MnO2 = O2 + Mn2O3

MnO_2 manganese dioxide ⟶ O_2 oxygen + Mn_2O_3 manganese(III) oxide

Balance the chemical equation algebraically: MnO_2 ⟶ O_2 + Mn_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 ⟶ c_2 O_2 + c_3 Mn_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn and O: Mn: | c_1 = 2 c_3 O: | 2 c_1 = 2 c_2 + 3 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 = 4 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 MnO_2 ⟶ O_2 + 2 Mn_2O_3

⟶ +

manganese dioxide ⟶ oxygen + manganese(III) oxide

| manganese dioxide | oxygen | manganese(III) oxide molecular enthalpy | -520 kJ/mol | 0 kJ/mol | -959 kJ/mol total enthalpy | -2080 kJ/mol | 0 kJ/mol | -1918 kJ/mol | H_initial = -2080 kJ/mol | H_final = -1918 kJ/mol | ΔH_rxn^0 | -1918 kJ/mol - -2080 kJ/mol = 162 kJ/mol (endothermic) | |

| manganese dioxide | oxygen | manganese(III) oxide molecular free energy | -465.1 kJ/mol | 231.7 kJ/mol | -881.1 kJ/mol total free energy | -1860 kJ/mol | 231.7 kJ/mol | -1762 kJ/mol | G_initial = -1860 kJ/mol | G_final = -1531 kJ/mol | ΔG_rxn^0 | -1531 kJ/mol - -1860 kJ/mol = 329.9 kJ/mol (endergonic) | |

| manganese dioxide | oxygen | manganese(III) oxide molecular entropy | 53 J/(mol K) | 205 J/(mol K) | 110 J/(mol K) total entropy | 212 J/(mol K) | 205 J/(mol K) | 220 J/(mol K) | S_initial = 212 J/(mol K) | S_final = 425 J/(mol K) | ΔS_rxn^0 | 425 J/(mol K) - 212 J/(mol K) = 213 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: MnO_2 ⟶ O_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: 4 MnO_2 ⟶ O_2 + 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 | 4 | -4 O_2 | 1 | 1 Mn_2O_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnO_2 | 4 | -4 | ([MnO2])^(-4) O_2 | 1 | 1 | [O2] Mn_2O_3 | 2 | 2 | ([Mn2O3])^2 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])^(-4) [O2] ([Mn2O3])^2 = ([O2] ([Mn2O3])^2)/([MnO2])^4

Construct the rate of reaction expression for: MnO_2 ⟶ O_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: 4 MnO_2 ⟶ O_2 + 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 | 4 | -4 O_2 | 1 | 1 Mn_2O_3 | 2 | 2 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 | 4 | -4 | -1/4 (Δ[MnO2])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) Mn_2O_3 | 2 | 2 | 1/2 (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 = -1/4 (Δ[MnO2])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[Mn2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese dioxide | oxygen | manganese(III) oxide formula | MnO_2 | O_2 | Mn_2O_3 name | manganese dioxide | oxygen | manganese(III) oxide IUPAC name | dioxomanganese | molecular oxygen | oxo-(oxomanganiooxy)manganese

| manganese dioxide | oxygen | manganese(III) oxide molar mass | 86.936 g/mol | 31.998 g/mol | 157.873 g/mol phase | solid (at STP) | gas (at STP) | solid (at STP) melting point | 535 °C | -218 °C | 1347 °C boiling point | | -183 °C | density | 5.03 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 4.5 g/cm^3 solubility in water | insoluble | | surface tension | | 0.01347 N/m | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | odor | | odorless |