#### Input interpretation

MnSO_4 manganese(II) sulfate + C activated charcoal ⟶ CO_2 carbon dioxide + SO_2 sulfur dioxide + MnO manganese monoxide

#### Balanced equation

Balance the chemical equation algebraically: MnSO_4 + C ⟶ CO_2 + SO_2 + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnSO_4 + c_2 C ⟶ c_3 CO_2 + c_4 SO_2 + c_5 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, S and C: Mn: | c_1 = c_5 O: | 4 c_1 = 2 c_3 + 2 c_4 + c_5 S: | c_1 = 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 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 MnSO_4 + C ⟶ CO_2 + 2 SO_2 + 2 MnO

#### Structures

+ ⟶ + +

#### Names

manganese(II) sulfate + activated charcoal ⟶ carbon dioxide + sulfur dioxide + manganese monoxide

#### Equilibrium constant

Construct the equilibrium constant, K, expression for: MnSO_4 + C ⟶ CO_2 + SO_2 + MnO 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 MnSO_4 + C ⟶ CO_2 + 2 SO_2 + 2 MnO 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 MnSO_4 | 2 | -2 C | 1 | -1 CO_2 | 1 | 1 SO_2 | 2 | 2 MnO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnSO_4 | 2 | -2 | ([MnSO4])^(-2) C | 1 | -1 | ([C])^(-1) CO_2 | 1 | 1 | [CO2] SO_2 | 2 | 2 | ([SO2])^2 MnO | 2 | 2 | ([MnO])^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 = ([MnSO4])^(-2) ([C])^(-1) [CO2] ([SO2])^2 ([MnO])^2 = ([CO2] ([SO2])^2 ([MnO])^2)/(([MnSO4])^2 [C])

#### Rate of reaction

Construct the rate of reaction expression for: MnSO_4 + C ⟶ CO_2 + SO_2 + MnO 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 MnSO_4 + C ⟶ CO_2 + 2 SO_2 + 2 MnO 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 MnSO_4 | 2 | -2 C | 1 | -1 CO_2 | 1 | 1 SO_2 | 2 | 2 MnO | 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 MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) MnO | 2 | 2 | 1/2 (Δ[MnO])/(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[MnSO4])/(Δt) = -(Δ[C])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/2 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

#### Chemical names and formulas

| manganese(II) sulfate | activated charcoal | carbon dioxide | sulfur dioxide | manganese monoxide formula | MnSO_4 | C | CO_2 | SO_2 | MnO Hill formula | MnSO_4 | C | CO_2 | O_2S | MnO name | manganese(II) sulfate | activated charcoal | carbon dioxide | sulfur dioxide | manganese monoxide IUPAC name | manganese(+2) cation sulfate | carbon | carbon dioxide | sulfur dioxide | oxomanganese