O2 + C2H6S = H2O + CO2 + SO2

O_2 oxygen + (CH_3)_2S dimethyl sulfide ⟶ H_2O water + CO_2 carbon dioxide + SO_2 sulfur dioxide

Balance the chemical equation algebraically: O_2 + (CH_3)_2S ⟶ H_2O + CO_2 + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 (CH_3)_2S ⟶ c_3 H_2O + c_4 CO_2 + c_5 SO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, C, H and S: O: | 2 c_1 = c_3 + 2 c_4 + 2 c_5 C: | 2 c_2 = c_4 H: | 6 c_2 = 2 c_3 S: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 9/2 c_2 = 1 c_3 = 3 c_4 = 2 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 9 c_2 = 2 c_3 = 6 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 O_2 + 2 (CH_3)_2S ⟶ 6 H_2O + 4 CO_2 + 2 SO_2

+ ⟶ + +

oxygen + dimethyl sulfide ⟶ water + carbon dioxide + sulfur dioxide

Construct the equilibrium constant, K, expression for: O_2 + (CH_3)_2S ⟶ H_2O + CO_2 + 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: 9 O_2 + 2 (CH_3)_2S ⟶ 6 H_2O + 4 CO_2 + 2 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 O_2 | 9 | -9 (CH_3)_2S | 2 | -2 H_2O | 6 | 6 CO_2 | 4 | 4 SO_2 | 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 | 9 | -9 | ([O2])^(-9) (CH_3)_2S | 2 | -2 | ([(CH3)2S])^(-2) H_2O | 6 | 6 | ([H2O])^6 CO_2 | 4 | 4 | ([CO2])^4 SO_2 | 2 | 2 | ([SO2])^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])^(-9) ([(CH3)2S])^(-2) ([H2O])^6 ([CO2])^4 ([SO2])^2 = (([H2O])^6 ([CO2])^4 ([SO2])^2)/(([O2])^9 ([(CH3)2S])^2)

Construct the rate of reaction expression for: O_2 + (CH_3)_2S ⟶ H_2O + CO_2 + 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: 9 O_2 + 2 (CH_3)_2S ⟶ 6 H_2O + 4 CO_2 + 2 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 O_2 | 9 | -9 (CH_3)_2S | 2 | -2 H_2O | 6 | 6 CO_2 | 4 | 4 SO_2 | 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 | 9 | -9 | -1/9 (Δ[O2])/(Δt) (CH_3)_2S | 2 | -2 | -1/2 (Δ[(CH3)2S])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CO_2 | 4 | 4 | 1/4 (Δ[CO2])/(Δt) SO_2 | 2 | 2 | 1/2 (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 = -1/9 (Δ[O2])/(Δt) = -1/2 (Δ[(CH3)2S])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[CO2])/(Δt) = 1/2 (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | dimethyl sulfide | water | carbon dioxide | sulfur dioxide formula | O_2 | (CH_3)_2S | H_2O | CO_2 | SO_2 Hill formula | O_2 | C_2H_6S | H_2O | CO_2 | O_2S name | oxygen | dimethyl sulfide | water | carbon dioxide | sulfur dioxide IUPAC name | molecular oxygen | (methylthio)methane | water | carbon dioxide | sulfur dioxide