Zn + H2S2O7 = H2O + H2S + ZnSO4

Zn zinc + H_2SO_4SO_3 oleum ⟶ H_2O water + H_2S hydrogen sulfide + ZnSO_4 zinc sulfate

Balance the chemical equation algebraically: Zn + H_2SO_4SO_3 ⟶ H_2O + H_2S + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 H_2SO_4SO_3 ⟶ c_3 H_2O + c_4 H_2S + c_5 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, H, O and S: Zn: | c_1 = c_5 H: | 2 c_2 = 2 c_3 + 2 c_4 O: | 7 c_2 = c_3 + 4 c_5 S: | 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 5/2 c_3 = 3/2 c_4 = 1 c_5 = 4 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 8 c_2 = 5 c_3 = 3 c_4 = 2 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Zn + 5 H_2SO_4SO_3 ⟶ 3 H_2O + 2 H_2S + 8 ZnSO_4

+ ⟶ + +

zinc + oleum ⟶ water + hydrogen sulfide + zinc sulfate

Construct the equilibrium constant, K, expression for: Zn + H_2SO_4SO_3 ⟶ H_2O + H_2S + ZnSO_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: 8 Zn + 5 H_2SO_4SO_3 ⟶ 3 H_2O + 2 H_2S + 8 ZnSO_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 Zn | 8 | -8 H_2SO_4SO_3 | 5 | -5 H_2O | 3 | 3 H_2S | 2 | 2 ZnSO_4 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 8 | -8 | ([Zn])^(-8) H_2SO_4SO_3 | 5 | -5 | ([H2SO4SO3])^(-5) H_2O | 3 | 3 | ([H2O])^3 H_2S | 2 | 2 | ([H2S])^2 ZnSO_4 | 8 | 8 | ([ZnSO4])^8 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 = ([Zn])^(-8) ([H2SO4SO3])^(-5) ([H2O])^3 ([H2S])^2 ([ZnSO4])^8 = (([H2O])^3 ([H2S])^2 ([ZnSO4])^8)/(([Zn])^8 ([H2SO4SO3])^5)

Construct the rate of reaction expression for: Zn + H_2SO_4SO_3 ⟶ H_2O + H_2S + ZnSO_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: 8 Zn + 5 H_2SO_4SO_3 ⟶ 3 H_2O + 2 H_2S + 8 ZnSO_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 Zn | 8 | -8 H_2SO_4SO_3 | 5 | -5 H_2O | 3 | 3 H_2S | 2 | 2 ZnSO_4 | 8 | 8 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 Zn | 8 | -8 | -1/8 (Δ[Zn])/(Δt) H_2SO_4SO_3 | 5 | -5 | -1/5 (Δ[H2SO4SO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) H_2S | 2 | 2 | 1/2 (Δ[H2S])/(Δt) ZnSO_4 | 8 | 8 | 1/8 (Δ[ZnSO4])/(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 = -1/8 (Δ[Zn])/(Δt) = -1/5 (Δ[H2SO4SO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[H2S])/(Δt) = 1/8 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| zinc | oleum | water | hydrogen sulfide | zinc sulfate formula | Zn | H_2SO_4SO_3 | H_2O | H_2S | ZnSO_4 Hill formula | Zn | H_2O_7S_2 | H_2O | H_2S | O_4SZn name | zinc | oleum | water | hydrogen sulfide | zinc sulfate IUPAC name | zinc | sulfuric acid; sulfur trioxide | water | hydrogen sulfide | zinc sulfate

| zinc | oleum | water | hydrogen sulfide | zinc sulfate molar mass | 65.38 g/mol | 178.1 g/mol | 18.015 g/mol | 34.08 g/mol | 161.4 g/mol phase | solid (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) | melting point | 420 °C | 1 °C | 0 °C | -85 °C | boiling point | 907 °C | 142 °C | 99.9839 °C | -60 °C | density | 7.14 g/cm^3 | 1.94 g/cm^3 | 1 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 1.005 g/cm^3 solubility in water | insoluble | reacts | | | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | | odorless