H2O2 + O3 = H2O + O2

H_2O_2 hydrogen peroxide + O_3 ozone ⟶ H_2O water + O_2 oxygen

Balance the chemical equation algebraically: H_2O_2 + O_3 ⟶ H_2O + O_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 O_3 ⟶ c_3 H_2O + c_4 O_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H and O: H: | 2 c_1 = 2 c_3 O: | 2 c_1 + 3 c_2 = c_3 + 2 c_4 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_2 = 1 c_3 = c_1 c_4 = c_1/2 + 3/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O_2 + O_3 ⟶ 3 H_2O + 3 O_2

+ ⟶ +

hydrogen peroxide + ozone ⟶ water + oxygen

| hydrogen peroxide | ozone | water | oxygen molecular free energy | -120.4 kJ/mol | 163.2 kJ/mol | -237.1 kJ/mol | 231.7 kJ/mol total free energy | -361.2 kJ/mol | 163.2 kJ/mol | -711.3 kJ/mol | 695.1 kJ/mol | G_initial = -198 kJ/mol | | G_final = -16.2 kJ/mol | ΔG_rxn^0 | -16.2 kJ/mol - -198 kJ/mol = 181.8 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: H_2O_2 + O_3 ⟶ H_2O + O_2 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 H_2O_2 + O_3 ⟶ 3 H_2O + 3 O_2 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 H_2O_2 | 3 | -3 O_3 | 1 | -1 H_2O | 3 | 3 O_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O_2 | 3 | -3 | ([H2O2])^(-3) O_3 | 1 | -1 | ([O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 O_2 | 3 | 3 | ([O2])^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 = ([H2O2])^(-3) ([O3])^(-1) ([H2O])^3 ([O2])^3 = (([H2O])^3 ([O2])^3)/(([H2O2])^3 [O3])

Construct the rate of reaction expression for: H_2O_2 + O_3 ⟶ H_2O + O_2 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 H_2O_2 + O_3 ⟶ 3 H_2O + 3 O_2 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 H_2O_2 | 3 | -3 O_3 | 1 | -1 H_2O | 3 | 3 O_2 | 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 H_2O_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) O_3 | 1 | -1 | -(Δ[O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) O_2 | 3 | 3 | 1/3 (Δ[O2])/(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[H2O2])/(Δt) = -(Δ[O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[O2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | ozone | water | oxygen formula | H_2O_2 | O_3 | H_2O | O_2 name | hydrogen peroxide | ozone | water | oxygen IUPAC name | hydrogen peroxide | ozone | water | molecular oxygen

| hydrogen peroxide | ozone | water | oxygen molar mass | 34.014 g/mol | 47.997 g/mol | 18.015 g/mol | 31.998 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | gas (at STP) melting point | -0.43 °C | -192.2 °C | 0 °C | -218 °C boiling point | 150.2 °C | -111.9 °C | 99.9839 °C | -183 °C density | 1.44 g/cm^3 | 0.001962 g/cm^3 (at 25 °C) | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) solubility in water | miscible | | | surface tension | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) odor | | | odorless | odorless