Fe + S8 = FeS

Fe iron + S_8 rhombic sulfur ⟶ FeS ferrous sulfide

Balance the chemical equation algebraically: Fe + S_8 ⟶ FeS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe + c_2 S_8 ⟶ c_3 FeS Set the number of atoms in the reactants equal to the number of atoms in the products for Fe and S: Fe: | c_1 = c_3 S: | 8 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 = 8 c_2 = 1 c_3 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 Fe + S_8 ⟶ 8 FeS

+ ⟶

iron + rhombic sulfur ⟶ ferrous sulfide

| iron | rhombic sulfur | ferrous sulfide molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -100 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -800 kJ/mol | H_initial = 0 kJ/mol | | H_final = -800 kJ/mol ΔH_rxn^0 | -800 kJ/mol - 0 kJ/mol = -800 kJ/mol (exothermic) | |

| iron | rhombic sulfur | ferrous sulfide molecular entropy | 27 J/(mol K) | 32.1 J/(mol K) | 67 J/(mol K) total entropy | 216 J/(mol K) | 32.1 J/(mol K) | 536 J/(mol K) | S_initial = 248.1 J/(mol K) | | S_final = 536 J/(mol K) ΔS_rxn^0 | 536 J/(mol K) - 248.1 J/(mol K) = 287.9 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: Fe + S_8 ⟶ FeS 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: 8 Fe + S_8 ⟶ 8 FeS 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 | 8 | -8 S_8 | 1 | -1 FeS | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe | 8 | -8 | ([Fe])^(-8) S_8 | 1 | -1 | ([S8])^(-1) FeS | 8 | 8 | ([FeS])^8 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])^(-8) ([S8])^(-1) ([FeS])^8 = ([FeS])^8/(([Fe])^8 [S8])

Construct the rate of reaction expression for: Fe + S_8 ⟶ FeS 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: 8 Fe + S_8 ⟶ 8 FeS 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 | 8 | -8 S_8 | 1 | -1 FeS | 8 | 8 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 | 8 | -8 | -1/8 (Δ[Fe])/(Δt) S_8 | 1 | -1 | -(Δ[S8])/(Δt) FeS | 8 | 8 | 1/8 (Δ[FeS])/(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 = -1/8 (Δ[Fe])/(Δt) = -(Δ[S8])/(Δt) = 1/8 (Δ[FeS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron | rhombic sulfur | ferrous sulfide formula | Fe | S_8 | FeS name | iron | rhombic sulfur | ferrous sulfide IUPAC name | iron | octathiocane |

| iron | rhombic sulfur | ferrous sulfide molar mass | 55.845 g/mol | 256.5 g/mol | 87.9 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1535 °C | | 1195 °C boiling point | 2750 °C | | density | 7.874 g/cm^3 | 2.07 g/cm^3 | 4.84 g/cm^3 solubility in water | insoluble | | insoluble dynamic viscosity | | | 0.00343 Pa s (at 1250 °C)