Input interpretation
H_2SO_4 sulfuric acid + Al aluminum + KClO_3 potassium chlorate ⟶ H_2O water + KCl potassium chloride + Al_2(SO_4)_3 aluminum sulfate
Balanced equation
Balance the chemical equation algebraically: H_2SO_4 + Al + KClO_3 ⟶ H_2O + KCl + Al_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Al + c_3 KClO_3 ⟶ c_4 H_2O + c_5 KCl + c_6 Al_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Al, Cl and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_3 = c_4 + 12 c_6 S: | c_1 = 3 c_6 Al: | c_2 = 2 c_6 Cl: | c_3 = c_5 K: | c_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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 3 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 Al + KClO_3 ⟶ 3 H_2O + KCl + Al_2(SO_4)_3
Structures
+ + ⟶ + +
Names
sulfuric acid + aluminum + potassium chlorate ⟶ water + potassium chloride + aluminum sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + Al + KClO_3 ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + KClO_3 ⟶ 3 H_2O + KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO_3 | 1 | -1 H_2O | 3 | 3 KCl | 1 | 1 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 H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Al | 2 | -2 | ([Al])^(-2) KClO_3 | 1 | -1 | ([KClO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 KCl | 1 | 1 | [KCl] 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 = ([H2SO4])^(-3) ([Al])^(-2) ([KClO3])^(-1) ([H2O])^3 [KCl] [Al2(SO4)3] = (([H2O])^3 [KCl] [Al2(SO4)3])/(([H2SO4])^3 ([Al])^2 [KClO3])](../image_source/3f3bfdf5ac8b26d95415b532d1619a6f.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + Al + KClO_3 ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + KClO_3 ⟶ 3 H_2O + KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO_3 | 1 | -1 H_2O | 3 | 3 KCl | 1 | 1 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 H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Al | 2 | -2 | ([Al])^(-2) KClO_3 | 1 | -1 | ([KClO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 KCl | 1 | 1 | [KCl] 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 = ([H2SO4])^(-3) ([Al])^(-2) ([KClO3])^(-1) ([H2O])^3 [KCl] [Al2(SO4)3] = (([H2O])^3 [KCl] [Al2(SO4)3])/(([H2SO4])^3 ([Al])^2 [KClO3])
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + Al + KClO_3 ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + KClO_3 ⟶ 3 H_2O + KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO_3 | 1 | -1 H_2O | 3 | 3 KCl | 1 | 1 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Al])/(Δt) = -(Δ[KClO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/a47318a0869588dbb4de1dc0ca4de05d.png)
Construct the rate of reaction expression for: H_2SO_4 + Al + KClO_3 ⟶ H_2O + KCl + 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: 3 H_2SO_4 + 2 Al + KClO_3 ⟶ 3 H_2O + KCl + 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 H_2SO_4 | 3 | -3 Al | 2 | -2 KClO_3 | 1 | -1 H_2O | 3 | 3 KCl | 1 | 1 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Al])/(Δt) = -(Δ[KClO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | aluminum | potassium chlorate | water | potassium chloride | aluminum sulfate formula | H_2SO_4 | Al | KClO_3 | H_2O | KCl | Al_2(SO_4)_3 Hill formula | H_2O_4S | Al | ClKO_3 | H_2O | ClK | Al_2O_12S_3 name | sulfuric acid | aluminum | potassium chlorate | water | potassium chloride | aluminum sulfate IUPAC name | sulfuric acid | aluminum | potassium chlorate | water | potassium chloride | dialuminum trisulfate