H2O + Br2 = HBr + HBrO3

H_2O water + Br_2 bromine ⟶ HBr hydrogen bromide + HO_3Br bromic acid

Balance the chemical equation algebraically: H_2O + Br_2 ⟶ HBr + HO_3Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Br_2 ⟶ c_3 HBr + c_4 HO_3Br Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Br: H: | 2 c_1 = c_3 + c_4 O: | c_1 = 3 c_4 Br: | 2 c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 5 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 3 Br_2 ⟶ 5 HBr + HO_3Br

+ ⟶ +

water + bromine ⟶ hydrogen bromide + bromic acid

Construct the equilibrium constant, K, expression for: H_2O + Br_2 ⟶ HBr + HO_3Br 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 + 3 Br_2 ⟶ 5 HBr + HO_3Br 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 | 3 | -3 Br_2 | 3 | -3 HBr | 5 | 5 HO_3Br | 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 | 3 | -3 | ([H2O])^(-3) Br_2 | 3 | -3 | ([Br2])^(-3) HBr | 5 | 5 | ([HBr])^5 HO_3Br | 1 | 1 | [H1O3Br1] 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])^(-3) ([Br2])^(-3) ([HBr])^5 [H1O3Br1] = (([HBr])^5 [H1O3Br1])/(([H2O])^3 ([Br2])^3)

Construct the rate of reaction expression for: H_2O + Br_2 ⟶ HBr + HO_3Br 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 + 3 Br_2 ⟶ 5 HBr + HO_3Br 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 | 3 | -3 Br_2 | 3 | -3 HBr | 5 | 5 HO_3Br | 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 | 3 | -3 | -1/3 (Δ[H2O])/(Δt) Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) HBr | 5 | 5 | 1/5 (Δ[HBr])/(Δt) HO_3Br | 1 | 1 | (Δ[H1O3Br1])/(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[H2O])/(Δt) = -1/3 (Δ[Br2])/(Δt) = 1/5 (Δ[HBr])/(Δt) = (Δ[H1O3Br1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromine | hydrogen bromide | bromic acid formula | H_2O | Br_2 | HBr | HO_3Br Hill formula | H_2O | Br_2 | BrH | BrHO_3 name | water | bromine | hydrogen bromide | bromic acid IUPAC name | water | molecular bromine | hydrogen bromide | bromic acid

| water | bromine | hydrogen bromide | bromic acid molar mass | 18.015 g/mol | 159.81 g/mol | 80.912 g/mol | 128.91 g/mol phase | liquid (at STP) | liquid (at STP) | gas (at STP) | melting point | 0 °C | -7.2 °C | -86.8 °C | boiling point | 99.9839 °C | 58.8 °C | -66.38 °C | density | 1 g/cm^3 | 3.119 g/cm^3 | 0.003307 g/cm^3 (at 25 °C) | solubility in water | | insoluble | miscible | surface tension | 0.0728 N/m | 0.0409 N/m | 0.0271 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 9.44×10^-4 Pa s (at 25 °C) | 8.4×10^-4 Pa s (at -75 °C) | odor | odorless | | |