Na + Fe2O3 = Fe + Na2O

Na sodium + Fe_2O_3 iron(III) oxide ⟶ Fe iron + Na_2O sodium oxide

Balance the chemical equation algebraically: Na + Fe_2O_3 ⟶ Fe + Na_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 Fe_2O_3 ⟶ c_3 Fe + c_4 Na_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Na, Fe and O: Na: | c_1 = 2 c_4 Fe: | 2 c_2 = c_3 O: | 3 c_2 = c_4 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 = 6 c_2 = 1 c_3 = 2 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Na + Fe_2O_3 ⟶ 2 Fe + 3 Na_2O

+ ⟶ +

sodium + iron(III) oxide ⟶ iron + sodium oxide

Construct the equilibrium constant, K, expression for: Na + Fe_2O_3 ⟶ Fe + Na_2O 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: 6 Na + Fe_2O_3 ⟶ 2 Fe + 3 Na_2O 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 Na | 6 | -6 Fe_2O_3 | 1 | -1 Fe | 2 | 2 Na_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 6 | -6 | ([Na])^(-6) Fe_2O_3 | 1 | -1 | ([Fe2O3])^(-1) Fe | 2 | 2 | ([Fe])^2 Na_2O | 3 | 3 | ([Na2O])^3 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 = ([Na])^(-6) ([Fe2O3])^(-1) ([Fe])^2 ([Na2O])^3 = (([Fe])^2 ([Na2O])^3)/(([Na])^6 [Fe2O3])

Construct the rate of reaction expression for: Na + Fe_2O_3 ⟶ Fe + Na_2O 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: 6 Na + Fe_2O_3 ⟶ 2 Fe + 3 Na_2O 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 Na | 6 | -6 Fe_2O_3 | 1 | -1 Fe | 2 | 2 Na_2O | 3 | 3 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 Na | 6 | -6 | -1/6 (Δ[Na])/(Δt) Fe_2O_3 | 1 | -1 | -(Δ[Fe2O3])/(Δt) Fe | 2 | 2 | 1/2 (Δ[Fe])/(Δt) Na_2O | 3 | 3 | 1/3 (Δ[Na2O])/(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 = -1/6 (Δ[Na])/(Δt) = -(Δ[Fe2O3])/(Δt) = 1/2 (Δ[Fe])/(Δt) = 1/3 (Δ[Na2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | iron(III) oxide | iron | sodium oxide formula | Na | Fe_2O_3 | Fe | Na_2O name | sodium | iron(III) oxide | iron | sodium oxide IUPAC name | sodium | | iron | disodium oxygen(-2) anion

| sodium | iron(III) oxide | iron | sodium oxide molar mass | 22.98976928 g/mol | 159.69 g/mol | 55.845 g/mol | 61.979 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 97.8 °C | 1565 °C | 1535 °C | boiling point | 883 °C | | 2750 °C | density | 0.968 g/cm^3 | 5.26 g/cm^3 | 7.874 g/cm^3 | 2.27 g/cm^3 solubility in water | decomposes | insoluble | insoluble | dynamic viscosity | 1.413×10^-5 Pa s (at 527 °C) | | | odor | | odorless | |