Mg(BrO3)2 + NaHS2O3 = H2O + NaBr + Na2S4O6 + MgS4O6

Mg(BrO3)2 + NaHS2O3 ⟶ H_2O water + NaBr sodium bromide + Na2S4O6 + MgS4O6

Balance the chemical equation algebraically: Mg(BrO3)2 + NaHS2O3 ⟶ H_2O + NaBr + Na2S4O6 + MgS4O6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg(BrO3)2 + c_2 NaHS2O3 ⟶ c_3 H_2O + c_4 NaBr + c_5 Na2S4O6 + c_6 MgS4O6 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Br, O, Na, H and S: Mg: | c_1 = c_6 Br: | 2 c_1 = c_4 O: | 6 c_1 + 3 c_2 = c_3 + 6 c_5 + 6 c_6 Na: | c_2 = c_4 + 2 c_5 H: | c_2 = 2 c_3 S: | 2 c_2 = 4 c_5 + 4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 12 c_3 = 6 c_4 = 2 c_5 = 5 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Mg(BrO3)2 + 12 NaHS2O3 ⟶ 6 H_2O + 2 NaBr + 5 Na2S4O6 + MgS4O6

Mg(BrO3)2 + NaHS2O3 ⟶ + + Na2S4O6 + MgS4O6

Mg(BrO3)2 + NaHS2O3 ⟶ water + sodium bromide + Na2S4O6 + MgS4O6

Construct the equilibrium constant, K, expression for: Mg(BrO3)2 + NaHS2O3 ⟶ H_2O + NaBr + Na2S4O6 + MgS4O6 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: Mg(BrO3)2 + 12 NaHS2O3 ⟶ 6 H_2O + 2 NaBr + 5 Na2S4O6 + MgS4O6 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 Mg(BrO3)2 | 1 | -1 NaHS2O3 | 12 | -12 H_2O | 6 | 6 NaBr | 2 | 2 Na2S4O6 | 5 | 5 MgS4O6 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg(BrO3)2 | 1 | -1 | ([Mg(BrO3)2])^(-1) NaHS2O3 | 12 | -12 | ([NaHS2O3])^(-12) H_2O | 6 | 6 | ([H2O])^6 NaBr | 2 | 2 | ([NaBr])^2 Na2S4O6 | 5 | 5 | ([Na2S4O6])^5 MgS4O6 | 1 | 1 | [MgS4O6] 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 = ([Mg(BrO3)2])^(-1) ([NaHS2O3])^(-12) ([H2O])^6 ([NaBr])^2 ([Na2S4O6])^5 [MgS4O6] = (([H2O])^6 ([NaBr])^2 ([Na2S4O6])^5 [MgS4O6])/([Mg(BrO3)2] ([NaHS2O3])^12)

Construct the rate of reaction expression for: Mg(BrO3)2 + NaHS2O3 ⟶ H_2O + NaBr + Na2S4O6 + MgS4O6 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: Mg(BrO3)2 + 12 NaHS2O3 ⟶ 6 H_2O + 2 NaBr + 5 Na2S4O6 + MgS4O6 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 Mg(BrO3)2 | 1 | -1 NaHS2O3 | 12 | -12 H_2O | 6 | 6 NaBr | 2 | 2 Na2S4O6 | 5 | 5 MgS4O6 | 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 Mg(BrO3)2 | 1 | -1 | -(Δ[Mg(BrO3)2])/(Δt) NaHS2O3 | 12 | -12 | -1/12 (Δ[NaHS2O3])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) NaBr | 2 | 2 | 1/2 (Δ[NaBr])/(Δt) Na2S4O6 | 5 | 5 | 1/5 (Δ[Na2S4O6])/(Δt) MgS4O6 | 1 | 1 | (Δ[MgS4O6])/(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[Mg(BrO3)2])/(Δt) = -1/12 (Δ[NaHS2O3])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[NaBr])/(Δt) = 1/5 (Δ[Na2S4O6])/(Δt) = (Δ[MgS4O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| Mg(BrO3)2 | NaHS2O3 | water | sodium bromide | Na2S4O6 | MgS4O6 formula | Mg(BrO3)2 | NaHS2O3 | H_2O | NaBr | Na2S4O6 | MgS4O6 Hill formula | Br2MgO6 | HNaO3S2 | H_2O | BrNa | Na2O6S4 | MgO6S4 name | | | water | sodium bromide | |

| Mg(BrO3)2 | NaHS2O3 | water | sodium bromide | Na2S4O6 | MgS4O6 molar mass | 280.11 g/mol | 136.1 g/mol | 18.015 g/mol | 102.89 g/mol | 270.2 g/mol | 248.5 g/mol phase | | | liquid (at STP) | solid (at STP) | | melting point | | | 0 °C | 755 °C | | boiling point | | | 99.9839 °C | 1396 °C | | density | | | 1 g/cm^3 | 3.2 g/cm^3 | | solubility in water | | | | soluble | | surface tension | | | 0.0728 N/m | | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | odorless | | |