O2 + P4S3 = SO2 + P4O6

O_2 oxygen + P_4S_3 phosphorus sesquisulfide ⟶ SO_2 sulfur dioxide + O_6P_4 tetraphosphorus(III) hexoxide

Balance the chemical equation algebraically: O_2 + P_4S_3 ⟶ SO_2 + O_6P_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 P_4S_3 ⟶ c_3 SO_2 + c_4 O_6P_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, P and S: O: | 2 c_1 = 2 c_3 + 6 c_4 P: | 4 c_2 = 4 c_4 S: | 3 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 = 6 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 O_2 + P_4S_3 ⟶ 3 SO_2 + O_6P_4

+ ⟶ +

oxygen + phosphorus sesquisulfide ⟶ sulfur dioxide + tetraphosphorus(III) hexoxide

Construct the equilibrium constant, K, expression for: O_2 + P_4S_3 ⟶ SO_2 + O_6P_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: 6 O_2 + P_4S_3 ⟶ 3 SO_2 + O_6P_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 O_2 | 6 | -6 P_4S_3 | 1 | -1 SO_2 | 3 | 3 O_6P_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 6 | -6 | ([O2])^(-6) P_4S_3 | 1 | -1 | ([P4S3])^(-1) SO_2 | 3 | 3 | ([SO2])^3 O_6P_4 | 1 | 1 | [O6P4] 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])^(-6) ([P4S3])^(-1) ([SO2])^3 [O6P4] = (([SO2])^3 [O6P4])/(([O2])^6 [P4S3])

Construct the rate of reaction expression for: O_2 + P_4S_3 ⟶ SO_2 + O_6P_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: 6 O_2 + P_4S_3 ⟶ 3 SO_2 + O_6P_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 O_2 | 6 | -6 P_4S_3 | 1 | -1 SO_2 | 3 | 3 O_6P_4 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[O2])/(Δt) P_4S_3 | 1 | -1 | -(Δ[P4S3])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) O_6P_4 | 1 | 1 | (Δ[O6P4])/(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 = -1/6 (Δ[O2])/(Δt) = -(Δ[P4S3])/(Δt) = 1/3 (Δ[SO2])/(Δt) = (Δ[O6P4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | phosphorus sesquisulfide | sulfur dioxide | tetraphosphorus(III) hexoxide formula | O_2 | P_4S_3 | SO_2 | O_6P_4 Hill formula | O_2 | P_4S_3 | O_2S | O_6P_4 name | oxygen | phosphorus sesquisulfide | sulfur dioxide | tetraphosphorus(III) hexoxide IUPAC name | molecular oxygen | | sulfur dioxide |