H2O + SO2 + HClO3 = H2SO4 + HCl

H_2O water + SO_2 sulfur dioxide + HClO3 ⟶ H_2SO_4 sulfuric acid + HCl hydrogen chloride

Balance the chemical equation algebraically: H_2O + SO_2 + HClO3 ⟶ H_2SO_4 + HCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 HClO3 ⟶ c_4 H_2SO_4 + c_5 HCl Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cl: H: | 2 c_1 + c_3 = 2 c_4 + c_5 O: | c_1 + 2 c_2 + 3 c_3 = 4 c_4 S: | c_2 = c_4 Cl: | 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 = 3 c_3 = 1 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 SO_2 + HClO3 ⟶ 3 H_2SO_4 + HCl

+ + HClO3 ⟶ +

water + sulfur dioxide + HClO3 ⟶ sulfuric acid + hydrogen chloride

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + HClO3 ⟶ H_2SO_4 + HCl 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 + 3 SO_2 + HClO3 ⟶ 3 H_2SO_4 + HCl 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 SO_2 | 3 | -3 HClO3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 1 | 1 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) SO_2 | 3 | -3 | ([SO2])^(-3) HClO3 | 1 | -1 | ([HClO3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 HCl | 1 | 1 | [HCl] 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) ([SO2])^(-3) ([HClO3])^(-1) ([H2SO4])^3 [HCl] = (([H2SO4])^3 [HCl])/(([H2O])^3 ([SO2])^3 [HClO3])

Construct the rate of reaction expression for: H_2O + SO_2 + HClO3 ⟶ H_2SO_4 + HCl 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 + 3 SO_2 + HClO3 ⟶ 3 H_2SO_4 + HCl 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 SO_2 | 3 | -3 HClO3 | 1 | -1 H_2SO_4 | 3 | 3 HCl | 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_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) HClO3 | 1 | -1 | -(Δ[HClO3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) HCl | 1 | 1 | (Δ[HCl])/(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) = -1/3 (Δ[SO2])/(Δt) = -(Δ[HClO3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = (Δ[HCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sulfur dioxide | HClO3 | sulfuric acid | hydrogen chloride formula | H_2O | SO_2 | HClO3 | H_2SO_4 | HCl Hill formula | H_2O | O_2S | HClO3 | H_2O_4S | ClH name | water | sulfur dioxide | | sulfuric acid | hydrogen chloride