O2 + H2S = SO2 + HO

O_2 oxygen + H_2S hydrogen sulfide ⟶ SO_2 sulfur dioxide + (HO)^• hydroxyl radical

Balance the chemical equation algebraically: O_2 + H_2S ⟶ SO_2 + (HO)^• Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 H_2S ⟶ c_3 SO_2 + c_4 HO^• Set the number of atoms in the reactants equal to the number of atoms in the products for O, H and S: O: | 2 c_1 = 2 c_3 + c_4 H: | 2 c_2 = c_4 S: | c_2 = c_3 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 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + H_2S ⟶ SO_2 + 2 HO^•

+ ⟶ + (HO)^•

oxygen + hydrogen sulfide ⟶ sulfur dioxide + hydroxyl radical

Construct the equilibrium constant, K, expression for: O_2 + H_2S ⟶ SO_2 + (HO)^• 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: 2 O_2 + H_2S ⟶ SO_2 + 2 HO^• 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 O_2 | 2 | -2 H_2S | 1 | -1 SO_2 | 1 | 1 HO^• | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) H_2S | 1 | -1 | ([H2S])^(-1) SO_2 | 1 | 1 | [SO2] HO^• | 2 | 2 | ([HO•])^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 = ([O2])^(-2) ([H2S])^(-1) [SO2] ([HO•])^2 = ([SO2] ([HO•])^2)/(([O2])^2 [H2S])

Construct the rate of reaction expression for: O_2 + H_2S ⟶ SO_2 + (HO)^• 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: 2 O_2 + H_2S ⟶ SO_2 + 2 HO^• 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 O_2 | 2 | -2 H_2S | 1 | -1 SO_2 | 1 | 1 HO^• | 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 O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) HO^• | 2 | 2 | 1/2 (Δ[HO•])/(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 = -1/2 (Δ[O2])/(Δt) = -(Δ[H2S])/(Δt) = (Δ[SO2])/(Δt) = 1/2 (Δ[HO•])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | hydrogen sulfide | sulfur dioxide | hydroxyl radical formula | O_2 | H_2S | SO_2 | (HO)^• Hill formula | O_2 | H_2S | O_2S | name | oxygen | hydrogen sulfide | sulfur dioxide | hydroxyl radical IUPAC name | molecular oxygen | hydrogen sulfide | sulfur dioxide |

| oxygen | hydrogen sulfide | sulfur dioxide | hydroxyl radical molar mass | 31.998 g/mol | 34.08 g/mol | 64.06 g/mol | 17.0073 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) | melting point | -218 °C | -85 °C | -73 °C | boiling point | -183 °C | -60 °C | -10 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.001393 g/cm^3 (at 25 °C) | 0.002619 g/cm^3 (at 25 °C) | surface tension | 0.01347 N/m | | 0.02859 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | |