NaOH + Fe(OH)2 + NaBiO3 = H2O + Bi2O3 + NaFeO2

NaOH sodium hydroxide + Fe(OH)_2 iron(II) hydroxide + NaBiO_3 sodium bismuthate ⟶ H_2O water + Bi_2O_3 bismuth trioxide + NaFeO2

Balance the chemical equation algebraically: NaOH + Fe(OH)_2 + NaBiO_3 ⟶ H_2O + Bi_2O_3 + NaFeO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Fe(OH)_2 + c_3 NaBiO_3 ⟶ c_4 H_2O + c_5 Bi_2O_3 + c_6 NaFeO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Fe and Bi: H: | c_1 + 2 c_2 = 2 c_4 Na: | c_1 + c_3 = c_6 O: | c_1 + 2 c_2 + 3 c_3 = c_4 + 3 c_5 + 2 c_6 Fe: | c_2 = c_6 Bi: | c_3 = 2 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 4 c_3 = 2 c_4 = 5 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 4 Fe(OH)_2 + 2 NaBiO_3 ⟶ 5 H_2O + Bi_2O_3 + 4 NaFeO2

+ + ⟶ + + NaFeO2

sodium hydroxide + iron(II) hydroxide + sodium bismuthate ⟶ water + bismuth trioxide + NaFeO2

Construct the equilibrium constant, K, expression for: NaOH + Fe(OH)_2 + NaBiO_3 ⟶ H_2O + Bi_2O_3 + NaFeO2 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 + 4 Fe(OH)_2 + 2 NaBiO_3 ⟶ 5 H_2O + Bi_2O_3 + 4 NaFeO2 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 Fe(OH)_2 | 4 | -4 NaBiO_3 | 2 | -2 H_2O | 5 | 5 Bi_2O_3 | 1 | 1 NaFeO2 | 4 | 4 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) Fe(OH)_2 | 4 | -4 | ([Fe(OH)2])^(-4) NaBiO_3 | 2 | -2 | ([NaBiO3])^(-2) H_2O | 5 | 5 | ([H2O])^5 Bi_2O_3 | 1 | 1 | [Bi2O3] NaFeO2 | 4 | 4 | ([NaFeO2])^4 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) ([Fe(OH)2])^(-4) ([NaBiO3])^(-2) ([H2O])^5 [Bi2O3] ([NaFeO2])^4 = (([H2O])^5 [Bi2O3] ([NaFeO2])^4)/(([NaOH])^2 ([Fe(OH)2])^4 ([NaBiO3])^2)

Construct the rate of reaction expression for: NaOH + Fe(OH)_2 + NaBiO_3 ⟶ H_2O + Bi_2O_3 + NaFeO2 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 + 4 Fe(OH)_2 + 2 NaBiO_3 ⟶ 5 H_2O + Bi_2O_3 + 4 NaFeO2 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 Fe(OH)_2 | 4 | -4 NaBiO_3 | 2 | -2 H_2O | 5 | 5 Bi_2O_3 | 1 | 1 NaFeO2 | 4 | 4 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) Fe(OH)_2 | 4 | -4 | -1/4 (Δ[Fe(OH)2])/(Δt) NaBiO_3 | 2 | -2 | -1/2 (Δ[NaBiO3])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) Bi_2O_3 | 1 | 1 | (Δ[Bi2O3])/(Δt) NaFeO2 | 4 | 4 | 1/4 (Δ[NaFeO2])/(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) = -1/4 (Δ[Fe(OH)2])/(Δt) = -1/2 (Δ[NaBiO3])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[Bi2O3])/(Δt) = 1/4 (Δ[NaFeO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | iron(II) hydroxide | sodium bismuthate | water | bismuth trioxide | NaFeO2 formula | NaOH | Fe(OH)_2 | NaBiO_3 | H_2O | Bi_2O_3 | NaFeO2 Hill formula | HNaO | FeH_2O_2 | BiNaO_3 | H_2O | Bi_2O_3 | FeNaO2 name | sodium hydroxide | iron(II) hydroxide | sodium bismuthate | water | bismuth trioxide | IUPAC name | sodium hydroxide | ferrous dihydroxide | sodium oxido-dioxobismuth | water | oxo-oxobismuthanyloxybismuthane |

| sodium hydroxide | iron(II) hydroxide | sodium bismuthate | water | bismuth trioxide | NaFeO2 molar mass | 39.997 g/mol | 89.86 g/mol | 279.967 g/mol | 18.015 g/mol | 465.958 g/mol | 110.83 g/mol phase | solid (at STP) | | | liquid (at STP) | solid (at STP) | melting point | 323 °C | | | 0 °C | 825 °C | boiling point | 1390 °C | | | 99.9839 °C | 1890 °C | density | 2.13 g/cm^3 | | | 1 g/cm^3 | 8.9 g/cm^3 | solubility in water | soluble | | insoluble | | decomposes | 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 |