H2O + Na2S + NaSO3 = NaOH + S

H_2O water + Na_2S sodium sulfide + NaSO3 ⟶ NaOH sodium hydroxide + S mixed sulfur

Balance the chemical equation algebraically: H_2O + Na_2S + NaSO3 ⟶ NaOH + S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2S + c_3 NaSO3 ⟶ c_4 NaOH + c_5 S 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 = c_4 O: | c_1 + 3 c_3 = c_4 Na: | 2 c_2 + c_3 = c_4 S: | c_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 = 3 c_2 = 5/2 c_3 = 1 c_4 = 6 c_5 = 7/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 5 c_3 = 2 c_4 = 12 c_5 = 7 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 5 Na_2S + 2 NaSO3 ⟶ 12 NaOH + 7 S

+ + NaSO3 ⟶ +

water + sodium sulfide + NaSO3 ⟶ sodium hydroxide + mixed sulfur

Construct the equilibrium constant, K, expression for: H_2O + Na_2S + NaSO3 ⟶ NaOH + S 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: 6 H_2O + 5 Na_2S + 2 NaSO3 ⟶ 12 NaOH + 7 S 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 | 6 | -6 Na_2S | 5 | -5 NaSO3 | 2 | -2 NaOH | 12 | 12 S | 7 | 7 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) Na_2S | 5 | -5 | ([Na2S])^(-5) NaSO3 | 2 | -2 | ([NaSO3])^(-2) NaOH | 12 | 12 | ([NaOH])^12 S | 7 | 7 | ([S])^7 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])^(-6) ([Na2S])^(-5) ([NaSO3])^(-2) ([NaOH])^12 ([S])^7 = (([NaOH])^12 ([S])^7)/(([H2O])^6 ([Na2S])^5 ([NaSO3])^2)

Construct the rate of reaction expression for: H_2O + Na_2S + NaSO3 ⟶ NaOH + S 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: 6 H_2O + 5 Na_2S + 2 NaSO3 ⟶ 12 NaOH + 7 S 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 | 6 | -6 Na_2S | 5 | -5 NaSO3 | 2 | -2 NaOH | 12 | 12 S | 7 | 7 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 | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Na_2S | 5 | -5 | -1/5 (Δ[Na2S])/(Δt) NaSO3 | 2 | -2 | -1/2 (Δ[NaSO3])/(Δt) NaOH | 12 | 12 | 1/12 (Δ[NaOH])/(Δt) S | 7 | 7 | 1/7 (Δ[S])/(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 = -1/6 (Δ[H2O])/(Δt) = -1/5 (Δ[Na2S])/(Δt) = -1/2 (Δ[NaSO3])/(Δt) = 1/12 (Δ[NaOH])/(Δt) = 1/7 (Δ[S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium sulfide | NaSO3 | sodium hydroxide | mixed sulfur formula | H_2O | Na_2S | NaSO3 | NaOH | S Hill formula | H_2O | Na_2S_1 | NaO3S | HNaO | S name | water | sodium sulfide | | sodium hydroxide | mixed sulfur IUPAC name | water | | | sodium hydroxide | sulfur

| water | sodium sulfide | NaSO3 | sodium hydroxide | mixed sulfur molar mass | 18.015 g/mol | 78.04 g/mol | 103 g/mol | 39.997 g/mol | 32.06 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 0 °C | 1172 °C | | 323 °C | 112.8 °C boiling point | 99.9839 °C | | | 1390 °C | 444.7 °C density | 1 g/cm^3 | 1.856 g/cm^3 | | 2.13 g/cm^3 | 2.07 g/cm^3 solubility in water | | | | soluble | surface tension | 0.0728 N/m | | | 0.07435 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.004 Pa s (at 350 °C) | odor | odorless | | | |