Fe + CO = CO2 + Fe3C

Fe iron + CO carbon monoxide ⟶ CO_2 carbon dioxide + Fe_3C iron carbide

Balance the chemical equation algebraically: Fe + CO ⟶ CO_2 + Fe_3C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe + c_2 CO ⟶ c_3 CO_2 + c_4 Fe_3C Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, C and O: Fe: | c_1 = 3 c_4 C: | c_2 = c_3 + c_4 O: | c_2 = 2 c_3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Fe + 2 CO ⟶ CO_2 + Fe_3C

+ ⟶ + Fe_3C

iron + carbon monoxide ⟶ carbon dioxide + iron carbide

Construct the equilibrium constant, K, expression for: Fe + CO ⟶ CO_2 + Fe_3C 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: 3 Fe + 2 CO ⟶ CO_2 + Fe_3C 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 Fe | 3 | -3 CO | 2 | -2 CO_2 | 1 | 1 Fe_3C | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe | 3 | -3 | ([Fe])^(-3) CO | 2 | -2 | ([CO])^(-2) CO_2 | 1 | 1 | [CO2] Fe_3C | 1 | 1 | [Fe3C] 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 = ([Fe])^(-3) ([CO])^(-2) [CO2] [Fe3C] = ([CO2] [Fe3C])/(([Fe])^3 ([CO])^2)

Construct the rate of reaction expression for: Fe + CO ⟶ CO_2 + Fe_3C 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: 3 Fe + 2 CO ⟶ CO_2 + Fe_3C 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 Fe | 3 | -3 CO | 2 | -2 CO_2 | 1 | 1 Fe_3C | 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 Fe | 3 | -3 | -1/3 (Δ[Fe])/(Δt) CO | 2 | -2 | -1/2 (Δ[CO])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) Fe_3C | 1 | 1 | (Δ[Fe3C])/(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 = -1/3 (Δ[Fe])/(Δt) = -1/2 (Δ[CO])/(Δt) = (Δ[CO2])/(Δt) = (Δ[Fe3C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron | carbon monoxide | carbon dioxide | iron carbide formula | Fe | CO | CO_2 | Fe_3C Hill formula | Fe | CO | CO_2 | CFe_3 name | iron | carbon monoxide | carbon dioxide | iron carbide

| iron | carbon monoxide | carbon dioxide | iron carbide molar mass | 55.845 g/mol | 28.01 g/mol | 44.009 g/mol | 179.5 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | melting point | 1535 °C | -205 °C | -56.56 °C (at triple point) | 1227 °C boiling point | 2750 °C | -191.5 °C | -78.5 °C (at sublimation point) | density | 7.874 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 0.00184212 g/cm^3 (at 20 °C) | 7.694 g/cm^3 solubility in water | insoluble | | | dynamic viscosity | | 1.772×10^-5 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | odorless | odorless |