Mg + MnO = MgO + Mn

Mg magnesium + MnO manganese monoxide ⟶ MgO magnesium oxide + Mn manganese

Balance the chemical equation algebraically: Mg + MnO ⟶ MgO + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 MnO ⟶ c_3 MgO + c_4 Mn Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Mn and O: Mg: | c_1 = c_3 Mn: | c_2 = c_4 O: | 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_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: | | Mg + MnO ⟶ MgO + Mn

+ ⟶ +

magnesium + manganese monoxide ⟶ magnesium oxide + manganese

| magnesium | manganese monoxide | magnesium oxide | manganese molecular enthalpy | 0 kJ/mol | -385.2 kJ/mol | -601.6 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -385.2 kJ/mol | -601.6 kJ/mol | 0 kJ/mol | H_initial = -385.2 kJ/mol | | H_final = -601.6 kJ/mol | ΔH_rxn^0 | -601.6 kJ/mol - -385.2 kJ/mol = -216.4 kJ/mol (exothermic) | | |

| magnesium | manganese monoxide | magnesium oxide | manganese molecular entropy | 33 J/(mol K) | 60 J/(mol K) | 27 J/(mol K) | 32 J/(mol K) total entropy | 33 J/(mol K) | 60 J/(mol K) | 27 J/(mol K) | 32 J/(mol K) | S_initial = 93 J/(mol K) | | S_final = 59 J/(mol K) | ΔS_rxn^0 | 59 J/(mol K) - 93 J/(mol K) = -34 J/(mol K) (exoentropic) | | |

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

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

| magnesium | manganese monoxide | magnesium oxide | manganese formula | Mg | MnO | MgO | Mn name | magnesium | manganese monoxide | magnesium oxide | manganese IUPAC name | magnesium | oxomanganese | oxomagnesium | manganese

| magnesium | manganese monoxide | magnesium oxide | manganese molar mass | 24.305 g/mol | 70.937 g/mol | 40.304 g/mol | 54.938044 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 648 °C | 1840 °C | 2852 °C | 1244 °C boiling point | 1090 °C | | 3600 °C | 1962 °C density | 1.738 g/cm^3 | 5.45 g/cm^3 | 3.58 g/cm^3 | 7.3 g/cm^3 solubility in water | reacts | insoluble | | insoluble odor | | | odorless |