MnO2 + CO = CO2 + Mn2O3

MnO_2 manganese dioxide + CO carbon monoxide ⟶ CO_2 carbon dioxide + Mn_2O_3 manganese(III) oxide

Balance the chemical equation algebraically: MnO_2 + CO ⟶ CO_2 + Mn_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 CO ⟶ c_3 CO_2 + c_4 Mn_2O_3 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 = 2 c_4 O: | 2 c_1 + c_2 = 2 c_3 + 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_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 MnO_2 + CO ⟶ CO_2 + Mn_2O_3

+ ⟶ +

manganese dioxide + carbon monoxide ⟶ carbon dioxide + manganese(III) oxide

| manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide molecular enthalpy | -520 kJ/mol | -110.5 kJ/mol | -393.5 kJ/mol | -959 kJ/mol total enthalpy | -1040 kJ/mol | -110.5 kJ/mol | -393.5 kJ/mol | -959 kJ/mol | H_initial = -1151 kJ/mol | | H_final = -1353 kJ/mol | ΔH_rxn^0 | -1353 kJ/mol - -1151 kJ/mol = -202 kJ/mol (exothermic) | | |

| manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide molecular free energy | -465.1 kJ/mol | -137 kJ/mol | -394.4 kJ/mol | -881.1 kJ/mol total free energy | -930.2 kJ/mol | -137 kJ/mol | -394.4 kJ/mol | -881.1 kJ/mol | G_initial = -1067 kJ/mol | | G_final = -1276 kJ/mol | ΔG_rxn^0 | -1276 kJ/mol - -1067 kJ/mol = -208.3 kJ/mol (exergonic) | | |

| manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide molecular entropy | 53 J/(mol K) | 198 J/(mol K) | 214 J/(mol K) | 110 J/(mol K) total entropy | 106 J/(mol K) | 198 J/(mol K) | 214 J/(mol K) | 110 J/(mol K) | S_initial = 304 J/(mol K) | | S_final = 324 J/(mol K) | ΔS_rxn^0 | 324 J/(mol K) - 304 J/(mol K) = 20 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: MnO_2 + CO ⟶ CO_2 + Mn_2O_3 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 MnO_2 + CO ⟶ CO_2 + Mn_2O_3 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 | 2 | -2 CO | 1 | -1 CO_2 | 1 | 1 Mn_2O_3 | 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 | 2 | -2 | ([MnO2])^(-2) CO | 1 | -1 | ([CO])^(-1) CO_2 | 1 | 1 | [CO2] Mn_2O_3 | 1 | 1 | [Mn2O3] 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])^(-2) ([CO])^(-1) [CO2] [Mn2O3] = ([CO2] [Mn2O3])/(([MnO2])^2 [CO])

Construct the rate of reaction expression for: MnO_2 + CO ⟶ CO_2 + Mn_2O_3 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 MnO_2 + CO ⟶ CO_2 + Mn_2O_3 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 | 2 | -2 CO | 1 | -1 CO_2 | 1 | 1 Mn_2O_3 | 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 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) CO | 1 | -1 | -(Δ[CO])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) Mn_2O_3 | 1 | 1 | (Δ[Mn2O3])/(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[MnO2])/(Δt) = -(Δ[CO])/(Δt) = (Δ[CO2])/(Δt) = (Δ[Mn2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide formula | MnO_2 | CO | CO_2 | Mn_2O_3 name | manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide IUPAC name | dioxomanganese | carbon monoxide | carbon dioxide | oxo-(oxomanganiooxy)manganese

| manganese dioxide | carbon monoxide | carbon dioxide | manganese(III) oxide molar mass | 86.936 g/mol | 28.01 g/mol | 44.009 g/mol | 157.873 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 535 °C | -205 °C | -56.56 °C (at triple point) | 1347 °C boiling point | | -191.5 °C | -78.5 °C (at sublimation point) | density | 5.03 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 0.00184212 g/cm^3 (at 20 °C) | 4.5 g/cm^3 solubility in water | insoluble | | | dynamic viscosity | | 1.772×10^-5 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | | odorless | odorless |