H2S + HBrO4 = H2O + S + Br2

H_2S hydrogen sulfide + HBrO4 ⟶ H_2O water + S mixed sulfur + Br_2 bromine

Balance the chemical equation algebraically: H_2S + HBrO4 ⟶ H_2O + S + Br_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 HBrO4 ⟶ c_3 H_2O + c_4 S + c_5 Br_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Br and O: H: | 2 c_1 + c_2 = 2 c_3 S: | c_1 = c_4 Br: | c_2 = 2 c_5 O: | 4 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 2 c_3 = 8 c_4 = 7 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 H_2S + 2 HBrO4 ⟶ 8 H_2O + 7 S + Br_2

+ HBrO4 ⟶ + +

hydrogen sulfide + HBrO4 ⟶ water + mixed sulfur + bromine

Construct the equilibrium constant, K, expression for: H_2S + HBrO4 ⟶ H_2O + S + Br_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: 7 H_2S + 2 HBrO4 ⟶ 8 H_2O + 7 S + Br_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_2S | 7 | -7 HBrO4 | 2 | -2 H_2O | 8 | 8 S | 7 | 7 Br_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_2S | 7 | -7 | ([H2S])^(-7) HBrO4 | 2 | -2 | ([HBrO4])^(-2) H_2O | 8 | 8 | ([H2O])^8 S | 7 | 7 | ([S])^7 Br_2 | 1 | 1 | [Br2] 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 = ([H2S])^(-7) ([HBrO4])^(-2) ([H2O])^8 ([S])^7 [Br2] = (([H2O])^8 ([S])^7 [Br2])/(([H2S])^7 ([HBrO4])^2)

Construct the rate of reaction expression for: H_2S + HBrO4 ⟶ H_2O + S + Br_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: 7 H_2S + 2 HBrO4 ⟶ 8 H_2O + 7 S + Br_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_2S | 7 | -7 HBrO4 | 2 | -2 H_2O | 8 | 8 S | 7 | 7 Br_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_2S | 7 | -7 | -1/7 (Δ[H2S])/(Δt) HBrO4 | 2 | -2 | -1/2 (Δ[HBrO4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) S | 7 | 7 | 1/7 (Δ[S])/(Δt) Br_2 | 1 | 1 | (Δ[Br2])/(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 = -1/7 (Δ[H2S])/(Δt) = -1/2 (Δ[HBrO4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/7 (Δ[S])/(Δt) = (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | HBrO4 | water | mixed sulfur | bromine formula | H_2S | HBrO4 | H_2O | S | Br_2 name | hydrogen sulfide | | water | mixed sulfur | bromine IUPAC name | hydrogen sulfide | | water | sulfur | molecular bromine

| hydrogen sulfide | HBrO4 | water | mixed sulfur | bromine molar mass | 34.08 g/mol | 144.91 g/mol | 18.015 g/mol | 32.06 g/mol | 159.81 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) | liquid (at STP) melting point | -85 °C | | 0 °C | 112.8 °C | -7.2 °C boiling point | -60 °C | | 99.9839 °C | 444.7 °C | 58.8 °C density | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 2.07 g/cm^3 | 3.119 g/cm^3 solubility in water | | | | | insoluble surface tension | | | 0.0728 N/m | | 0.0409 N/m dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 9.44×10^-4 Pa s (at 25 °C) odor | | | odorless | |