HCl + HClO2 = H2O + Cl2

HCl hydrogen chloride + HClO2 ⟶ H_2O water + Cl_2 chlorine

Balance the chemical equation algebraically: HCl + HClO2 ⟶ H_2O + Cl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HClO2 ⟶ c_3 H_2O + c_4 Cl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and O: Cl: | c_1 + c_2 = 2 c_4 H: | c_1 + c_2 = 2 c_3 O: | 2 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 = 3 c_2 = 1 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 HCl + HClO2 ⟶ 2 H_2O + 2 Cl_2

+ HClO2 ⟶ +

hydrogen chloride + HClO2 ⟶ water + chlorine

Construct the equilibrium constant, K, expression for: HCl + HClO2 ⟶ H_2O + 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: 3 HCl + HClO2 ⟶ 2 H_2O + 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 HCl | 3 | -3 HClO2 | 1 | -1 H_2O | 2 | 2 Cl_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 3 | -3 | ([HCl])^(-3) HClO2 | 1 | -1 | ([HClO2])^(-1) H_2O | 2 | 2 | ([H2O])^2 Cl_2 | 2 | 2 | ([Cl2])^2 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 = ([HCl])^(-3) ([HClO2])^(-1) ([H2O])^2 ([Cl2])^2 = (([H2O])^2 ([Cl2])^2)/(([HCl])^3 [HClO2])

Construct the rate of reaction expression for: HCl + HClO2 ⟶ H_2O + 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: 3 HCl + HClO2 ⟶ 2 H_2O + 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 HCl | 3 | -3 HClO2 | 1 | -1 H_2O | 2 | 2 Cl_2 | 2 | 2 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 HCl | 3 | -3 | -1/3 (Δ[HCl])/(Δt) HClO2 | 1 | -1 | -(Δ[HClO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) Cl_2 | 2 | 2 | 1/2 (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 = -1/3 (Δ[HCl])/(Δt) = -(Δ[HClO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[Cl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | HClO2 | water | chlorine formula | HCl | HClO2 | H_2O | Cl_2 Hill formula | ClH | HClO2 | H_2O | Cl_2 name | hydrogen chloride | | water | chlorine IUPAC name | hydrogen chloride | | water | molecular chlorine

| hydrogen chloride | HClO2 | water | chlorine molar mass | 36.46 g/mol | 68.46 g/mol | 18.015 g/mol | 70.9 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) melting point | -114.17 °C | | 0 °C | -101 °C boiling point | -85 °C | | 99.9839 °C | -34 °C density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) solubility in water | miscible | | | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |