H2O + Na2SO3 = H2 + Na2SO4

H_2O water + Na_2SO_3 sodium sulfite ⟶ H_2 hydrogen + Na_2SO_4 sodium sulfate

Balance the chemical equation algebraically: H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2SO_3 ⟶ c_3 H_2 + c_4 Na_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and S: H: | 2 c_1 = 2 c_3 O: | c_1 + 3 c_2 = 4 c_4 Na: | 2 c_2 = 2 c_4 S: | c_2 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_4

+ ⟶ +

water + sodium sulfite ⟶ hydrogen + sodium sulfate

| water | sodium sulfite | hydrogen | sodium sulfate molecular enthalpy | -285.8 kJ/mol | -1101 kJ/mol | 0 kJ/mol | -1387 kJ/mol total enthalpy | -285.8 kJ/mol | -1101 kJ/mol | 0 kJ/mol | -1387 kJ/mol | H_initial = -1387 kJ/mol | | H_final = -1387 kJ/mol | ΔH_rxn^0 | -1387 kJ/mol - -1387 kJ/mol = -0.47 kJ/mol (exothermic) | | |

| water | sodium sulfite | hydrogen | sodium sulfate molecular free energy | -237.1 kJ/mol | -10125 kJ/mol | 0 kJ/mol | -1270 kJ/mol total free energy | -237.1 kJ/mol | -10125 kJ/mol | 0 kJ/mol | -1270 kJ/mol | G_initial = -10362 kJ/mol | | G_final = -1270 kJ/mol | ΔG_rxn^0 | -1270 kJ/mol - -10362 kJ/mol = 9092 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_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: H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_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 | 1 | -1 Na_2SO_3 | 1 | -1 H_2 | 1 | 1 Na_2SO_4 | 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 | 1 | -1 | ([H2O])^(-1) Na_2SO_3 | 1 | -1 | ([Na2SO3])^(-1) H_2 | 1 | 1 | [H2] Na_2SO_4 | 1 | 1 | [Na2SO4] 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])^(-1) ([Na2SO3])^(-1) [H2] [Na2SO4] = ([H2] [Na2SO4])/([H2O] [Na2SO3])

Construct the rate of reaction expression for: H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_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: H_2O + Na_2SO_3 ⟶ H_2 + Na_2SO_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 | 1 | -1 Na_2SO_3 | 1 | -1 H_2 | 1 | 1 Na_2SO_4 | 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 | 1 | -1 | -(Δ[H2O])/(Δt) Na_2SO_3 | 1 | -1 | -(Δ[Na2SO3])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(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 = -(Δ[H2O])/(Δt) = -(Δ[Na2SO3])/(Δt) = (Δ[H2])/(Δt) = (Δ[Na2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium sulfite | hydrogen | sodium sulfate formula | H_2O | Na_2SO_3 | H_2 | Na_2SO_4 Hill formula | H_2O | Na_2O_3S | H_2 | Na_2O_4S name | water | sodium sulfite | hydrogen | sodium sulfate IUPAC name | water | disodium sulfite | molecular hydrogen | disodium sulfate

| water | sodium sulfite | hydrogen | sodium sulfate molar mass | 18.015 g/mol | 126.04 g/mol | 2.016 g/mol | 142.04 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 0 °C | 500 °C | -259.2 °C | 884 °C boiling point | 99.9839 °C | | -252.8 °C | 1429 °C density | 1 g/cm^3 | 2.63 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.68 g/cm^3 solubility in water | | | | soluble surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |