H2O + Cl2 + Na2S2O3 = HCl + NaHSO4

H_2O (water) + Cl_2 (chlorine) + Na_2S_2O_3 (sodium hyposulfite) ⟶ HCl (hydrogen chloride) + NaHSO_4 (sodium bisulfate)

Balance the chemical equation algebraically: H_2O + Cl_2 + Na_2S_2O_3 ⟶ HCl + NaHSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2 + c_3 Na_2S_2O_3 ⟶ c_4 HCl + c_5 NaHSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, Na and S: H: | 2 c_1 = c_4 + c_5 O: | c_1 + 3 c_3 = 4 c_5 Cl: | 2 c_2 = c_4 Na: | 2 c_3 = c_5 S: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5 c_2 = 4 c_3 = 1 c_4 = 8 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O + 4 Cl_2 + Na_2S_2O_3 ⟶ 8 HCl + 2 NaHSO_4

+ + ⟶ +

water + chlorine + sodium hyposulfite ⟶ hydrogen chloride + sodium bisulfate

Construct the equilibrium constant, K, expression for: H_2O + Cl_2 + Na_2S_2O_3 ⟶ HCl + NaHSO_4 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: 5 H_2O + 4 Cl_2 + Na_2S_2O_3 ⟶ 8 HCl + 2 NaHSO_4 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 | 5 | -5 Cl_2 | 4 | -4 Na_2S_2O_3 | 1 | -1 HCl | 8 | 8 NaHSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 5 | -5 | ([H2O])^(-5) Cl_2 | 4 | -4 | ([Cl2])^(-4) Na_2S_2O_3 | 1 | -1 | ([Na2S2O3])^(-1) HCl | 8 | 8 | ([HCl])^8 NaHSO_4 | 2 | 2 | ([NaHSO4])^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 = ([H2O])^(-5) ([Cl2])^(-4) ([Na2S2O3])^(-1) ([HCl])^8 ([NaHSO4])^2 = (([HCl])^8 ([NaHSO4])^2)/(([H2O])^5 ([Cl2])^4 [Na2S2O3])

Construct the rate of reaction expression for: H_2O + Cl_2 + Na_2S_2O_3 ⟶ HCl + NaHSO_4 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: 5 H_2O + 4 Cl_2 + Na_2S_2O_3 ⟶ 8 HCl + 2 NaHSO_4 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 | 5 | -5 Cl_2 | 4 | -4 Na_2S_2O_3 | 1 | -1 HCl | 8 | 8 NaHSO_4 | 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_2O | 5 | -5 | -1/5 (Δ[H2O])/(Δt) Cl_2 | 4 | -4 | -1/4 (Δ[Cl2])/(Δt) Na_2S_2O_3 | 1 | -1 | -(Δ[Na2S2O3])/(Δt) HCl | 8 | 8 | 1/8 (Δ[HCl])/(Δt) NaHSO_4 | 2 | 2 | 1/2 (Δ[NaHSO4])/(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 = -1/5 (Δ[H2O])/(Δt) = -1/4 (Δ[Cl2])/(Δt) = -(Δ[Na2S2O3])/(Δt) = 1/8 (Δ[HCl])/(Δt) = 1/2 (Δ[NaHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | chlorine | sodium hyposulfite | hydrogen chloride | sodium bisulfate formula | H_2O | Cl_2 | Na_2S_2O_3 | HCl | NaHSO_4 Hill formula | H_2O | Cl_2 | Na_2O_3S_2 | ClH | HNaO_4S name | water | chlorine | sodium hyposulfite | hydrogen chloride | sodium bisulfate IUPAC name | water | molecular chlorine | | hydrogen chloride |