MnO2 + CO = CO2 + MnO

MnO_2 manganese dioxide + CO carbon monoxide ⟶ CO_2 carbon dioxide + MnO manganese monoxide

Balance the chemical equation algebraically: MnO_2 + CO ⟶ CO_2 + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 CO ⟶ c_3 CO_2 + c_4 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O and C: Mn: | c_1 = c_4 O: | 2 c_1 + c_2 = 2 c_3 + c_4 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_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: | | MnO_2 + CO ⟶ CO_2 + MnO

+ ⟶ +

manganese dioxide + carbon monoxide ⟶ carbon dioxide + manganese monoxide

| manganese dioxide | carbon monoxide | carbon dioxide | manganese monoxide molecular enthalpy | -520 kJ/mol | -110.5 kJ/mol | -393.5 kJ/mol | -385.2 kJ/mol total enthalpy | -520 kJ/mol | -110.5 kJ/mol | -393.5 kJ/mol | -385.2 kJ/mol | H_initial = -630.5 kJ/mol | | H_final = -778.7 kJ/mol | ΔH_rxn^0 | -778.7 kJ/mol - -630.5 kJ/mol = -148.2 kJ/mol (exothermic) | | |

| manganese dioxide | carbon monoxide | carbon dioxide | manganese monoxide molecular free energy | -465.1 kJ/mol | -137 kJ/mol | -394.4 kJ/mol | -362.9 kJ/mol total free energy | -465.1 kJ/mol | -137 kJ/mol | -394.4 kJ/mol | -362.9 kJ/mol | G_initial = -602.1 kJ/mol | | G_final = -757.3 kJ/mol | ΔG_rxn^0 | -757.3 kJ/mol - -602.1 kJ/mol = -155.2 kJ/mol (exergonic) | | |

| manganese dioxide | carbon monoxide | carbon dioxide | manganese monoxide molecular entropy | 53 J/(mol K) | 198 J/(mol K) | 214 J/(mol K) | 60 J/(mol K) total entropy | 53 J/(mol K) | 198 J/(mol K) | 214 J/(mol K) | 60 J/(mol K) | S_initial = 251 J/(mol K) | | S_final = 274 J/(mol K) | ΔS_rxn^0 | 274 J/(mol K) - 251 J/(mol K) = 23 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: MnO_2 + CO ⟶ CO_2 + 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: MnO_2 + CO ⟶ CO_2 + 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 MnO_2 | 1 | -1 CO | 1 | -1 CO_2 | 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 MnO_2 | 1 | -1 | ([MnO2])^(-1) CO | 1 | -1 | ([CO])^(-1) CO_2 | 1 | 1 | [CO2] 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 = ([MnO2])^(-1) ([CO])^(-1) [CO2] [MnO] = ([CO2] [MnO])/([MnO2] [CO])

Construct the rate of reaction expression for: MnO_2 + CO ⟶ CO_2 + 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: MnO_2 + CO ⟶ CO_2 + 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 MnO_2 | 1 | -1 CO | 1 | -1 CO_2 | 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 MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) CO | 1 | -1 | -(Δ[CO])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(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[MnO2])/(Δt) = -(Δ[CO])/(Δt) = (Δ[CO2])/(Δt) = (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | carbon monoxide | carbon dioxide | manganese monoxide formula | MnO_2 | CO | CO_2 | MnO name | manganese dioxide | carbon monoxide | carbon dioxide | manganese monoxide IUPAC name | dioxomanganese | carbon monoxide | carbon dioxide | oxomanganese