SO2 + O3 = SO3

SO_2 sulfur dioxide + O_3 ozone ⟶ SO_3 sulfur trioxide

Balance the chemical equation algebraically: SO_2 + O_3 ⟶ SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 O_3 ⟶ 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_2 = 3 c_3 S: | c_1 = 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 = 3 c_2 = 1 c_3 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SO_2 + O_3 ⟶ 3 SO_3

+ ⟶

sulfur dioxide + ozone ⟶ sulfur trioxide

| sulfur dioxide | ozone | sulfur trioxide molecular free energy | -300.1 kJ/mol | 163.2 kJ/mol | -373.8 kJ/mol total free energy | -900.3 kJ/mol | 163.2 kJ/mol | -1121 kJ/mol | G_initial = -737.1 kJ/mol | | G_final = -1121 kJ/mol ΔG_rxn^0 | -1121 kJ/mol - -737.1 kJ/mol = -384.3 kJ/mol (exergonic) | |

Construct the equilibrium constant, K, expression for: SO_2 + O_3 ⟶ 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: 3 SO_2 + O_3 ⟶ 3 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 SO_2 | 3 | -3 O_3 | 1 | -1 SO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 3 | -3 | ([SO2])^(-3) O_3 | 1 | -1 | ([O3])^(-1) SO_3 | 3 | 3 | ([SO3])^3 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 = ([SO2])^(-3) ([O3])^(-1) ([SO3])^3 = ([SO3])^3/(([SO2])^3 [O3])

Construct the rate of reaction expression for: SO_2 + O_3 ⟶ 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: 3 SO_2 + O_3 ⟶ 3 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 SO_2 | 3 | -3 O_3 | 1 | -1 SO_3 | 3 | 3 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 SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) O_3 | 1 | -1 | -(Δ[O3])/(Δt) SO_3 | 3 | 3 | 1/3 (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 = -1/3 (Δ[SO2])/(Δt) = -(Δ[O3])/(Δt) = 1/3 (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | ozone | sulfur trioxide formula | SO_2 | O_3 | SO_3 Hill formula | O_2S | O_3 | O_3S name | sulfur dioxide | ozone | sulfur trioxide

| sulfur dioxide | ozone | sulfur trioxide molar mass | 64.06 g/mol | 47.997 g/mol | 80.06 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) melting point | -73 °C | -192.2 °C | 16.8 °C boiling point | -10 °C | -111.9 °C | 44.7 °C density | 0.002619 g/cm^3 (at 25 °C) | 0.001962 g/cm^3 (at 25 °C) | 1.97 g/cm^3 solubility in water | | | reacts surface tension | 0.02859 N/m | | dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C)