NaOH + SO2 + H2S = H2O + Na2S2O3

NaOH sodium hydroxide + SO_2 sulfur dioxide + H_2S hydrogen sulfide ⟶ H_2O water + Na_2S_2O_3 sodium hyposulfite

Balance the chemical equation algebraically: NaOH + SO_2 + H_2S ⟶ H_2O + Na_2S_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 SO_2 + c_3 H_2S ⟶ c_4 H_2O + c_5 Na_2S_2O_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_4 Na: | c_1 = 2 c_5 O: | c_1 + 2 c_2 = c_4 + 3 c_5 S: | c_2 + c_3 = 2 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 = 2 c_3 = 1 c_4 = 5/2 c_5 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 4 c_3 = 2 c_4 = 5 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + 4 SO_2 + 2 H_2S ⟶ 5 H_2O + 3 Na_2S_2O_3

+ + ⟶ +

sodium hydroxide + sulfur dioxide + hydrogen sulfide ⟶ water + sodium hyposulfite

Construct the equilibrium constant, K, expression for: NaOH + SO_2 + H_2S ⟶ H_2O + Na_2S_2O_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: 6 NaOH + 4 SO_2 + 2 H_2S ⟶ 5 H_2O + 3 Na_2S_2O_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 | 6 | -6 SO_2 | 4 | -4 H_2S | 2 | -2 H_2O | 5 | 5 Na_2S_2O_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) SO_2 | 4 | -4 | ([SO2])^(-4) H_2S | 2 | -2 | ([H2S])^(-2) H_2O | 5 | 5 | ([H2O])^5 Na_2S_2O_3 | 3 | 3 | ([Na2S2O3])^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 = ([NaOH])^(-6) ([SO2])^(-4) ([H2S])^(-2) ([H2O])^5 ([Na2S2O3])^3 = (([H2O])^5 ([Na2S2O3])^3)/(([NaOH])^6 ([SO2])^4 ([H2S])^2)

Construct the rate of reaction expression for: NaOH + SO_2 + H_2S ⟶ H_2O + Na_2S_2O_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: 6 NaOH + 4 SO_2 + 2 H_2S ⟶ 5 H_2O + 3 Na_2S_2O_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 | 6 | -6 SO_2 | 4 | -4 H_2S | 2 | -2 H_2O | 5 | 5 Na_2S_2O_3 | 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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) SO_2 | 4 | -4 | -1/4 (Δ[SO2])/(Δt) H_2S | 2 | -2 | -1/2 (Δ[H2S])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) Na_2S_2O_3 | 3 | 3 | 1/3 (Δ[Na2S2O3])/(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[NaOH])/(Δt) = -1/4 (Δ[SO2])/(Δt) = -1/2 (Δ[H2S])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/3 (Δ[Na2S2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | sulfur dioxide | hydrogen sulfide | water | sodium hyposulfite formula | NaOH | SO_2 | H_2S | H_2O | Na_2S_2O_3 Hill formula | HNaO | O_2S | H_2S | H_2O | Na_2O_3S_2 name | sodium hydroxide | sulfur dioxide | hydrogen sulfide | water | sodium hyposulfite