H2O2 + HClO2 = H2O + O2 + Cl2

H_2O_2 hydrogen peroxide + HClO2 ⟶ H_2O water + O_2 oxygen + Cl_2 chlorine

Balance the chemical equation algebraically: H_2O_2 + HClO2 ⟶ H_2O + O_2 + Cl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 HClO2 ⟶ c_3 H_2O + c_4 O_2 + c_5 Cl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Cl: H: | 2 c_1 + c_2 = 2 c_3 O: | 2 c_1 + 2 c_2 = c_3 + 2 c_4 Cl: | c_2 = 2 c_5 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_3 = c_2/2 + 1 c_4 = (3 c_2)/4 + 1/2 c_5 = c_2/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 2 and solve for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O_2 + 2 HClO2 ⟶ 2 H_2O + 2 O_2 + Cl_2

+ HClO2 ⟶ + +

hydrogen peroxide + HClO2 ⟶ water + oxygen + chlorine

Construct the equilibrium constant, K, expression for: H_2O_2 + HClO2 ⟶ H_2O + O_2 + Cl_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: H_2O_2 + 2 HClO2 ⟶ 2 H_2O + 2 O_2 + Cl_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 | 1 | -1 HClO2 | 2 | -2 H_2O | 2 | 2 O_2 | 2 | 2 Cl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O_2 | 1 | -1 | ([H2O2])^(-1) HClO2 | 2 | -2 | ([HClO2])^(-2) H_2O | 2 | 2 | ([H2O])^2 O_2 | 2 | 2 | ([O2])^2 Cl_2 | 1 | 1 | [Cl2] 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])^(-1) ([HClO2])^(-2) ([H2O])^2 ([O2])^2 [Cl2] = (([H2O])^2 ([O2])^2 [Cl2])/([H2O2] ([HClO2])^2)

Construct the rate of reaction expression for: H_2O_2 + HClO2 ⟶ H_2O + O_2 + Cl_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: H_2O_2 + 2 HClO2 ⟶ 2 H_2O + 2 O_2 + Cl_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 | 1 | -1 HClO2 | 2 | -2 H_2O | 2 | 2 O_2 | 2 | 2 Cl_2 | 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 H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) HClO2 | 2 | -2 | -1/2 (Δ[HClO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(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[H2O2])/(Δt) = -1/2 (Δ[HClO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[Cl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | HClO2 | water | oxygen | chlorine formula | H_2O_2 | HClO2 | H_2O | O_2 | Cl_2 name | hydrogen peroxide | | water | oxygen | chlorine IUPAC name | hydrogen peroxide | | water | molecular oxygen | molecular chlorine

| hydrogen peroxide | HClO2 | water | oxygen | chlorine molar mass | 34.014 g/mol | 68.46 g/mol | 18.015 g/mol | 31.998 g/mol | 70.9 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | gas (at STP) melting point | -0.43 °C | | 0 °C | -218 °C | -101 °C boiling point | 150.2 °C | | 99.9839 °C | -183 °C | -34 °C density | 1.44 g/cm^3 | | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.003214 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 |