H2SO4 + Zn = H2O + S + SO2 + H2S + ZnSO4

H_2SO_4 sulfuric acid + Zn zinc ⟶ H_2O water + S mixed sulfur + SO_2 sulfur dioxide + H_2S hydrogen sulfide + ZnSO_4 zinc sulfate

Balance the chemical equation algebraically: H_2SO_4 + Zn ⟶ H_2O + S + SO_2 + H_2S + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Zn ⟶ c_3 H_2O + c_4 S + c_5 SO_2 + c_6 H_2S + c_7 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Zn: H: | 2 c_1 = 2 c_3 + 2 c_6 O: | 4 c_1 = c_3 + 2 c_5 + 4 c_7 S: | c_1 = c_4 + c_5 + c_6 + c_7 Zn: | c_2 = c_7 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_3 = 2/3 + (4 c_1)/3 - (2 c_2)/3 c_4 = 1 c_5 = -1/3 + (4 c_1)/3 - (5 c_2)/3 c_6 = -2/3 - c_1/3 + (2 c_2)/3 c_7 = c_2 The resulting system of equations is still underdetermined, so additional coefficients must be set arbitrarily. Set c_1 = 25 and c_2 = 18 and solve for the remaining coefficients: c_1 = 25 c_2 = 18 c_3 = 22 c_4 = 1 c_5 = 3 c_6 = 3 c_7 = 18 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 25 H_2SO_4 + 18 Zn ⟶ 22 H_2O + S + 3 SO_2 + 3 H_2S + 18 ZnSO_4

+ ⟶ + + + +

sulfuric acid + zinc ⟶ water + mixed sulfur + sulfur dioxide + hydrogen sulfide + zinc sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + Zn ⟶ H_2O + S + SO_2 + 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: 25 H_2SO_4 + 18 Zn ⟶ 22 H_2O + S + 3 SO_2 + 3 H_2S + 18 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 H_2SO_4 | 25 | -25 Zn | 18 | -18 H_2O | 22 | 22 S | 1 | 1 SO_2 | 3 | 3 H_2S | 3 | 3 ZnSO_4 | 18 | 18 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 25 | -25 | ([H2SO4])^(-25) Zn | 18 | -18 | ([Zn])^(-18) H_2O | 22 | 22 | ([H2O])^22 S | 1 | 1 | [S] SO_2 | 3 | 3 | ([SO2])^3 H_2S | 3 | 3 | ([H2S])^3 ZnSO_4 | 18 | 18 | ([ZnSO4])^18 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])^(-25) ([Zn])^(-18) ([H2O])^22 [S] ([SO2])^3 ([H2S])^3 ([ZnSO4])^18 = (([H2O])^22 [S] ([SO2])^3 ([H2S])^3 ([ZnSO4])^18)/(([H2SO4])^25 ([Zn])^18)

Construct the rate of reaction expression for: H_2SO_4 + Zn ⟶ H_2O + S + SO_2 + 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: 25 H_2SO_4 + 18 Zn ⟶ 22 H_2O + S + 3 SO_2 + 3 H_2S + 18 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 H_2SO_4 | 25 | -25 Zn | 18 | -18 H_2O | 22 | 22 S | 1 | 1 SO_2 | 3 | 3 H_2S | 3 | 3 ZnSO_4 | 18 | 18 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 | 25 | -25 | -1/25 (Δ[H2SO4])/(Δt) Zn | 18 | -18 | -1/18 (Δ[Zn])/(Δt) H_2O | 22 | 22 | 1/22 (Δ[H2O])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) H_2S | 3 | 3 | 1/3 (Δ[H2S])/(Δt) ZnSO_4 | 18 | 18 | 1/18 (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 = -1/25 (Δ[H2SO4])/(Δt) = -1/18 (Δ[Zn])/(Δt) = 1/22 (Δ[H2O])/(Δt) = (Δ[S])/(Δt) = 1/3 (Δ[SO2])/(Δt) = 1/3 (Δ[H2S])/(Δt) = 1/18 (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | zinc | water | mixed sulfur | sulfur dioxide | hydrogen sulfide | zinc sulfate formula | H_2SO_4 | Zn | H_2O | S | SO_2 | H_2S | ZnSO_4 Hill formula | H_2O_4S | Zn | H_2O | S | O_2S | H_2S | O_4SZn name | sulfuric acid | zinc | water | mixed sulfur | sulfur dioxide | hydrogen sulfide | zinc sulfate IUPAC name | sulfuric acid | zinc | water | sulfur | sulfur dioxide | hydrogen sulfide | zinc sulfate

| sulfuric acid | zinc | water | mixed sulfur | sulfur dioxide | hydrogen sulfide | zinc sulfate molar mass | 98.07 g/mol | 65.38 g/mol | 18.015 g/mol | 32.06 g/mol | 64.06 g/mol | 34.08 g/mol | 161.4 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) | melting point | 10.371 °C | 420 °C | 0 °C | 112.8 °C | -73 °C | -85 °C | boiling point | 279.6 °C | 907 °C | 99.9839 °C | 444.7 °C | -10 °C | -60 °C | density | 1.8305 g/cm^3 | 7.14 g/cm^3 | 1 g/cm^3 | 2.07 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 0.001393 g/cm^3 (at 25 °C) | 1.005 g/cm^3 solubility in water | very soluble | insoluble | | | | | soluble surface tension | 0.0735 N/m | | 0.0728 N/m | | 0.02859 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 1.282×10^-5 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | odorless | | | | odorless