NaOH + SO2 = H2 + Na2SO4

NaOH sodium hydroxide + SO_2 sulfur dioxide ⟶ H_2 hydrogen + Na_2SO_4 sodium sulfate

Balance the chemical equation algebraically: NaOH + SO_2 ⟶ H_2 + Na_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 SO_2 ⟶ 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, Na, O and S: H: | c_1 = 2 c_3 Na: | c_1 = 2 c_4 O: | c_1 + 2 c_2 = 4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + SO_2 ⟶ H_2 + Na_2SO_4

+ ⟶ +

sodium hydroxide + sulfur dioxide ⟶ hydrogen + sodium sulfate

| sodium hydroxide | sulfur dioxide | hydrogen | sodium sulfate molecular enthalpy | -425.8 kJ/mol | -296.8 kJ/mol | 0 kJ/mol | -1387 kJ/mol total enthalpy | -851.6 kJ/mol | -296.8 kJ/mol | 0 kJ/mol | -1387 kJ/mol | H_initial = -1148 kJ/mol | | H_final = -1387 kJ/mol | ΔH_rxn^0 | -1387 kJ/mol - -1148 kJ/mol = -238.7 kJ/mol (exothermic) | | |

| sodium hydroxide | sulfur dioxide | hydrogen | sodium sulfate molecular free energy | -379.7 kJ/mol | -300.1 kJ/mol | 0 kJ/mol | -1270 kJ/mol total free energy | -759.4 kJ/mol | -300.1 kJ/mol | 0 kJ/mol | -1270 kJ/mol | G_initial = -1060 kJ/mol | | G_final = -1270 kJ/mol | ΔG_rxn^0 | -1270 kJ/mol - -1060 kJ/mol = -210.7 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: NaOH + SO_2 ⟶ 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: 2 NaOH + SO_2 ⟶ 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 NaOH | 2 | -2 SO_2 | 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 NaOH | 2 | -2 | ([NaOH])^(-2) SO_2 | 1 | -1 | ([SO2])^(-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 = ([NaOH])^(-2) ([SO2])^(-1) [H2] [Na2SO4] = ([H2] [Na2SO4])/(([NaOH])^2 [SO2])

Construct the rate of reaction expression for: NaOH + SO_2 ⟶ 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: 2 NaOH + SO_2 ⟶ 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 NaOH | 2 | -2 SO_2 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) SO_2 | 1 | -1 | -(Δ[SO2])/(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 = -1/2 (Δ[NaOH])/(Δt) = -(Δ[SO2])/(Δt) = (Δ[H2])/(Δt) = (Δ[Na2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | sulfur dioxide | hydrogen | sodium sulfate formula | NaOH | SO_2 | H_2 | Na_2SO_4 Hill formula | HNaO | O_2S | H_2 | Na_2O_4S name | sodium hydroxide | sulfur dioxide | hydrogen | sodium sulfate IUPAC name | sodium hydroxide | sulfur dioxide | molecular hydrogen | disodium sulfate

| sodium hydroxide | sulfur dioxide | hydrogen | sodium sulfate molar mass | 39.997 g/mol | 64.06 g/mol | 2.016 g/mol | 142.04 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 323 °C | -73 °C | -259.2 °C | 884 °C boiling point | 1390 °C | -10 °C | -252.8 °C | 1429 °C density | 2.13 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.68 g/cm^3 solubility in water | soluble | | | soluble surface tension | 0.07435 N/m | 0.02859 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 1.282×10^-5 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |