H2O + Br2 + Sb = HBr + H3SbO3

H_2O water + Br_2 bromine + Sb gray antimony ⟶ HBr hydrogen bromide + H3SbO3

Balance the chemical equation algebraically: H_2O + Br_2 + Sb ⟶ HBr + H3SbO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Br_2 + c_3 Sb ⟶ c_4 HBr + c_5 H3SbO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br and Sb: H: | 2 c_1 = c_4 + 3 c_5 O: | c_1 = 3 c_5 Br: | 2 c_2 = c_4 Sb: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3/2 c_3 = 1 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 3 c_3 = 2 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + 3 Br_2 + 2 Sb ⟶ 6 HBr + 2 H3SbO3

+ + ⟶ + H3SbO3

water + bromine + gray antimony ⟶ hydrogen bromide + H3SbO3

Construct the equilibrium constant, K, expression for: H_2O + Br_2 + Sb ⟶ HBr + H3SbO3 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: 6 H_2O + 3 Br_2 + 2 Sb ⟶ 6 HBr + 2 H3SbO3 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 | 6 | -6 Br_2 | 3 | -3 Sb | 2 | -2 HBr | 6 | 6 H3SbO3 | 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 | 6 | -6 | ([H2O])^(-6) Br_2 | 3 | -3 | ([Br2])^(-3) Sb | 2 | -2 | ([Sb])^(-2) HBr | 6 | 6 | ([HBr])^6 H3SbO3 | 2 | 2 | ([H3SbO3])^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])^(-6) ([Br2])^(-3) ([Sb])^(-2) ([HBr])^6 ([H3SbO3])^2 = (([HBr])^6 ([H3SbO3])^2)/(([H2O])^6 ([Br2])^3 ([Sb])^2)

Construct the rate of reaction expression for: H_2O + Br_2 + Sb ⟶ HBr + H3SbO3 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: 6 H_2O + 3 Br_2 + 2 Sb ⟶ 6 HBr + 2 H3SbO3 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 | 6 | -6 Br_2 | 3 | -3 Sb | 2 | -2 HBr | 6 | 6 H3SbO3 | 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 | 6 | -6 | -1/6 (Δ[H2O])/(Δt) Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) Sb | 2 | -2 | -1/2 (Δ[Sb])/(Δt) HBr | 6 | 6 | 1/6 (Δ[HBr])/(Δt) H3SbO3 | 2 | 2 | 1/2 (Δ[H3SbO3])/(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 = -1/6 (Δ[H2O])/(Δt) = -1/3 (Δ[Br2])/(Δt) = -1/2 (Δ[Sb])/(Δt) = 1/6 (Δ[HBr])/(Δt) = 1/2 (Δ[H3SbO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromine | gray antimony | hydrogen bromide | H3SbO3 formula | H_2O | Br_2 | Sb | HBr | H3SbO3 Hill formula | H_2O | Br_2 | Sb | BrH | H3O3Sb name | water | bromine | gray antimony | hydrogen bromide | IUPAC name | water | molecular bromine | antimony | hydrogen bromide |

| water | bromine | gray antimony | hydrogen bromide | H3SbO3 molar mass | 18.015 g/mol | 159.81 g/mol | 121.76 g/mol | 80.912 g/mol | 172.78 g/mol phase | liquid (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | -7.2 °C | 630 °C | -86.8 °C | boiling point | 99.9839 °C | 58.8 °C | 1587 °C | -66.38 °C | density | 1 g/cm^3 | 3.119 g/cm^3 | 6.69 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 | | | |