SO2 + MnO2 = MnS2O6

SO_2 sulfur dioxide + MnO_2 manganese dioxide ⟶ MnS2O6

Balance the chemical equation algebraically: SO_2 + MnO_2 ⟶ MnS2O6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 MnO_2 ⟶ c_3 MnS2O6 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and Mn: O: | 2 c_1 + 2 c_2 = 6 c_3 S: | c_1 = 2 c_3 Mn: | 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 SO_2 + MnO_2 ⟶ MnS2O6

+ ⟶ MnS2O6

sulfur dioxide + manganese dioxide ⟶ MnS2O6

Construct the equilibrium constant, K, expression for: SO_2 + MnO_2 ⟶ MnS2O6 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 SO_2 + MnO_2 ⟶ MnS2O6 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 SO_2 | 2 | -2 MnO_2 | 1 | -1 MnS2O6 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 2 | -2 | ([SO2])^(-2) MnO_2 | 1 | -1 | ([MnO2])^(-1) MnS2O6 | 1 | 1 | [MnS2O6] 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 = ([SO2])^(-2) ([MnO2])^(-1) [MnS2O6] = ([MnS2O6])/(([SO2])^2 [MnO2])

Construct the rate of reaction expression for: SO_2 + MnO_2 ⟶ MnS2O6 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 SO_2 + MnO_2 ⟶ MnS2O6 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 SO_2 | 2 | -2 MnO_2 | 1 | -1 MnS2O6 | 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 SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) MnS2O6 | 1 | 1 | (Δ[MnS2O6])/(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[SO2])/(Δt) = -(Δ[MnO2])/(Δt) = (Δ[MnS2O6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | manganese dioxide | MnS2O6 formula | SO_2 | MnO_2 | MnS2O6 Hill formula | O_2S | MnO_2 | MnO6S2 name | sulfur dioxide | manganese dioxide | IUPAC name | sulfur dioxide | dioxomanganese |

| sulfur dioxide | manganese dioxide | MnS2O6 molar mass | 64.06 g/mol | 86.936 g/mol | 215.1 g/mol phase | gas (at STP) | solid (at STP) | melting point | -73 °C | 535 °C | boiling point | -10 °C | | density | 0.002619 g/cm^3 (at 25 °C) | 5.03 g/cm^3 | solubility in water | | insoluble | surface tension | 0.02859 N/m | | dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | |