H2SO4 + Na2S = H2O + S + SO2 + NaHSO4SO4

H_2SO_4 sulfuric acid + Na_2S sodium sulfide ⟶ H_2O water + S mixed sulfur + SO_2 sulfur dioxide + NaHSO4SO4

Balance the chemical equation algebraically: H_2SO_4 + Na_2S ⟶ H_2O + S + SO_2 + NaHSO4SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Na_2S ⟶ c_3 H_2O + c_4 S + c_5 SO_2 + c_6 NaHSO4SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Na: H: | 2 c_1 = 2 c_3 + c_6 O: | 4 c_1 = c_3 + 2 c_5 + 8 c_6 S: | c_1 + c_2 = c_4 + c_5 + 2 c_6 Na: | 2 c_2 = c_6 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_2 = 1 c_3 = c_1 - 1 c_4 = 9/2 - c_1/2 c_5 = (3 c_1)/2 - 15/2 c_6 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 7 and solve for the remaining coefficients: c_1 = 7 c_2 = 1 c_3 = 6 c_4 = 1 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2SO_4 + Na_2S ⟶ 6 H_2O + S + 3 SO_2 + 2 NaHSO4SO4

+ ⟶ + + + NaHSO4SO4

sulfuric acid + sodium sulfide ⟶ water + mixed sulfur + sulfur dioxide + NaHSO4SO4

Construct the equilibrium constant, K, expression for: H_2SO_4 + Na_2S ⟶ H_2O + S + SO_2 + NaHSO4SO4 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: 7 H_2SO_4 + Na_2S ⟶ 6 H_2O + S + 3 SO_2 + 2 NaHSO4SO4 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_2SO_4 | 7 | -7 Na_2S | 1 | -1 H_2O | 6 | 6 S | 1 | 1 SO_2 | 3 | 3 NaHSO4SO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 7 | -7 | ([H2SO4])^(-7) Na_2S | 1 | -1 | ([Na2S])^(-1) H_2O | 6 | 6 | ([H2O])^6 S | 1 | 1 | [S] SO_2 | 3 | 3 | ([SO2])^3 NaHSO4SO4 | 2 | 2 | ([NaHSO4SO4])^2 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 = ([H2SO4])^(-7) ([Na2S])^(-1) ([H2O])^6 [S] ([SO2])^3 ([NaHSO4SO4])^2 = (([H2O])^6 [S] ([SO2])^3 ([NaHSO4SO4])^2)/(([H2SO4])^7 [Na2S])

Construct the rate of reaction expression for: H_2SO_4 + Na_2S ⟶ H_2O + S + SO_2 + NaHSO4SO4 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: 7 H_2SO_4 + Na_2S ⟶ 6 H_2O + S + 3 SO_2 + 2 NaHSO4SO4 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_2SO_4 | 7 | -7 Na_2S | 1 | -1 H_2O | 6 | 6 S | 1 | 1 SO_2 | 3 | 3 NaHSO4SO4 | 2 | 2 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_2SO_4 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) NaHSO4SO4 | 2 | 2 | 1/2 (Δ[NaHSO4SO4])/(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 = -1/7 (Δ[H2SO4])/(Δt) = -(Δ[Na2S])/(Δt) = 1/6 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[SO2])/(Δt) = 1/2 (Δ[NaHSO4SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | sodium sulfide | water | mixed sulfur | sulfur dioxide | NaHSO4SO4 formula | H_2SO_4 | Na_2S | H_2O | S | SO_2 | NaHSO4SO4 Hill formula | H_2O_4S | Na_2S_1 | H_2O | S | O_2S | HNaO8S2 name | sulfuric acid | sodium sulfide | water | mixed sulfur | sulfur dioxide | IUPAC name | sulfuric acid | | water | sulfur | sulfur dioxide |