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H2SO4 + KClO4 + Ti2(SO4)3 = H2O + KCl + Ti(SO4)2

Input interpretation

H_2SO_4 sulfuric acid + KClO_4 potassium perchlorate + Ti_2(SO_4)_3 titanium(III) sulfate ⟶ H_2O water + KCl potassium chloride + O_8S_2Ti_1 titanium(IV) sulfate
H_2SO_4 sulfuric acid + KClO_4 potassium perchlorate + Ti_2(SO_4)_3 titanium(III) sulfate ⟶ H_2O water + KCl potassium chloride + O_8S_2Ti_1 titanium(IV) sulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_4 + c_3 Ti_2(SO_4)_3 ⟶ c_4 H_2O + c_5 KCl + c_6 O_8S_2Ti_1 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, K and Ti: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 12 c_3 = c_4 + 8 c_6 S: | c_1 + 3 c_3 = 2 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 Ti: | 2 c_3 = c_6 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 = 4 c_2 = 1 c_3 = 4 c_4 = 4 c_5 = 1 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1
Balance the chemical equation algebraically: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_4 + c_3 Ti_2(SO_4)_3 ⟶ c_4 H_2O + c_5 KCl + c_6 O_8S_2Ti_1 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl, K and Ti: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 + 12 c_3 = c_4 + 8 c_6 S: | c_1 + 3 c_3 = 2 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 Ti: | 2 c_3 = c_6 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 = 4 c_2 = 1 c_3 = 4 c_4 = 4 c_5 = 1 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

sulfuric acid + potassium perchlorate + titanium(III) sulfate ⟶ water + potassium chloride + titanium(IV) sulfate
sulfuric acid + potassium perchlorate + titanium(III) sulfate ⟶ water + potassium chloride + titanium(IV) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 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: 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1 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 | 4 | -4 KClO_4 | 1 | -1 Ti_2(SO_4)_3 | 4 | -4 H_2O | 4 | 4 KCl | 1 | 1 O_8S_2Ti_1 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KClO_4 | 1 | -1 | ([KClO4])^(-1) Ti_2(SO_4)_3 | 4 | -4 | ([Ti2(SO4)3])^(-4) H_2O | 4 | 4 | ([H2O])^4 KCl | 1 | 1 | [KCl] O_8S_2Ti_1 | 8 | 8 | ([O8S2Ti1])^8 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])^(-4) ([KClO4])^(-1) ([Ti2(SO4)3])^(-4) ([H2O])^4 [KCl] ([O8S2Ti1])^8 = (([H2O])^4 [KCl] ([O8S2Ti1])^8)/(([H2SO4])^4 [KClO4] ([Ti2(SO4)3])^4)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 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: 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1 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 | 4 | -4 KClO_4 | 1 | -1 Ti_2(SO_4)_3 | 4 | -4 H_2O | 4 | 4 KCl | 1 | 1 O_8S_2Ti_1 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KClO_4 | 1 | -1 | ([KClO4])^(-1) Ti_2(SO_4)_3 | 4 | -4 | ([Ti2(SO4)3])^(-4) H_2O | 4 | 4 | ([H2O])^4 KCl | 1 | 1 | [KCl] O_8S_2Ti_1 | 8 | 8 | ([O8S2Ti1])^8 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])^(-4) ([KClO4])^(-1) ([Ti2(SO4)3])^(-4) ([H2O])^4 [KCl] ([O8S2Ti1])^8 = (([H2O])^4 [KCl] ([O8S2Ti1])^8)/(([H2SO4])^4 [KClO4] ([Ti2(SO4)3])^4)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 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: 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1 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 | 4 | -4 KClO_4 | 1 | -1 Ti_2(SO_4)_3 | 4 | -4 H_2O | 4 | 4 KCl | 1 | 1 O_8S_2Ti_1 | 8 | 8 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KClO_4 | 1 | -1 | -(Δ[KClO4])/(Δt) Ti_2(SO_4)_3 | 4 | -4 | -1/4 (Δ[Ti2(SO4)3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) O_8S_2Ti_1 | 8 | 8 | 1/8 (Δ[O8S2Ti1])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -(Δ[KClO4])/(Δt) = -1/4 (Δ[Ti2(SO4)3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = 1/8 (Δ[O8S2Ti1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KClO_4 + Ti_2(SO_4)_3 ⟶ H_2O + KCl + O_8S_2Ti_1 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: 4 H_2SO_4 + KClO_4 + 4 Ti_2(SO_4)_3 ⟶ 4 H_2O + KCl + 8 O_8S_2Ti_1 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 | 4 | -4 KClO_4 | 1 | -1 Ti_2(SO_4)_3 | 4 | -4 H_2O | 4 | 4 KCl | 1 | 1 O_8S_2Ti_1 | 8 | 8 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KClO_4 | 1 | -1 | -(Δ[KClO4])/(Δt) Ti_2(SO_4)_3 | 4 | -4 | -1/4 (Δ[Ti2(SO4)3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) O_8S_2Ti_1 | 8 | 8 | 1/8 (Δ[O8S2Ti1])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -(Δ[KClO4])/(Δt) = -1/4 (Δ[Ti2(SO4)3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[KCl])/(Δt) = 1/8 (Δ[O8S2Ti1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium perchlorate | titanium(III) sulfate | water | potassium chloride | titanium(IV) sulfate formula | H_2SO_4 | KClO_4 | Ti_2(SO_4)_3 | H_2O | KCl | O_8S_2Ti_1 Hill formula | H_2O_4S | ClKO_4 | O_12S_3Ti_2 | H_2O | ClK | O_8S_2Ti name | sulfuric acid | potassium perchlorate | titanium(III) sulfate | water | potassium chloride | titanium(IV) sulfate IUPAC name | sulfuric acid | potassium perchlorate | titanium(+3) cation trisulfate | water | potassium chloride | titanium(4+) disulfate
| sulfuric acid | potassium perchlorate | titanium(III) sulfate | water | potassium chloride | titanium(IV) sulfate formula | H_2SO_4 | KClO_4 | Ti_2(SO_4)_3 | H_2O | KCl | O_8S_2Ti_1 Hill formula | H_2O_4S | ClKO_4 | O_12S_3Ti_2 | H_2O | ClK | O_8S_2Ti name | sulfuric acid | potassium perchlorate | titanium(III) sulfate | water | potassium chloride | titanium(IV) sulfate IUPAC name | sulfuric acid | potassium perchlorate | titanium(+3) cation trisulfate | water | potassium chloride | titanium(4+) disulfate

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