C + Mn2O3 = CO + MnO

C activated charcoal + Mn_2O_3 manganese(III) oxide ⟶ CO carbon monoxide + MnO manganese monoxide

Balance the chemical equation algebraically: C + Mn_2O_3 ⟶ CO + MnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Mn_2O_3 ⟶ c_3 CO + c_4 MnO Set the number of atoms in the reactants equal to the number of atoms in the products for C, Mn and O: C: | c_1 = c_3 Mn: | 2 c_2 = c_4 O: | 3 c_2 = c_3 + c_4 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 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C + Mn_2O_3 ⟶ CO + 2 MnO

+ ⟶ +

activated charcoal + manganese(III) oxide ⟶ carbon monoxide + manganese monoxide

Construct the equilibrium constant, K, expression for: C + Mn_2O_3 ⟶ CO + 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: C + Mn_2O_3 ⟶ CO + 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 C | 1 | -1 Mn_2O_3 | 1 | -1 CO | 1 | 1 MnO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 1 | -1 | ([C])^(-1) Mn_2O_3 | 1 | -1 | ([Mn2O3])^(-1) CO | 1 | 1 | [CO] 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 = ([C])^(-1) ([Mn2O3])^(-1) [CO] ([MnO])^2 = ([CO] ([MnO])^2)/([C] [Mn2O3])

Construct the rate of reaction expression for: C + Mn_2O_3 ⟶ CO + 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: C + Mn_2O_3 ⟶ CO + 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 C | 1 | -1 Mn_2O_3 | 1 | -1 CO | 1 | 1 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 C | 1 | -1 | -(Δ[C])/(Δt) Mn_2O_3 | 1 | -1 | -(Δ[Mn2O3])/(Δt) CO | 1 | 1 | (Δ[CO])/(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 = -(Δ[C])/(Δt) = -(Δ[Mn2O3])/(Δt) = (Δ[CO])/(Δt) = 1/2 (Δ[MnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | manganese(III) oxide | carbon monoxide | manganese monoxide formula | C | Mn_2O_3 | CO | MnO name | activated charcoal | manganese(III) oxide | carbon monoxide | manganese monoxide IUPAC name | carbon | oxo-(oxomanganiooxy)manganese | carbon monoxide | oxomanganese

| activated charcoal | manganese(III) oxide | carbon monoxide | manganese monoxide molar mass | 12.011 g/mol | 157.873 g/mol | 28.01 g/mol | 70.937 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 1347 °C | -205 °C | 1840 °C boiling point | 4027 °C | | -191.5 °C | density | 2.26 g/cm^3 | 4.5 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 5.45 g/cm^3 solubility in water | insoluble | | | insoluble dynamic viscosity | | | 1.772×10^-5 Pa s (at 25 °C) | odor | | | odorless |