HNO_3 | 15 | 15 | ([HNO3])^15 Al | 4 | 4 | ([Al])^4 Al(OH)_3 | 1 | 1 | [Al(OH)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 = ([H2O])^(-11) ([Al(NO3)3])^(-5) ([O2])^4 ([H2])^2 ([HNO3])^15 ([Al])^4 [Al(OH)3] = (([O2])^4 ([H2])^2 ([HNO3])^15 ([Al])^4 [Al(OH)3])/(([H2O])^11 ([Al(NO3)3])^5)
Construct the equilibrium constant, K, expression for: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_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: 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_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 | 11 | -11 Al(NO_3)_3 | 5 | -5 O_2 | 4 | 4 H_2 | 2 | 2 HNO_3 | 15 | 15 Al | 4 | 4 Al(OH)_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 | 11 | -11 | ([H2O])^(-11) Al(NO_3)_3 | 5 | -5 | ([Al(NO3)3])^(-5) O_2 | 4 | 4 | ([O2])^4 H_2 | 2 | 2 | ([H2])^2 HNO_3 | 15 | 15 | ([HNO3])^15 Al | 4 | 4 | ([Al])^4 Al(OH)_3 | 1 | 1 | [Al(OH)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 = ([H2O])^(-11) ([Al(NO3)3])^(-5) ([O2])^4 ([H2])^2 ([HNO3])^15 ([Al])^4 [Al(OH)3] = (([O2])^4 ([H2])^2 ([HNO3])^15 ([Al])^4 [Al(OH)3])/(([H2O])^11 ([Al(NO3)3])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_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: 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_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 | 11 | -11 Al(NO_3)_3 | 5 | -5 O_2 | 4 | 4 H_2 | 2 | 2 HNO_3 | 15 | 15 Al | 4 | 4 Al(OH)_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 | 11 | -11 | -1/11 (Δ[H2O])/(Δt) Al(NO_3)_3 | 5 | -5 | -1/5 (Δ[Al(NO3)3])/(Δt) O_2 | 4 | 4 | 1/4 (Δ[O2])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) HNO_3 | 15 | 15 | 1/15 (Δ[HNO3])/(Δt) Al | 4 | 4 | 1/4 (Δ[Al])/(Δt) Al(OH)_3 | 1 | 1 | (Δ[Al(OH)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 = -1/11 (Δ[H2O])/(Δt) = -1/5 (Δ[Al(NO3)3])/(Δt) = 1/4 (Δ[O2])/(Δt) = 1/2 (Δ[H2])/(Δt) = 1/15 (Δ[HNO3])/(Δt) = 1/4 (Δ[Al])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Al(NO_3)_3 ⟶ O_2 + H_2 + HNO_3 + Al + Al(OH)_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: 11 H_2O + 5 Al(NO_3)_3 ⟶ 4 O_2 + 2 H_2 + 15 HNO_3 + 4 Al + Al(OH)_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 | 11 | -11 Al(NO_3)_3 | 5 | -5 O_2 | 4 | 4 H_2 | 2 | 2 HNO_3 | 15 | 15 Al | 4 | 4 Al(OH)_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 | 11 | -11 | -1/11 (Δ[H2O])/(Δt) Al(NO_3)_3 | 5 | -5 | -1/5 (Δ[Al(NO3)3])/(Δt) O_2 | 4 | 4 | 1/4 (Δ[O2])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) HNO_3 | 15 | 15 | 1/15 (Δ[HNO3])/(Δt) Al | 4 | 4 | 1/4 (Δ[Al])/(Δt) Al(OH)_3 | 1 | 1 | (Δ[Al(OH)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 = -1/11 (Δ[H2O])/(Δt) = -1/5 (Δ[Al(NO3)3])/(Δt) = 1/4 (Δ[O2])/(Δt) = 1/2 (Δ[H2])/(Δt) = 1/15 (Δ[HNO3])/(Δt) = 1/4 (Δ[Al])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | aluminum nitrate | oxygen | hydrogen | nitric acid | aluminum | aluminum hydroxide formula | H_2O | Al(NO_3)_3 | O_2 | H_2 | HNO_3 | Al | Al(OH)_3 Hill formula | H_2O | AlN_3O_9 | O_2 | H_2 | HNO_3 | Al | AlH_3O_3 name | water | aluminum nitrate | oxygen | hydrogen | nitric acid | aluminum | aluminum hydroxide IUPAC name | water | aluminum(+3) cation trinitrate | molecular oxygen | molecular hydrogen | nitric acid | aluminum | aluminum hydroxide
| water | aluminum nitrate | oxygen | hydrogen | nitric acid | aluminum | aluminum hydroxide formula | H_2O | Al(NO_3)_3 | O_2 | H_2 | HNO_3 | Al | Al(OH)_3 Hill formula | H_2O | AlN_3O_9 | O_2 | H_2 | HNO_3 | Al | AlH_3O_3 name | water | aluminum nitrate | oxygen | hydrogen | nitric acid | aluminum | aluminum hydroxide IUPAC name | water | aluminum(+3) cation trinitrate | molecular oxygen | molecular hydrogen | nitric acid | aluminum | aluminum hydroxide

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