H2O + Br2 + K2SO3 = K2SO4 + HBr

H_2O water + Br_2 bromine + K_2SO_3 potassium sulfite ⟶ K_2SO_4 potassium sulfate + HBr hydrogen bromide

Balance the chemical equation algebraically: H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + HBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Br_2 + c_3 K_2SO_3 ⟶ c_4 K_2SO_4 + c_5 HBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br, K and S: H: | 2 c_1 = c_5 O: | c_1 + 3 c_3 = 4 c_4 Br: | 2 c_2 = c_5 K: | 2 c_3 = 2 c_4 S: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + 2 HBr

+ + ⟶ +

water + bromine + potassium sulfite ⟶ potassium sulfate + hydrogen bromide

Construct the equilibrium constant, K, expression for: H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + HBr 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: H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + 2 HBr 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 | 1 | -1 Br_2 | 1 | -1 K_2SO_3 | 1 | -1 K_2SO_4 | 1 | 1 HBr | 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 | 1 | -1 | ([H2O])^(-1) Br_2 | 1 | -1 | ([Br2])^(-1) K_2SO_3 | 1 | -1 | ([K2SO3])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] HBr | 2 | 2 | ([HBr])^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])^(-1) ([Br2])^(-1) ([K2SO3])^(-1) [K2SO4] ([HBr])^2 = ([K2SO4] ([HBr])^2)/([H2O] [Br2] [K2SO3])

Construct the rate of reaction expression for: H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + HBr 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: H_2O + Br_2 + K_2SO_3 ⟶ K_2SO_4 + 2 HBr 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 | 1 | -1 Br_2 | 1 | -1 K_2SO_3 | 1 | -1 K_2SO_4 | 1 | 1 HBr | 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 | 1 | -1 | -(Δ[H2O])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) K_2SO_3 | 1 | -1 | -(Δ[K2SO3])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) HBr | 2 | 2 | 1/2 (Δ[HBr])/(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 = -(Δ[H2O])/(Δt) = -(Δ[Br2])/(Δt) = -(Δ[K2SO3])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[HBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromine | potassium sulfite | potassium sulfate | hydrogen bromide formula | H_2O | Br_2 | K_2SO_3 | K_2SO_4 | HBr Hill formula | H_2O | Br_2 | K_2O_3S | K_2O_4S | BrH name | water | bromine | potassium sulfite | potassium sulfate | hydrogen bromide IUPAC name | water | molecular bromine | dipotassium sulfite | dipotassium sulfate | hydrogen bromide