O2 + S8 = SO3

O_2 (oxygen) + S_8 (rhombic sulfur) ⟶ SO_3 (sulfur trioxide)

Balance the chemical equation algebraically: O_2 + S_8 ⟶ SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 S_8 ⟶ c_3 SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O and S: O: | 2 c_1 = 3 c_3 S: | 8 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 = 12 c_2 = 1 c_3 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 O_2 + S_8 ⟶ 8 SO_3

+ ⟶

oxygen + rhombic sulfur ⟶ sulfur trioxide

Construct the equilibrium constant, K, expression for: O_2 + S_8 ⟶ SO_3 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: 12 O_2 + S_8 ⟶ 8 SO_3 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 | 12 | -12 S_8 | 1 | -1 SO_3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 12 | -12 | ([O2])^(-12) S_8 | 1 | -1 | ([S8])^(-1) SO_3 | 8 | 8 | ([SO3])^8 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])^(-12) ([S8])^(-1) ([SO3])^8 = ([SO3])^8/(([O2])^12 [S8])

Construct the rate of reaction expression for: O_2 + S_8 ⟶ SO_3 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: 12 O_2 + S_8 ⟶ 8 SO_3 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 | 12 | -12 S_8 | 1 | -1 SO_3 | 8 | 8 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 | 12 | -12 | -1/12 (Δ[O2])/(Δt) S_8 | 1 | -1 | -(Δ[S8])/(Δt) SO_3 | 8 | 8 | 1/8 (Δ[SO3])/(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 = -1/12 (Δ[O2])/(Δt) = -(Δ[S8])/(Δt) = 1/8 (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | rhombic sulfur | sulfur trioxide formula | O_2 | S_8 | SO_3 Hill formula | O_2 | S_8 | O_3S name | oxygen | rhombic sulfur | sulfur trioxide IUPAC name | molecular oxygen | octathiocane | sulfur trioxide

| oxygen | rhombic sulfur | sulfur trioxide molar mass | 31.998 g/mol | 256.5 g/mol | 80.06 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) melting point | -218 °C | | 16.8 °C boiling point | -183 °C | | 44.7 °C density | 0.001429 g/cm^3 (at 0 °C) | 2.07 g/cm^3 | 1.97 g/cm^3 solubility in water | | | reacts surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) odor | odorless | |