O2 + MnO2 = Mn2O7

O_2 oxygen + MnO_2 manganese dioxide ⟶ Mn_2O_7 manganese(VII) oxide

Balance the chemical equation algebraically: O_2 + MnO_2 ⟶ Mn_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 MnO_2 ⟶ c_3 Mn_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for O and Mn: O: | 2 c_1 + 2 c_2 = 7 c_3 Mn: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 4 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 4 MnO_2 ⟶ 2 Mn_2O_7

+ ⟶

oxygen + manganese dioxide ⟶ manganese(VII) oxide

Construct the equilibrium constant, K, expression for: O_2 + MnO_2 ⟶ Mn_2O_7 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: 3 O_2 + 4 MnO_2 ⟶ 2 Mn_2O_7 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 | 3 | -3 MnO_2 | 4 | -4 Mn_2O_7 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) MnO_2 | 4 | -4 | ([MnO2])^(-4) Mn_2O_7 | 2 | 2 | ([Mn2O7])^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 = ([O2])^(-3) ([MnO2])^(-4) ([Mn2O7])^2 = ([Mn2O7])^2/(([O2])^3 ([MnO2])^4)

Construct the rate of reaction expression for: O_2 + MnO_2 ⟶ Mn_2O_7 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: 3 O_2 + 4 MnO_2 ⟶ 2 Mn_2O_7 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 | 3 | -3 MnO_2 | 4 | -4 Mn_2O_7 | 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) MnO_2 | 4 | -4 | -1/4 (Δ[MnO2])/(Δt) Mn_2O_7 | 2 | 2 | 1/2 (Δ[Mn2O7])/(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 = -1/3 (Δ[O2])/(Δt) = -1/4 (Δ[MnO2])/(Δt) = 1/2 (Δ[Mn2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | manganese dioxide | manganese(VII) oxide formula | O_2 | MnO_2 | Mn_2O_7 name | oxygen | manganese dioxide | manganese(VII) oxide IUPAC name | molecular oxygen | dioxomanganese |

| oxygen | manganese dioxide | manganese(VII) oxide molar mass | 31.998 g/mol | 86.936 g/mol | 221.87 g/mol phase | gas (at STP) | solid (at STP) | melting point | -218 °C | 535 °C | 5.9 °C boiling point | -183 °C | | density | 0.001429 g/cm^3 (at 0 °C) | 5.03 g/cm^3 | 2.4 g/cm^3 solubility in water | | insoluble | soluble surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | |