HBr + SO3 = H2O + SO2 + Br2

HBr hydrogen bromide + SO_3 sulfur trioxide ⟶ H_2O water + SO_2 sulfur dioxide + Br_2 bromine

Balance the chemical equation algebraically: HBr + SO_3 ⟶ H_2O + SO_2 + Br_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HBr + c_2 SO_3 ⟶ c_3 H_2O + c_4 SO_2 + c_5 Br_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Br, H, O and S: Br: | c_1 = 2 c_5 H: | c_1 = 2 c_3 O: | 3 c_2 = c_3 + 2 c_4 S: | c_2 = 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 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HBr + SO_3 ⟶ H_2O + SO_2 + Br_2

+ ⟶ + +

hydrogen bromide + sulfur trioxide ⟶ water + sulfur dioxide + bromine

| hydrogen bromide | sulfur trioxide | water | sulfur dioxide | bromine molecular free energy | -53.4 kJ/mol | -373.8 kJ/mol | -237.1 kJ/mol | -300.1 kJ/mol | 0 kJ/mol total free energy | -106.8 kJ/mol | -373.8 kJ/mol | -237.1 kJ/mol | -300.1 kJ/mol | 0 kJ/mol | G_initial = -480.6 kJ/mol | | G_final = -537.2 kJ/mol | | ΔG_rxn^0 | -537.2 kJ/mol - -480.6 kJ/mol = -56.6 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: HBr + SO_3 ⟶ H_2O + SO_2 + 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: 2 HBr + SO_3 ⟶ H_2O + SO_2 + 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 HBr | 2 | -2 SO_3 | 1 | -1 H_2O | 1 | 1 SO_2 | 1 | 1 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 HBr | 2 | -2 | ([HBr])^(-2) SO_3 | 1 | -1 | ([SO3])^(-1) H_2O | 1 | 1 | [H2O] SO_2 | 1 | 1 | [SO2] 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 = ([HBr])^(-2) ([SO3])^(-1) [H2O] [SO2] [Br2] = ([H2O] [SO2] [Br2])/(([HBr])^2 [SO3])

Construct the rate of reaction expression for: HBr + SO_3 ⟶ H_2O + SO_2 + 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: 2 HBr + SO_3 ⟶ H_2O + SO_2 + 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 HBr | 2 | -2 SO_3 | 1 | -1 H_2O | 1 | 1 SO_2 | 1 | 1 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 HBr | 2 | -2 | -1/2 (Δ[HBr])/(Δt) SO_3 | 1 | -1 | -(Δ[SO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(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 = -1/2 (Δ[HBr])/(Δt) = -(Δ[SO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[SO2])/(Δt) = (Δ[Br2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen bromide | sulfur trioxide | water | sulfur dioxide | bromine formula | HBr | SO_3 | H_2O | SO_2 | Br_2 Hill formula | BrH | O_3S | H_2O | O_2S | Br_2 name | hydrogen bromide | sulfur trioxide | water | sulfur dioxide | bromine IUPAC name | hydrogen bromide | sulfur trioxide | water | sulfur dioxide | molecular bromine