NaOH + Br2 + Na2SeO3 = H2O + NaBr + Na2SeO4

NaOH sodium hydroxide + Br_2 bromine + Na_2SeO_3 sodium selenite ⟶ H_2O water + NaBr sodium bromide + Na_2SeO_4 sodium selenate

Balance the chemical equation algebraically: NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + NaBr + Na_2SeO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 Na_2SeO_3 ⟶ c_4 H_2O + c_5 NaBr + c_6 Na_2SeO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br and Se: H: | c_1 = 2 c_4 Na: | c_1 + 2 c_3 = c_5 + 2 c_6 O: | c_1 + 3 c_3 = c_4 + 4 c_6 Br: | 2 c_2 = c_5 Se: | c_3 = c_6 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 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + 2 NaBr + Na_2SeO_4

+ + ⟶ + +

sodium hydroxide + bromine + sodium selenite ⟶ water + sodium bromide + sodium selenate

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + NaBr + Na_2SeO_4 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 NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + 2 NaBr + Na_2SeO_4 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 NaOH | 2 | -2 Br_2 | 1 | -1 Na_2SeO_3 | 1 | -1 H_2O | 1 | 1 NaBr | 2 | 2 Na_2SeO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) Br_2 | 1 | -1 | ([Br2])^(-1) Na_2SeO_3 | 1 | -1 | ([Na2SeO3])^(-1) H_2O | 1 | 1 | [H2O] NaBr | 2 | 2 | ([NaBr])^2 Na_2SeO_4 | 1 | 1 | [Na2SeO4] 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 = ([NaOH])^(-2) ([Br2])^(-1) ([Na2SeO3])^(-1) [H2O] ([NaBr])^2 [Na2SeO4] = ([H2O] ([NaBr])^2 [Na2SeO4])/(([NaOH])^2 [Br2] [Na2SeO3])

Construct the rate of reaction expression for: NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + NaBr + Na_2SeO_4 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 NaOH + Br_2 + Na_2SeO_3 ⟶ H_2O + 2 NaBr + Na_2SeO_4 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 NaOH | 2 | -2 Br_2 | 1 | -1 Na_2SeO_3 | 1 | -1 H_2O | 1 | 1 NaBr | 2 | 2 Na_2SeO_4 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) Na_2SeO_3 | 1 | -1 | -(Δ[Na2SeO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(Δt) Na_2SeO_4 | 1 | 1 | (Δ[Na2SeO4])/(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[NaOH])/(Δt) = -(Δ[Br2])/(Δt) = -(Δ[Na2SeO3])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[NaBr])/(Δt) = (Δ[Na2SeO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | bromine | sodium selenite | water | sodium bromide | sodium selenate formula | NaOH | Br_2 | Na_2SeO_3 | H_2O | NaBr | Na_2SeO_4 Hill formula | HNaO | Br_2 | Na_2O_3Se | H_2O | BrNa | Na_2O_4Se_1 name | sodium hydroxide | bromine | sodium selenite | water | sodium bromide | sodium selenate IUPAC name | sodium hydroxide | molecular bromine | | water | sodium bromide |