MnO2 + CO = CO2 + Mn

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

Balance the chemical equation algebraically: MnO_2 + CO ⟶ CO_2 + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 CO ⟶ c_3 CO_2 + c_4 Mn 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: | 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 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnO_2 + 2 CO ⟶ 2 CO_2 + Mn

+ ⟶ +

manganese dioxide + carbon monoxide ⟶ carbon dioxide + manganese

| manganese dioxide | carbon monoxide | carbon dioxide | manganese molecular enthalpy | -520 kJ/mol | -110.5 kJ/mol | -393.5 kJ/mol | 0 kJ/mol total enthalpy | -520 kJ/mol | -221 kJ/mol | -787 kJ/mol | 0 kJ/mol | H_initial = -741 kJ/mol | | H_final = -787 kJ/mol | ΔH_rxn^0 | -787 kJ/mol - -741 kJ/mol = -46 kJ/mol (exothermic) | | |

| manganese dioxide | carbon monoxide | carbon dioxide | manganese molecular entropy | 53 J/(mol K) | 198 J/(mol K) | 214 J/(mol K) | 32 J/(mol K) total entropy | 53 J/(mol K) | 396 J/(mol K) | 428 J/(mol K) | 32 J/(mol K) | S_initial = 449 J/(mol K) | | S_final = 460 J/(mol K) | ΔS_rxn^0 | 460 J/(mol K) - 449 J/(mol K) = 11 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: MnO_2 + CO ⟶ CO_2 + 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: MnO_2 + 2 CO ⟶ 2 CO_2 + 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 MnO_2 | 1 | -1 CO | 2 | -2 CO_2 | 2 | 2 Mn | 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 | 2 | -2 | ([CO])^(-2) CO_2 | 2 | 2 | ([CO2])^2 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 = ([MnO2])^(-1) ([CO])^(-2) ([CO2])^2 [Mn] = (([CO2])^2 [Mn])/([MnO2] ([CO])^2)

Construct the rate of reaction expression for: MnO_2 + CO ⟶ CO_2 + 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: MnO_2 + 2 CO ⟶ 2 CO_2 + 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 MnO_2 | 1 | -1 CO | 2 | -2 CO_2 | 2 | 2 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 MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) CO | 2 | -2 | -1/2 (Δ[CO])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(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[MnO2])/(Δt) = -1/2 (Δ[CO])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

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