H2S + SO3 = H2O + SO2

H_2S hydrogen sulfide + SO_3 sulfur trioxide ⟶ H_2O water + SO_2 sulfur dioxide

Balance the chemical equation algebraically: H_2S + SO_3 ⟶ H_2O + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 SO_3 ⟶ 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, S and O: H: | 2 c_1 = 2 c_3 S: | c_1 + c_2 = c_4 O: | 3 c_2 = c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 1 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2S + 3 SO_3 ⟶ H_2O + 4 SO_2

+ ⟶ +

hydrogen sulfide + sulfur trioxide ⟶ water + sulfur dioxide

| hydrogen sulfide | sulfur trioxide | water | sulfur dioxide molecular free energy | -33.4 kJ/mol | -373.8 kJ/mol | -237.1 kJ/mol | -300.1 kJ/mol total free energy | -33.4 kJ/mol | -1121 kJ/mol | -237.1 kJ/mol | -1200 kJ/mol | G_initial = -1155 kJ/mol | | G_final = -1438 kJ/mol | ΔG_rxn^0 | -1438 kJ/mol - -1155 kJ/mol = -282.7 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: H_2S + SO_3 ⟶ 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: H_2S + 3 SO_3 ⟶ 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_2S | 1 | -1 SO_3 | 3 | -3 H_2O | 1 | 1 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_2S | 1 | -1 | ([H2S])^(-1) SO_3 | 3 | -3 | ([SO3])^(-3) H_2O | 1 | 1 | [H2O] 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 = ([H2S])^(-1) ([SO3])^(-3) [H2O] ([SO2])^4 = ([H2O] ([SO2])^4)/([H2S] ([SO3])^3)

Construct the rate of reaction expression for: H_2S + SO_3 ⟶ 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: H_2S + 3 SO_3 ⟶ 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_2S | 1 | -1 SO_3 | 3 | -3 H_2O | 1 | 1 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_2S | 1 | -1 | -(Δ[H2S])/(Δt) SO_3 | 3 | -3 | -1/3 (Δ[SO3])/(Δt) H_2O | 1 | 1 | (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 = -(Δ[H2S])/(Δt) = -1/3 (Δ[SO3])/(Δt) = (Δ[H2O])/(Δt) = 1/4 (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | sulfur trioxide | water | sulfur dioxide formula | H_2S | SO_3 | H_2O | SO_2 Hill formula | H_2S | O_3S | H_2O | O_2S name | hydrogen sulfide | sulfur trioxide | water | sulfur dioxide

| hydrogen sulfide | sulfur trioxide | water | sulfur dioxide molar mass | 34.08 g/mol | 80.06 g/mol | 18.015 g/mol | 64.06 g/mol phase | gas (at STP) | liquid (at STP) | liquid (at STP) | gas (at STP) melting point | -85 °C | 16.8 °C | 0 °C | -73 °C boiling point | -60 °C | 44.7 °C | 99.9839 °C | -10 °C density | 0.001393 g/cm^3 (at 25 °C) | 1.97 g/cm^3 | 1 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) solubility in water | | reacts | | surface tension | | | 0.0728 N/m | 0.02859 N/m dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | 0.00159 Pa s (at 30 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) odor | | | odorless |