HCl + Mg + Na2SO3 = H2O + NaCl + H2S + MgCl2

HCl hydrogen chloride + Mg magnesium + Na_2SO_3 sodium sulfite ⟶ H_2O water + NaCl sodium chloride + H_2S hydrogen sulfide + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: HCl + Mg + Na_2SO_3 ⟶ H_2O + NaCl + H_2S + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Mg + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 NaCl + c_6 H_2S + c_7 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mg, Na, O and S: Cl: | c_1 = c_5 + 2 c_7 H: | c_1 = 2 c_4 + 2 c_6 Mg: | c_2 = c_7 Na: | 2 c_3 = c_5 O: | 3 c_3 = c_4 S: | c_3 = c_6 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 = 8 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 2 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 3 Mg + Na_2SO_3 ⟶ 3 H_2O + 2 NaCl + H_2S + 3 MgCl_2

+ + ⟶ + + +

hydrogen chloride + magnesium + sodium sulfite ⟶ water + sodium chloride + hydrogen sulfide + magnesium chloride

| hydrogen chloride | magnesium | sodium sulfite | water | sodium chloride | hydrogen sulfide | magnesium chloride molecular enthalpy | -92.3 kJ/mol | 0 kJ/mol | -1101 kJ/mol | -285.8 kJ/mol | -411.2 kJ/mol | -20.6 kJ/mol | -641.3 kJ/mol total enthalpy | -738.4 kJ/mol | 0 kJ/mol | -1101 kJ/mol | -857.5 kJ/mol | -822.4 kJ/mol | -20.6 kJ/mol | -1924 kJ/mol | H_initial = -1839 kJ/mol | | | H_final = -3624 kJ/mol | | | ΔH_rxn^0 | -3624 kJ/mol - -1839 kJ/mol = -1785 kJ/mol (exothermic) | | | | | |

Construct the equilibrium constant, K, expression for: HCl + Mg + Na_2SO_3 ⟶ H_2O + NaCl + H_2S + MgCl_2 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: 8 HCl + 3 Mg + Na_2SO_3 ⟶ 3 H_2O + 2 NaCl + H_2S + 3 MgCl_2 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 | 8 | -8 Mg | 3 | -3 Na_2SO_3 | 1 | -1 H_2O | 3 | 3 NaCl | 2 | 2 H_2S | 1 | 1 MgCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) Mg | 3 | -3 | ([Mg])^(-3) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 NaCl | 2 | 2 | ([NaCl])^2 H_2S | 1 | 1 | [H2S] MgCl_2 | 3 | 3 | ([MgCl2])^3 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])^(-8) ([Mg])^(-3) ([Na2SO3])^(-1) ([H2O])^3 ([NaCl])^2 [H2S] ([MgCl2])^3 = (([H2O])^3 ([NaCl])^2 [H2S] ([MgCl2])^3)/(([HCl])^8 ([Mg])^3 [Na2SO3])

Construct the rate of reaction expression for: HCl + Mg + Na_2SO_3 ⟶ H_2O + NaCl + H_2S + MgCl_2 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: 8 HCl + 3 Mg + Na_2SO_3 ⟶ 3 H_2O + 2 NaCl + H_2S + 3 MgCl_2 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 | 8 | -8 Mg | 3 | -3 Na_2SO_3 | 1 | -1 H_2O | 3 | 3 NaCl | 2 | 2 H_2S | 1 | 1 MgCl_2 | 3 | 3 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) Mg | 3 | -3 | -1/3 (Δ[Mg])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(Δt) MgCl_2 | 3 | 3 | 1/3 (Δ[MgCl2])/(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 = -1/8 (Δ[HCl])/(Δt) = -1/3 (Δ[Mg])/(Δt) = -(Δ[Na2SO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[H2S])/(Δt) = 1/3 (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | magnesium | sodium sulfite | water | sodium chloride | hydrogen sulfide | magnesium chloride formula | HCl | Mg | Na_2SO_3 | H_2O | NaCl | H_2S | MgCl_2 Hill formula | ClH | Mg | Na_2O_3S | H_2O | ClNa | H_2S | Cl_2Mg name | hydrogen chloride | magnesium | sodium sulfite | water | sodium chloride | hydrogen sulfide | magnesium chloride IUPAC name | hydrogen chloride | magnesium | disodium sulfite | water | sodium chloride | hydrogen sulfide | magnesium dichloride