Fe + C = Fe3C

Fe iron + C activated charcoal ⟶ Fe_3C iron carbide

Balance the chemical equation algebraically: Fe + C ⟶ Fe_3C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe + c_2 C ⟶ c_3 Fe_3C Set the number of atoms in the reactants equal to the number of atoms in the products for Fe and C: Fe: | c_1 = 3 c_3 C: | c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Fe + C ⟶ Fe_3C

+ ⟶ Fe_3C

iron + activated charcoal ⟶ iron carbide

Construct the equilibrium constant, K, expression for: Fe + C ⟶ 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 + C ⟶ 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 C | 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) C | 1 | -1 | ([C])^(-1) 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) ([C])^(-1) [Fe3C] = ([Fe3C])/(([Fe])^3 [C])

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

| iron | activated charcoal | iron carbide formula | Fe | C | Fe_3C Hill formula | Fe | C | CFe_3 name | iron | activated charcoal | iron carbide IUPAC name | iron | carbon |

| iron | activated charcoal | iron carbide molar mass | 55.845 g/mol | 12.011 g/mol | 179.5 g/mol phase | solid (at STP) | solid (at STP) | melting point | 1535 °C | 3550 °C | 1227 °C boiling point | 2750 °C | 4027 °C | density | 7.874 g/cm^3 | 2.26 g/cm^3 | 7.694 g/cm^3 solubility in water | insoluble | insoluble |