O2 + MnS = SO2 + MnO2

O_2 oxygen + MnS manganese sulfide ⟶ SO_2 sulfur dioxide + MnO_2 manganese dioxide

Balance the chemical equation algebraically: O_2 + MnS ⟶ SO_2 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 MnS ⟶ c_3 SO_2 + c_4 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Mn and S: O: | 2 c_1 = 2 c_3 + 2 c_4 Mn: | c_2 = c_4 S: | 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + MnS ⟶ SO_2 + MnO_2

+ ⟶ +

oxygen + manganese sulfide ⟶ sulfur dioxide + manganese dioxide

| oxygen | manganese sulfide | sulfur dioxide | manganese dioxide molecular enthalpy | 0 kJ/mol | -214.2 kJ/mol | -296.8 kJ/mol | -520 kJ/mol total enthalpy | 0 kJ/mol | -214.2 kJ/mol | -296.8 kJ/mol | -520 kJ/mol | H_initial = -214.2 kJ/mol | | H_final = -816.8 kJ/mol | ΔH_rxn^0 | -816.8 kJ/mol - -214.2 kJ/mol = -602.6 kJ/mol (exothermic) | | |

| oxygen | manganese sulfide | sulfur dioxide | manganese dioxide molecular free energy | 231.7 kJ/mol | -218.4 kJ/mol | -300.1 kJ/mol | -465.1 kJ/mol total free energy | 463.4 kJ/mol | -218.4 kJ/mol | -300.1 kJ/mol | -465.1 kJ/mol | G_initial = 245 kJ/mol | | G_final = -765.2 kJ/mol | ΔG_rxn^0 | -765.2 kJ/mol - 245 kJ/mol = -1010 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: O_2 + MnS ⟶ SO_2 + MnO_2 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: 2 O_2 + MnS ⟶ SO_2 + MnO_2 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 O_2 | 2 | -2 MnS | 1 | -1 SO_2 | 1 | 1 MnO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) MnS | 1 | -1 | ([MnS])^(-1) SO_2 | 1 | 1 | [SO2] MnO_2 | 1 | 1 | [MnO2] 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 = ([O2])^(-2) ([MnS])^(-1) [SO2] [MnO2] = ([SO2] [MnO2])/(([O2])^2 [MnS])

Construct the rate of reaction expression for: O_2 + MnS ⟶ SO_2 + MnO_2 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: 2 O_2 + MnS ⟶ SO_2 + MnO_2 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 O_2 | 2 | -2 MnS | 1 | -1 SO_2 | 1 | 1 MnO_2 | 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 O_2 | 2 | -2 | -1/2 (Δ[O2])/(Δt) MnS | 1 | -1 | -(Δ[MnS])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) MnO_2 | 1 | 1 | (Δ[MnO2])/(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 = -1/2 (Δ[O2])/(Δt) = -(Δ[MnS])/(Δt) = (Δ[SO2])/(Δt) = (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | manganese sulfide | sulfur dioxide | manganese dioxide formula | O_2 | MnS | SO_2 | MnO_2 Hill formula | O_2 | MnS | O_2S | MnO_2 name | oxygen | manganese sulfide | sulfur dioxide | manganese dioxide IUPAC name | molecular oxygen | | sulfur dioxide | dioxomanganese