H2SO4 + H2S = H2O + SO2

H_2SO_4 (sulfuric acid) + H_2S (hydrogen sulfide) ⟶ H_2O (water) + SO_2 (sulfur dioxide)

Balance the chemical equation algebraically: H_2SO_4 + H_2S ⟶ H_2O + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2S ⟶ c_3 H_2O + c_4 SO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and S: H: | 2 c_1 + 2 c_2 = 2 c_3 O: | 4 c_1 = c_3 + 2 c_4 S: | c_1 + c_2 = c_4 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_1 = 3 c_2 = 1 c_3 = 4 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + H_2S ⟶ 4 H_2O + 4 SO_2

+ ⟶ +

sulfuric acid + hydrogen sulfide ⟶ water + sulfur dioxide

| sulfuric acid | hydrogen sulfide | water | sulfur dioxide molecular enthalpy | -814 kJ/mol | -20.6 kJ/mol | -285.8 kJ/mol | -296.8 kJ/mol total enthalpy | -2442 kJ/mol | -20.6 kJ/mol | -1143 kJ/mol | -1187 kJ/mol | H_initial = -2463 kJ/mol | | H_final = -2331 kJ/mol | ΔH_rxn^0 | -2331 kJ/mol - -2463 kJ/mol = 132.1 kJ/mol (endothermic) | | |

| sulfuric acid | hydrogen sulfide | water | sulfur dioxide molecular free energy | -690 kJ/mol | -33.4 kJ/mol | -237.1 kJ/mol | -300.1 kJ/mol total free energy | -2070 kJ/mol | -33.4 kJ/mol | -948.4 kJ/mol | -1200 kJ/mol | G_initial = -2103 kJ/mol | | G_final = -2149 kJ/mol | ΔG_rxn^0 | -2149 kJ/mol - -2103 kJ/mol = -45.4 kJ/mol (exergonic) | | |

| sulfuric acid | hydrogen sulfide | water | sulfur dioxide molecular entropy | 157 J/(mol K) | 206 J/(mol K) | 69.91 J/(mol K) | 248 J/(mol K) total entropy | 471 J/(mol K) | 206 J/(mol K) | 279.6 J/(mol K) | 992 J/(mol K) | S_initial = 677 J/(mol K) | | S_final = 1272 J/(mol K) | ΔS_rxn^0 | 1272 J/(mol K) - 677 J/(mol K) = 594.6 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S ⟶ H_2O + SO_2 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: 3 H_2SO_4 + H_2S ⟶ 4 H_2O + 4 SO_2 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 | 3 | -3 H_2S | 1 | -1 H_2O | 4 | 4 SO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) H_2S | 1 | -1 | ([H2S])^(-1) H_2O | 4 | 4 | ([H2O])^4 SO_2 | 4 | 4 | ([SO2])^4 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])^(-3) ([H2S])^(-1) ([H2O])^4 ([SO2])^4 = (([H2O])^4 ([SO2])^4)/(([H2SO4])^3 [H2S])

Construct the rate of reaction expression for: H_2SO_4 + H_2S ⟶ H_2O + SO_2 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: 3 H_2SO_4 + H_2S ⟶ 4 H_2O + 4 SO_2 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 | 3 | -3 H_2S | 1 | -1 H_2O | 4 | 4 SO_2 | 4 | 4 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 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) SO_2 | 4 | 4 | 1/4 (Δ[SO2])/(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 = -1/3 (Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/4 (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | hydrogen sulfide | water | sulfur dioxide formula | H_2SO_4 | H_2S | H_2O | SO_2 Hill formula | H_2O_4S | H_2S | H_2O | O_2S name | sulfuric acid | hydrogen sulfide | water | sulfur dioxide

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