H2SO4 + KClO3 + K2S = H2O + K2SO4 + S + KCl

Input interpretation

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H_2SO_4 sulfuric acid + KClO_3 potassium chlorate + K2S ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + KCl potassium chloride

Balanced equation

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$Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + K_2SO_4 + S + KCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 K2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 KCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + 4 c_5 S: | c_1 + c_3 = c_5 + c_6 Cl: | c_2 = c_7 K: | c_2 + 2 c_3 = 2 c_5 + c_7 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_3 = (3 c_2)/4 + 3/4 c_4 = 1 c_5 = (3 c_2)/4 + 3/4 c_6 = 1 c_7 = c_2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_3 = (3 c_2)/4 + 3/2 c_4 = 2 c_5 = (3 c_2)/4 + 3/2 c_6 = 2 c_7 = c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 KClO_3 + 3 K2S ⟶ 2 H_2O + 3 K_2SO_4 + 2 S + 2 KCl$

Balance the chemical equation algebraically: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + K_2SO_4 + S + KCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KClO_3 + c_3 K2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 KCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cl and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + 4 c_5 S: | c_1 + c_3 = c_5 + c_6 Cl: | c_2 = c_7 K: | c_2 + 2 c_3 = 2 c_5 + c_7 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_3 = (3 c_2)/4 + 3/4 c_4 = 1 c_5 = (3 c_2)/4 + 3/4 c_6 = 1 c_7 = c_2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_3 = (3 c_2)/4 + 3/2 c_4 = 2 c_5 = (3 c_2)/4 + 3/2 c_6 = 2 c_7 = c_2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 KClO_3 + 3 K2S ⟶ 2 H_2O + 3 K_2SO_4 + 2 S + 2 KCl

+ + K2S ⟶ + + +

Names

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sulfuric acid + potassium chlorate + K2S ⟶ water + potassium sulfate + mixed sulfur + potassium chloride

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + K_2SO_4 + S + KCl 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: 2 H_2SO_4 + 2 KClO_3 + 3 K2S ⟶ 2 H_2O + 3 K_2SO_4 + 2 S + 2 KCl 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 | 2 | -2 KClO_3 | 2 | -2 K2S | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 3 | 3 S | 2 | 2 KCl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) KClO_3 | 2 | -2 | ([KClO3])^(-2) K2S | 3 | -3 | ([K2S])^(-3) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 3 | 3 | ([K2SO4])^3 S | 2 | 2 | ([S])^2 KCl | 2 | 2 | ([KCl])^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 = ([H2SO4])^(-2) ([KClO3])^(-2) ([K2S])^(-3) ([H2O])^2 ([K2SO4])^3 ([S])^2 ([KCl])^2 = (([H2O])^2 ([K2SO4])^3 ([S])^2 ([KCl])^2)/(([H2SO4])^2 ([KClO3])^2 ([K2S])^3)

Rate of reaction

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Construct the rate of reaction expression for: H_2SO_4 + KClO_3 + K2S ⟶ H_2O + K_2SO_4 + S + KCl 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: 2 H_2SO_4 + 2 KClO_3 + 3 K2S ⟶ 2 H_2O + 3 K_2SO_4 + 2 S + 2 KCl 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 | 2 | -2 KClO_3 | 2 | -2 K2S | 3 | -3 H_2O | 2 | 2 K_2SO_4 | 3 | 3 S | 2 | 2 KCl | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) KClO_3 | 2 | -2 | -1/2 (Δ[KClO3])/(Δt) K2S | 3 | -3 | -1/3 (Δ[K2S])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KClO3])/(Δt) = -1/3 (Δ[K2S])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/2 (Δ[KCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)