NaOH + S = H2O + Na2S + H2SO3

NaOH sodium hydroxide + S mixed sulfur ⟶ H_2O water + Na_2S sodium sulfide + H_2SO_3 sulfurous acid

Balance the chemical equation algebraically: NaOH + S ⟶ H_2O + Na_2S + H_2SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 S ⟶ c_3 H_2O + c_4 Na_2S + c_5 H_2SO_3 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 + 2 c_5 Na: | c_1 = 2 c_4 O: | c_1 = c_3 + 3 c_5 S: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 1 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 NaOH + 3 S ⟶ H_2O + 2 Na_2S + H_2SO_3

+ ⟶ + +

sodium hydroxide + mixed sulfur ⟶ water + sodium sulfide + sulfurous acid

Construct the equilibrium constant, K, expression for: NaOH + S ⟶ H_2O + Na_2S + H_2SO_3 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: 4 NaOH + 3 S ⟶ H_2O + 2 Na_2S + H_2SO_3 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 | 4 | -4 S | 3 | -3 H_2O | 1 | 1 Na_2S | 2 | 2 H_2SO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 4 | -4 | ([NaOH])^(-4) S | 3 | -3 | ([S])^(-3) H_2O | 1 | 1 | [H2O] Na_2S | 2 | 2 | ([Na2S])^2 H_2SO_3 | 1 | 1 | [H2SO3] 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])^(-4) ([S])^(-3) [H2O] ([Na2S])^2 [H2SO3] = ([H2O] ([Na2S])^2 [H2SO3])/(([NaOH])^4 ([S])^3)

Construct the rate of reaction expression for: NaOH + S ⟶ H_2O + Na_2S + H_2SO_3 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: 4 NaOH + 3 S ⟶ H_2O + 2 Na_2S + H_2SO_3 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 | 4 | -4 S | 3 | -3 H_2O | 1 | 1 Na_2S | 2 | 2 H_2SO_3 | 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 | 4 | -4 | -1/4 (Δ[NaOH])/(Δt) S | 3 | -3 | -1/3 (Δ[S])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Na_2S | 2 | 2 | 1/2 (Δ[Na2S])/(Δt) H_2SO_3 | 1 | 1 | (Δ[H2SO3])/(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 = -1/4 (Δ[NaOH])/(Δt) = -1/3 (Δ[S])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[Na2S])/(Δt) = (Δ[H2SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | mixed sulfur | water | sodium sulfide | sulfurous acid formula | NaOH | S | H_2O | Na_2S | H_2SO_3 Hill formula | HNaO | S | H_2O | Na_2S_1 | H_2O_3S name | sodium hydroxide | mixed sulfur | water | sodium sulfide | sulfurous acid IUPAC name | sodium hydroxide | sulfur | water | | sulfurous acid

| sodium hydroxide | mixed sulfur | water | sodium sulfide | sulfurous acid molar mass | 39.997 g/mol | 32.06 g/mol | 18.015 g/mol | 78.04 g/mol | 82.07 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | melting point | 323 °C | 112.8 °C | 0 °C | 1172 °C | boiling point | 1390 °C | 444.7 °C | 99.9839 °C | | density | 2.13 g/cm^3 | 2.07 g/cm^3 | 1 g/cm^3 | 1.856 g/cm^3 | 1.03 g/cm^3 solubility in water | soluble | | | | very soluble surface tension | 0.07435 N/m | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |