H2O + Br2 + Na2S2O3 = H2SO4 + S + NaBr

H_2O water + Br_2 bromine + Na_2S_2O_3 sodium hyposulfite ⟶ H_2SO_4 sulfuric acid + S mixed sulfur + NaBr sodium bromide

Balance the chemical equation algebraically: H_2O + Br_2 + Na_2S_2O_3 ⟶ H_2SO_4 + S + NaBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Br_2 + c_3 Na_2S_2O_3 ⟶ c_4 H_2SO_4 + c_5 S + c_6 NaBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br, Na and S: H: | 2 c_1 = 2 c_4 O: | c_1 + 3 c_3 = 4 c_4 Br: | 2 c_2 = c_6 Na: | 2 c_3 = c_6 S: | 2 c_3 = c_4 + 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_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 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + Br_2 + Na_2S_2O_3 ⟶ H_2SO_4 + S + 2 NaBr

+ + ⟶ + +

water + bromine + sodium hyposulfite ⟶ sulfuric acid + mixed sulfur + sodium bromide

Construct the equilibrium constant, K, expression for: H_2O + Br_2 + Na_2S_2O_3 ⟶ H_2SO_4 + S + NaBr 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 + Na_2S_2O_3 ⟶ H_2SO_4 + S + 2 NaBr 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 Na_2S_2O_3 | 1 | -1 H_2SO_4 | 1 | 1 S | 1 | 1 NaBr | 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) Na_2S_2O_3 | 1 | -1 | ([Na2S2O3])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] S | 1 | 1 | [S] NaBr | 2 | 2 | ([NaBr])^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) ([Na2S2O3])^(-1) [H2SO4] [S] ([NaBr])^2 = ([H2SO4] [S] ([NaBr])^2)/([H2O] [Br2] [Na2S2O3])

Construct the rate of reaction expression for: H_2O + Br_2 + Na_2S_2O_3 ⟶ H_2SO_4 + S + NaBr 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 + Na_2S_2O_3 ⟶ H_2SO_4 + S + 2 NaBr 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 Na_2S_2O_3 | 1 | -1 H_2SO_4 | 1 | 1 S | 1 | 1 NaBr | 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) Na_2S_2O_3 | 1 | -1 | -(Δ[Na2S2O3])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(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[Na2S2O3])/(Δt) = (Δ[H2SO4])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[NaBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | bromine | sodium hyposulfite | sulfuric acid | mixed sulfur | sodium bromide formula | H_2O | Br_2 | Na_2S_2O_3 | H_2SO_4 | S | NaBr Hill formula | H_2O | Br_2 | Na_2O_3S_2 | H_2O_4S | S | BrNa name | water | bromine | sodium hyposulfite | sulfuric acid | mixed sulfur | sodium bromide IUPAC name | water | molecular bromine | | sulfuric acid | sulfur | sodium bromide