Mn2O7 = O2 + MnO2

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

Balance the chemical equation algebraically: Mn_2O_7 ⟶ O_2 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mn_2O_7 ⟶ c_2 O_2 + c_3 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn and O: Mn: | 2 c_1 = c_3 O: | 7 c_1 = 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3/2 c_3 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Mn_2O_7 ⟶ 3 O_2 + 4 MnO_2

⟶ +

manganese(VII) oxide ⟶ oxygen + manganese dioxide

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

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

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

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