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H2O + Al2(SO4)3 + K2CO3 = CO2 + K2SO4 + Al(OH)3

Input interpretation

H_2O water + Al_2(SO_4)_3 aluminum sulfate + K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + K_2SO_4 potassium sulfate + Al(OH)_3 aluminum hydroxide
H_2O water + Al_2(SO_4)_3 aluminum sulfate + K_2CO_3 pearl ash ⟶ CO_2 carbon dioxide + K_2SO_4 potassium sulfate + Al(OH)_3 aluminum hydroxide

Balanced equation

Balance the chemical equation algebraically: H_2O + Al_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al_2(SO_4)_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 K_2SO_4 + c_6 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al, S, C and K: H: | 2 c_1 = 3 c_6 O: | c_1 + 12 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 3 c_6 Al: | 2 c_2 = c_6 S: | 3 c_2 = c_5 C: | c_3 = c_4 K: | 2 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 Al(OH)_3
Balance the chemical equation algebraically: H_2O + Al_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al_2(SO_4)_3 + c_3 K_2CO_3 ⟶ c_4 CO_2 + c_5 K_2SO_4 + c_6 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al, S, C and K: H: | 2 c_1 = 3 c_6 O: | c_1 + 12 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 3 c_6 Al: | 2 c_2 = c_6 S: | 3 c_2 = c_5 C: | c_3 = c_4 K: | 2 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 3 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 Al(OH)_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + aluminum sulfate + pearl ash ⟶ carbon dioxide + potassium sulfate + aluminum hydroxide
water + aluminum sulfate + pearl ash ⟶ carbon dioxide + potassium sulfate + aluminum hydroxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Al_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + 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: 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 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 | 3 | -3 Al_2(SO_4)_3 | 1 | -1 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 K_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) K_2CO_3 | 3 | -3 | ([K2CO3])^(-3) CO_2 | 3 | 3 | ([CO2])^3 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al(OH)_3 | 2 | 2 | ([Al(OH)3])^2 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])^(-3) ([Al2(SO4)3])^(-1) ([K2CO3])^(-3) ([CO2])^3 ([K2SO4])^3 ([Al(OH)3])^2 = (([CO2])^3 ([K2SO4])^3 ([Al(OH)3])^2)/(([H2O])^3 [Al2(SO4)3] ([K2CO3])^3)
Construct the equilibrium constant, K, expression for: H_2O + Al_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + 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: 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 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 | 3 | -3 Al_2(SO_4)_3 | 1 | -1 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 K_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) Al_2(SO_4)_3 | 1 | -1 | ([Al2(SO4)3])^(-1) K_2CO_3 | 3 | -3 | ([K2CO3])^(-3) CO_2 | 3 | 3 | ([CO2])^3 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al(OH)_3 | 2 | 2 | ([Al(OH)3])^2 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])^(-3) ([Al2(SO4)3])^(-1) ([K2CO3])^(-3) ([CO2])^3 ([K2SO4])^3 ([Al(OH)3])^2 = (([CO2])^3 ([K2SO4])^3 ([Al(OH)3])^2)/(([H2O])^3 [Al2(SO4)3] ([K2CO3])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2O + Al_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + 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: 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 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 | 3 | -3 Al_2(SO_4)_3 | 1 | -1 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 K_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) K_2CO_3 | 3 | -3 | -1/3 (Δ[K2CO3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (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 = -1/3 (Δ[H2O])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = -1/3 (Δ[K2CO3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (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_2(SO_4)_3 + K_2CO_3 ⟶ CO_2 + K_2SO_4 + 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: 3 H_2O + Al_2(SO_4)_3 + 3 K_2CO_3 ⟶ 3 CO_2 + 3 K_2SO_4 + 2 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 | 3 | -3 Al_2(SO_4)_3 | 1 | -1 K_2CO_3 | 3 | -3 CO_2 | 3 | 3 K_2SO_4 | 3 | 3 Al(OH)_3 | 2 | 2 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) Al_2(SO_4)_3 | 1 | -1 | -(Δ[Al2(SO4)3])/(Δt) K_2CO_3 | 3 | -3 | -1/3 (Δ[K2CO3])/(Δt) CO_2 | 3 | 3 | 1/3 (Δ[CO2])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al(OH)_3 | 2 | 2 | 1/2 (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 = -1/3 (Δ[H2O])/(Δt) = -(Δ[Al2(SO4)3])/(Δt) = -1/3 (Δ[K2CO3])/(Δt) = 1/3 (Δ[CO2])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | aluminum sulfate | pearl ash | carbon dioxide | potassium sulfate | aluminum hydroxide formula | H_2O | Al_2(SO_4)_3 | K_2CO_3 | CO_2 | K_2SO_4 | Al(OH)_3 Hill formula | H_2O | Al_2O_12S_3 | CK_2O_3 | CO_2 | K_2O_4S | AlH_3O_3 name | water | aluminum sulfate | pearl ash | carbon dioxide | potassium sulfate | aluminum hydroxide IUPAC name | water | dialuminum trisulfate | dipotassium carbonate | carbon dioxide | dipotassium sulfate | aluminum hydroxide
| water | aluminum sulfate | pearl ash | carbon dioxide | potassium sulfate | aluminum hydroxide formula | H_2O | Al_2(SO_4)_3 | K_2CO_3 | CO_2 | K_2SO_4 | Al(OH)_3 Hill formula | H_2O | Al_2O_12S_3 | CK_2O_3 | CO_2 | K_2O_4S | AlH_3O_3 name | water | aluminum sulfate | pearl ash | carbon dioxide | potassium sulfate | aluminum hydroxide IUPAC name | water | dialuminum trisulfate | dipotassium carbonate | carbon dioxide | dipotassium sulfate | aluminum hydroxide

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