HCl + Na2S2O3 = H2O + S + SO2 + NaCl

HCl (hydrogen chloride) + Na_2S_2O_3 (sodium hyposulfite) ⟶ H_2O (water) + S (mixed sulfur) + SO_2 (sulfur dioxide) + NaCl (sodium chloride)

Balance the chemical equation algebraically: HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Na_2S_2O_3 ⟶ c_3 H_2O + c_4 S + c_5 SO_2 + 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_3 Na: | 2 c_2 = c_6 O: | 3 c_2 = c_3 + 2 c_5 S: | 2 c_2 = c_4 + 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + 2 NaCl

+ ⟶ + + +

hydrogen chloride + sodium hyposulfite ⟶ water + mixed sulfur + sulfur dioxide + sodium chloride

Construct the equilibrium constant, K, expression for: HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + 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: 2 HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + 2 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 | 2 | -2 Na_2S_2O_3 | 1 | -1 H_2O | 1 | 1 S | 1 | 1 SO_2 | 1 | 1 NaCl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) Na_2S_2O_3 | 1 | -1 | ([Na2S2O3])^(-1) H_2O | 1 | 1 | [H2O] S | 1 | 1 | [S] SO_2 | 1 | 1 | [SO2] NaCl | 2 | 2 | ([NaCl])^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 = ([HCl])^(-2) ([Na2S2O3])^(-1) [H2O] [S] [SO2] ([NaCl])^2 = ([H2O] [S] [SO2] ([NaCl])^2)/(([HCl])^2 [Na2S2O3])

Construct the rate of reaction expression for: HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + 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: 2 HCl + Na_2S_2O_3 ⟶ H_2O + S + SO_2 + 2 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 | 2 | -2 Na_2S_2O_3 | 1 | -1 H_2O | 1 | 1 S | 1 | 1 SO_2 | 1 | 1 NaCl | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) Na_2S_2O_3 | 1 | -1 | -(Δ[Na2S2O3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) NaCl | 2 | 2 | 1/2 (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 = -1/2 (Δ[HCl])/(Δt) = -(Δ[Na2S2O3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = (Δ[SO2])/(Δt) = 1/2 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sodium hyposulfite | water | mixed sulfur | sulfur dioxide | sodium chloride formula | HCl | Na_2S_2O_3 | H_2O | S | SO_2 | NaCl Hill formula | ClH | Na_2O_3S_2 | H_2O | S | O_2S | ClNa name | hydrogen chloride | sodium hyposulfite | water | mixed sulfur | sulfur dioxide | sodium chloride IUPAC name | hydrogen chloride | | water | sulfur | sulfur dioxide | sodium chloride