HCl + Na2SO3 + Na2S = H2O + S + NaCl

HCl hydrogen chloride + Na_2SO_3 sodium sulfite + Na_2S sodium sulfide ⟶ H_2O water + S mixed sulfur + NaCl sodium chloride

Balance the chemical equation algebraically: HCl + Na_2SO_3 + Na_2S ⟶ H_2O + S + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Na_2SO_3 + c_3 Na_2S ⟶ c_4 H_2O + c_5 S + c_6 NaCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Na, O and S: Cl: | c_1 = c_6 H: | c_1 = 2 c_4 Na: | 2 c_2 + 2 c_3 = c_6 O: | 3 c_2 = c_4 S: | c_2 + 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 c_4 = 3 c_5 = 3 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + Na_2SO_3 + 2 Na_2S ⟶ 3 H_2O + 3 S + 6 NaCl

hydrogen chloride + sodium sulfite + sodium sulfide ⟶ water + mixed sulfur + sodium chloride

Construct the equilibrium constant, K, expression for: HCl + Na_2SO_3 + Na_2S ⟶ H_2O + S + NaCl 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: 6 HCl + Na_2SO_3 + 2 Na_2S ⟶ 3 H_2O + 3 S + 6 NaCl 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 HCl | 6 | -6 Na_2SO_3 | 1 | -1 Na_2S | 2 | -2 H_2O | 3 | 3 S | 3 | 3 NaCl | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) Na_2S | 2 | -2 | ([Na2S])^(-2) H_2O | 3 | 3 | ([H2O])^3 S | 3 | 3 | ([S])^3 NaCl | 6 | 6 | ([NaCl])^6 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 = ([HCl])^(-6) ([Na2SO3])^(-1) ([Na2S])^(-2) ([H2O])^3 ([S])^3 ([NaCl])^6 = (([H2O])^3 ([S])^3 ([NaCl])^6)/(([HCl])^6 [Na2SO3] ([Na2S])^2)

Construct the rate of reaction expression for: HCl + Na_2SO_3 + Na_2S ⟶ H_2O + S + NaCl 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: 6 HCl + Na_2SO_3 + 2 Na_2S ⟶ 3 H_2O + 3 S + 6 NaCl 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 HCl | 6 | -6 Na_2SO_3 | 1 | -1 Na_2S | 2 | -2 H_2O | 3 | 3 S | 3 | 3 NaCl | 6 | 6 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 HCl | 6 | -6 | -1/6 (Δ[HCl])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) Na_2S | 2 | -2 | -1/2 (Δ[Na2S])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[Na2SO3])/(Δt) = -1/2 (Δ[Na2S])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/6 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sodium sulfite | sodium sulfide | water | mixed sulfur | sodium chloride formula | HCl | Na_2SO_3 | Na_2S | H_2O | S | NaCl Hill formula | ClH | Na_2O_3S | Na_2S_1 | H_2O | S | ClNa name | hydrogen chloride | sodium sulfite | sodium sulfide | water | mixed sulfur | sodium chloride IUPAC name | hydrogen chloride | disodium sulfite | | water | sulfur | sodium chloride