NaOH + Bi2O3 + NaOCl = H2O + NaCl + NaBiO3

NaOH sodium hydroxide + Bi_2O_3 bismuth trioxide + NaOCl sodium hypochlorite ⟶ H_2O water + NaCl sodium chloride + NaBiO_3 sodium bismuthate

Balance the chemical equation algebraically: NaOH + Bi_2O_3 + NaOCl ⟶ H_2O + NaCl + NaBiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Bi_2O_3 + c_3 NaOCl ⟶ c_4 H_2O + c_5 NaCl + c_6 NaBiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Bi and Cl: H: | c_1 = 2 c_4 Na: | c_1 + c_3 = c_5 + c_6 O: | c_1 + 3 c_2 + c_3 = c_4 + 3 c_6 Bi: | 2 c_2 = c_6 Cl: | c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + Bi_2O_3 + 2 NaOCl ⟶ H_2O + 2 NaCl + 2 NaBiO_3

+ + ⟶ + +

sodium hydroxide + bismuth trioxide + sodium hypochlorite ⟶ water + sodium chloride + sodium bismuthate

Construct the equilibrium constant, K, expression for: NaOH + Bi_2O_3 + NaOCl ⟶ H_2O + NaCl + NaBiO_3 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 + Bi_2O_3 + 2 NaOCl ⟶ H_2O + 2 NaCl + 2 NaBiO_3 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 Bi_2O_3 | 1 | -1 NaOCl | 2 | -2 H_2O | 1 | 1 NaCl | 2 | 2 NaBiO_3 | 2 | 2 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) Bi_2O_3 | 1 | -1 | ([Bi2O3])^(-1) NaOCl | 2 | -2 | ([NaOCl])^(-2) H_2O | 1 | 1 | [H2O] NaCl | 2 | 2 | ([NaCl])^2 NaBiO_3 | 2 | 2 | ([NaBiO3])^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 = ([NaOH])^(-2) ([Bi2O3])^(-1) ([NaOCl])^(-2) [H2O] ([NaCl])^2 ([NaBiO3])^2 = ([H2O] ([NaCl])^2 ([NaBiO3])^2)/(([NaOH])^2 [Bi2O3] ([NaOCl])^2)

Construct the rate of reaction expression for: NaOH + Bi_2O_3 + NaOCl ⟶ H_2O + NaCl + NaBiO_3 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 + Bi_2O_3 + 2 NaOCl ⟶ H_2O + 2 NaCl + 2 NaBiO_3 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 Bi_2O_3 | 1 | -1 NaOCl | 2 | -2 H_2O | 1 | 1 NaCl | 2 | 2 NaBiO_3 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) Bi_2O_3 | 1 | -1 | -(Δ[Bi2O3])/(Δt) NaOCl | 2 | -2 | -1/2 (Δ[NaOCl])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) NaBiO_3 | 2 | 2 | 1/2 (Δ[NaBiO3])/(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[Bi2O3])/(Δt) = -1/2 (Δ[NaOCl])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/2 (Δ[NaBiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | bismuth trioxide | sodium hypochlorite | water | sodium chloride | sodium bismuthate formula | NaOH | Bi_2O_3 | NaOCl | H_2O | NaCl | NaBiO_3 Hill formula | HNaO | Bi_2O_3 | ClNaO | H_2O | ClNa | BiNaO_3 name | sodium hydroxide | bismuth trioxide | sodium hypochlorite | water | sodium chloride | sodium bismuthate IUPAC name | sodium hydroxide | oxo-oxobismuthanyloxybismuthane | sodium hypochlorite | water | sodium chloride | sodium oxido-dioxobismuth

| sodium hydroxide | bismuth trioxide | sodium hypochlorite | water | sodium chloride | sodium bismuthate molar mass | 39.997 g/mol | 465.958 g/mol | 74.44 g/mol | 18.015 g/mol | 58.44 g/mol | 279.967 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) | melting point | 323 °C | 825 °C | -6 °C | 0 °C | 801 °C | boiling point | 1390 °C | 1890 °C | | 99.9839 °C | 1413 °C | density | 2.13 g/cm^3 | 8.9 g/cm^3 | 1.11 g/cm^3 | 1 g/cm^3 | 2.16 g/cm^3 | solubility in water | soluble | decomposes | miscible | | soluble | insoluble surface tension | 0.07435 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | odorless |