O2 + P2S3 = SO2 + P4O10

O_2 oxygen + P_2S_3 phosphorus trisulfide ⟶ SO_2 sulfur dioxide + P_4O_10 phosphorus pentoxide

Balance the chemical equation algebraically: O_2 + P_2S_3 ⟶ SO_2 + P_4O_10 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 P_2S_3 ⟶ c_3 SO_2 + c_4 P_4O_10 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 + 10 c_4 P: | 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 11 c_2 = 2 c_3 = 6 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 11 O_2 + 2 P_2S_3 ⟶ 6 SO_2 + P_4O_10

+ ⟶ +

oxygen + phosphorus trisulfide ⟶ sulfur dioxide + phosphorus pentoxide

Construct the equilibrium constant, K, expression for: O_2 + P_2S_3 ⟶ SO_2 + P_4O_10 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: 11 O_2 + 2 P_2S_3 ⟶ 6 SO_2 + P_4O_10 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 | 11 | -11 P_2S_3 | 2 | -2 SO_2 | 6 | 6 P_4O_10 | 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 | 11 | -11 | ([O2])^(-11) P_2S_3 | 2 | -2 | ([P2S3])^(-2) SO_2 | 6 | 6 | ([SO2])^6 P_4O_10 | 1 | 1 | [P4O10] 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])^(-11) ([P2S3])^(-2) ([SO2])^6 [P4O10] = (([SO2])^6 [P4O10])/(([O2])^11 ([P2S3])^2)

Construct the rate of reaction expression for: O_2 + P_2S_3 ⟶ SO_2 + P_4O_10 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: 11 O_2 + 2 P_2S_3 ⟶ 6 SO_2 + P_4O_10 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 | 11 | -11 P_2S_3 | 2 | -2 SO_2 | 6 | 6 P_4O_10 | 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 | 11 | -11 | -1/11 (Δ[O2])/(Δt) P_2S_3 | 2 | -2 | -1/2 (Δ[P2S3])/(Δt) SO_2 | 6 | 6 | 1/6 (Δ[SO2])/(Δt) P_4O_10 | 1 | 1 | (Δ[P4O10])/(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 = -1/11 (Δ[O2])/(Δt) = -1/2 (Δ[P2S3])/(Δt) = 1/6 (Δ[SO2])/(Δt) = (Δ[P4O10])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | phosphorus trisulfide | sulfur dioxide | phosphorus pentoxide formula | O_2 | P_2S_3 | SO_2 | P_4O_10 Hill formula | O_2 | P_2S_3 | O_2S | O_10P_4 name | oxygen | phosphorus trisulfide | sulfur dioxide | phosphorus pentoxide IUPAC name | molecular oxygen | | sulfur dioxide |

| oxygen | phosphorus trisulfide | sulfur dioxide | phosphorus pentoxide molar mass | 31.998 g/mol | 158.1 g/mol | 64.06 g/mol | 283.89 g/mol phase | gas (at STP) | | gas (at STP) | solid (at STP) melting point | -218 °C | | -73 °C | 340 °C boiling point | -183 °C | | -10 °C | density | 0.001429 g/cm^3 (at 0 °C) | | 0.002619 g/cm^3 (at 25 °C) | 2.3 g/cm^3 surface tension | 0.01347 N/m | | 0.02859 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | |