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Al2O3 + KHSO4 = H2O + K2SO4 + Al2(SO4)3

Input interpretation

Al_2O_3 aluminum oxide + KHSO_4 potassium bisulfate ⟶ H_2O water + K_2SO_4 potassium sulfate + Al_2(SO_4)_3 aluminum sulfate
Al_2O_3 aluminum oxide + KHSO_4 potassium bisulfate ⟶ H_2O water + K_2SO_4 potassium sulfate + Al_2(SO_4)_3 aluminum sulfate

Balanced equation

Balance the chemical equation algebraically: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 KHSO_4 ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O, H, K and S: Al: | 2 c_1 = 2 c_5 O: | 3 c_1 + 4 c_2 = c_3 + 4 c_4 + 12 c_5 H: | c_2 = 2 c_3 K: | c_2 = 2 c_4 S: | c_2 = c_4 + 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 6 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_3
Balance the chemical equation algebraically: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al_2O_3 + c_2 KHSO_4 ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al, O, H, K and S: Al: | 2 c_1 = 2 c_5 O: | 3 c_1 + 4 c_2 = c_3 + 4 c_4 + 12 c_5 H: | c_2 = 2 c_3 K: | c_2 = 2 c_4 S: | c_2 = c_4 + 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 6 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_3

Structures

+ ⟶ + +
+ ⟶ + +

Names

aluminum oxide + potassium bisulfate ⟶ water + potassium sulfate + aluminum sulfate
aluminum oxide + potassium bisulfate ⟶ water + potassium sulfate + aluminum sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_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: Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_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_2O_3 | 1 | -1 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 3 | 3 Al_2(SO_4)_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_2O_3 | 1 | -1 | ([Al2O3])^(-1) KHSO_4 | 6 | -6 | ([KHSO4])^(-6) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)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 = ([Al2O3])^(-1) ([KHSO4])^(-6) ([H2O])^3 ([K2SO4])^3 [Al2(SO4)3] = (([H2O])^3 ([K2SO4])^3 [Al2(SO4)3])/([Al2O3] ([KHSO4])^6)
Construct the equilibrium constant, K, expression for: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_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: Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_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_2O_3 | 1 | -1 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 3 | 3 Al_2(SO_4)_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_2O_3 | 1 | -1 | ([Al2O3])^(-1) KHSO_4 | 6 | -6 | ([KHSO4])^(-6) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al_2(SO_4)_3 | 1 | 1 | [Al2(SO4)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 = ([Al2O3])^(-1) ([KHSO4])^(-6) ([H2O])^3 ([K2SO4])^3 [Al2(SO4)3] = (([H2O])^3 ([K2SO4])^3 [Al2(SO4)3])/([Al2O3] ([KHSO4])^6)

Rate of reaction

Construct the rate of reaction expression for: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_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: Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_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_2O_3 | 1 | -1 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 3 | 3 Al_2(SO_4)_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_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) KHSO_4 | 6 | -6 | -1/6 (Δ[KHSO4])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)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 = -(Δ[Al2O3])/(Δt) = -1/6 (Δ[KHSO4])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Al_2O_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_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: Al_2O_3 + 6 KHSO_4 ⟶ 3 H_2O + 3 K_2SO_4 + Al_2(SO_4)_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_2O_3 | 1 | -1 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 3 | 3 Al_2(SO_4)_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_2O_3 | 1 | -1 | -(Δ[Al2O3])/(Δt) KHSO_4 | 6 | -6 | -1/6 (Δ[KHSO4])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al_2(SO_4)_3 | 1 | 1 | (Δ[Al2(SO4)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 = -(Δ[Al2O3])/(Δt) = -1/6 (Δ[KHSO4])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| aluminum oxide | potassium bisulfate | water | potassium sulfate | aluminum sulfate formula | Al_2O_3 | KHSO_4 | H_2O | K_2SO_4 | Al_2(SO_4)_3 Hill formula | Al_2O_3 | HKO_4S | H_2O | K_2O_4S | Al_2O_12S_3 name | aluminum oxide | potassium bisulfate | water | potassium sulfate | aluminum sulfate IUPAC name | dialuminum;oxygen(2-) | potassium hydrogen sulfate | water | dipotassium sulfate | dialuminum trisulfate
| aluminum oxide | potassium bisulfate | water | potassium sulfate | aluminum sulfate formula | Al_2O_3 | KHSO_4 | H_2O | K_2SO_4 | Al_2(SO_4)_3 Hill formula | Al_2O_3 | HKO_4S | H_2O | K_2O_4S | Al_2O_12S_3 name | aluminum oxide | potassium bisulfate | water | potassium sulfate | aluminum sulfate IUPAC name | dialuminum;oxygen(2-) | potassium hydrogen sulfate | water | dipotassium sulfate | dialuminum trisulfate

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