FeO + Mn = Fe + MnO

FeO (iron(II) oxide) + Mn (manganese) ⟶ Fe (iron) + MnO (manganese monoxide)

Balance the chemical equation algebraically: FeO + Mn ⟶ Fe + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 FeO + c_2 Mn ⟶ c_3 Fe + c_4 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, O and Mn: Fe: | c_1 = c_3 O: | c_1 = c_4 Mn: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | FeO + Mn ⟶ Fe + MnO

+ ⟶ +

iron(II) oxide + manganese ⟶ iron + manganese monoxide

| iron(II) oxide | manganese | iron | manganese monoxide molecular enthalpy | -272 kJ/mol | 0 kJ/mol | 0 kJ/mol | -385.2 kJ/mol total enthalpy | -272 kJ/mol | 0 kJ/mol | 0 kJ/mol | -385.2 kJ/mol | H_initial = -272 kJ/mol | | H_final = -385.2 kJ/mol | ΔH_rxn^0 | -385.2 kJ/mol - -272 kJ/mol = -113.2 kJ/mol (exothermic) | | |

| iron(II) oxide | manganese | iron | manganese monoxide molecular entropy | 61 J/(mol K) | 32 J/(mol K) | 27 J/(mol K) | 60 J/(mol K) total entropy | 61 J/(mol K) | 32 J/(mol K) | 27 J/(mol K) | 60 J/(mol K) | S_initial = 93 J/(mol K) | | S_final = 87 J/(mol K) | ΔS_rxn^0 | 87 J/(mol K) - 93 J/(mol K) = -6 J/(mol K) (exoentropic) | | |

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

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

| iron(II) oxide | manganese | iron | manganese monoxide formula | FeO | Mn | Fe | MnO name | iron(II) oxide | manganese | iron | manganese monoxide IUPAC name | oxoiron | manganese | iron | oxomanganese

| iron(II) oxide | manganese | iron | manganese monoxide molar mass | 71.844 g/mol | 54.938044 g/mol | 55.845 g/mol | 70.937 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1360 °C | 1244 °C | 1535 °C | 1840 °C boiling point | | 1962 °C | 2750 °C | density | 5.7 g/cm^3 | 7.3 g/cm^3 | 7.874 g/cm^3 | 5.45 g/cm^3 solubility in water | insoluble | insoluble | insoluble | insoluble