MnO2 + C = CO + Mn

MnO_2 manganese dioxide + C activated charcoal ⟶ CO carbon monoxide + Mn manganese

Balance the chemical equation algebraically: MnO_2 + C ⟶ CO + Mn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnO_2 + c_2 C ⟶ c_3 CO + c_4 Mn Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O and C: Mn: | c_1 = c_4 O: | 2 c_1 = c_3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnO_2 + 2 C ⟶ 2 CO + Mn

+ ⟶ +

manganese dioxide + activated charcoal ⟶ carbon monoxide + manganese

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

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

| manganese dioxide | activated charcoal | carbon monoxide | manganese formula | MnO_2 | C | CO | Mn name | manganese dioxide | activated charcoal | carbon monoxide | manganese IUPAC name | dioxomanganese | carbon | carbon monoxide | manganese

| manganese dioxide | activated charcoal | carbon monoxide | manganese molar mass | 86.936 g/mol | 12.011 g/mol | 28.01 g/mol | 54.938044 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 535 °C | 3550 °C | -205 °C | 1244 °C boiling point | | 4027 °C | -191.5 °C | 1962 °C density | 5.03 g/cm^3 | 2.26 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 7.3 g/cm^3 solubility in water | insoluble | insoluble | | insoluble dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | odor | | | odorless |