H2O + Br2 + HClO = HCl + H2BrO3

H_2O water + Br_2 bromine + HOCl hypochlorous acid ⟶ HCl hydrogen chloride + H2BrO3

Balance the chemical equation algebraically: H_2O + Br_2 + HOCl ⟶ HCl + H2BrO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Br_2 + c_3 HOCl ⟶ c_4 HCl + c_5 H2BrO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br and Cl: H: | 2 c_1 + c_3 = c_4 + 2 c_5 O: | c_1 + c_3 = 3 c_5 Br: | 2 c_2 = c_5 Cl: | c_3 = 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_1 = 2 c_2 = 1 c_3 = 4 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + Br_2 + 4 HOCl ⟶ 4 HCl + 2 H2BrO3

+ + ⟶ + H2BrO3

water + bromine + hypochlorous acid ⟶ hydrogen chloride + H2BrO3

Construct the equilibrium constant, K, expression for: H_2O + Br_2 + HOCl ⟶ HCl + H2BrO3 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: 2 H_2O + Br_2 + 4 HOCl ⟶ 4 HCl + 2 H2BrO3 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 | -2 Br_2 | 1 | -1 HOCl | 4 | -4 HCl | 4 | 4 H2BrO3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) Br_2 | 1 | -1 | ([Br2])^(-1) HOCl | 4 | -4 | ([HOCl])^(-4) HCl | 4 | 4 | ([HCl])^4 H2BrO3 | 2 | 2 | ([H2BrO3])^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 = ([H2O])^(-2) ([Br2])^(-1) ([HOCl])^(-4) ([HCl])^4 ([H2BrO3])^2 = (([HCl])^4 ([H2BrO3])^2)/(([H2O])^2 [Br2] ([HOCl])^4)

Construct the rate of reaction expression for: H_2O + Br_2 + HOCl ⟶ HCl + H2BrO3 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: 2 H_2O + Br_2 + 4 HOCl ⟶ 4 HCl + 2 H2BrO3 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 | -2 Br_2 | 1 | -1 HOCl | 4 | -4 HCl | 4 | 4 H2BrO3 | 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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) HOCl | 4 | -4 | -1/4 (Δ[HOCl])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(Δt) H2BrO3 | 2 | 2 | 1/2 (Δ[H2BrO3])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[Br2])/(Δt) = -1/4 (Δ[HOCl])/(Δt) = 1/4 (Δ[HCl])/(Δt) = 1/2 (Δ[H2BrO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromine | hypochlorous acid | hydrogen chloride | H2BrO3 formula | H_2O | Br_2 | HOCl | HCl | H2BrO3 Hill formula | H_2O | Br_2 | ClHO | ClH | H2BrO3 name | water | bromine | hypochlorous acid | hydrogen chloride | IUPAC name | water | molecular bromine | hypochlorous acid | hydrogen chloride |

| water | bromine | hypochlorous acid | hydrogen chloride | H2BrO3 molar mass | 18.015 g/mol | 159.81 g/mol | 52.46 g/mol | 36.46 g/mol | 129.92 g/mol phase | liquid (at STP) | liquid (at STP) | | gas (at STP) | melting point | 0 °C | -7.2 °C | | -114.17 °C | boiling point | 99.9839 °C | 58.8 °C | | -85 °C | density | 1 g/cm^3 | 3.119 g/cm^3 | | 0.00149 g/cm^3 (at 25 °C) | solubility in water | | insoluble | soluble | miscible | surface tension | 0.0728 N/m | 0.0409 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 9.44×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | |