SO2 + H2O2 = H2SO4

SO_2 sulfur dioxide + H_2O_2 hydrogen peroxide ⟶ H_2SO_4 sulfuric acid

Balance the chemical equation algebraically: SO_2 + H_2O_2 ⟶ H_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 H_2O_2 ⟶ c_3 H_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and H: O: | 2 c_1 + 2 c_2 = 4 c_3 S: | c_1 = c_3 H: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | SO_2 + H_2O_2 ⟶ H_2SO_4

+ ⟶

sulfur dioxide + hydrogen peroxide ⟶ sulfuric acid

| sulfur dioxide | hydrogen peroxide | sulfuric acid molecular free energy | -300.1 kJ/mol | -120.4 kJ/mol | -690 kJ/mol total free energy | -300.1 kJ/mol | -120.4 kJ/mol | -690 kJ/mol | G_initial = -420.5 kJ/mol | | G_final = -690 kJ/mol ΔG_rxn^0 | -690 kJ/mol - -420.5 kJ/mol = -269.5 kJ/mol (exergonic) | |

Construct the equilibrium constant, K, expression for: SO_2 + H_2O_2 ⟶ H_2SO_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: SO_2 + H_2O_2 ⟶ H_2SO_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 SO_2 | 1 | -1 H_2O_2 | 1 | -1 H_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 1 | -1 | ([SO2])^(-1) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] 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])^(-1) ([H2O2])^(-1) [H2SO4] = ([H2SO4])/([SO2] [H2O2])

Construct the rate of reaction expression for: SO_2 + H_2O_2 ⟶ H_2SO_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: SO_2 + H_2O_2 ⟶ H_2SO_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 SO_2 | 1 | -1 H_2O_2 | 1 | -1 H_2SO_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 SO_2 | 1 | -1 | -(Δ[SO2])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(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 = -(Δ[SO2])/(Δt) = -(Δ[H2O2])/(Δt) = (Δ[H2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | hydrogen peroxide | sulfuric acid formula | SO_2 | H_2O_2 | H_2SO_4 Hill formula | O_2S | H_2O_2 | H_2O_4S name | sulfur dioxide | hydrogen peroxide | sulfuric acid

| sulfur dioxide | hydrogen peroxide | sulfuric acid molar mass | 64.06 g/mol | 34.014 g/mol | 98.07 g/mol phase | gas (at STP) | liquid (at STP) | liquid (at STP) melting point | -73 °C | -0.43 °C | 10.371 °C boiling point | -10 °C | 150.2 °C | 279.6 °C density | 0.002619 g/cm^3 (at 25 °C) | 1.44 g/cm^3 | 1.8305 g/cm^3 solubility in water | | miscible | very soluble surface tension | 0.02859 N/m | 0.0804 N/m | 0.0735 N/m dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | 0.001249 Pa s (at 20 °C) | 0.021 Pa s (at 25 °C) odor | | | odorless