NO2 + C = CO2 + N2

NO_2 nitrogen dioxide + C activated charcoal ⟶ CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: NO_2 + C ⟶ CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO_2 + c_2 C ⟶ c_3 CO_2 + c_4 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O and C: N: | c_1 = 2 c_4 O: | 2 c_1 = 2 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NO_2 + 2 C ⟶ 2 CO_2 + N_2

+ ⟶ +

nitrogen dioxide + activated charcoal ⟶ carbon dioxide + nitrogen

Construct the equilibrium constant, K, expression for: NO_2 + C ⟶ CO_2 + N_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 NO_2 + 2 C ⟶ 2 CO_2 + N_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 NO_2 | 2 | -2 C | 2 | -2 CO_2 | 2 | 2 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NO_2 | 2 | -2 | ([NO2])^(-2) C | 2 | -2 | ([C])^(-2) CO_2 | 2 | 2 | ([CO2])^2 N_2 | 1 | 1 | [N2] 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 = ([NO2])^(-2) ([C])^(-2) ([CO2])^2 [N2] = (([CO2])^2 [N2])/(([NO2])^2 ([C])^2)

Construct the rate of reaction expression for: NO_2 + C ⟶ CO_2 + N_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 NO_2 + 2 C ⟶ 2 CO_2 + N_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 NO_2 | 2 | -2 C | 2 | -2 CO_2 | 2 | 2 N_2 | 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 NO_2 | 2 | -2 | -1/2 (Δ[NO2])/(Δt) C | 2 | -2 | -1/2 (Δ[C])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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[NO2])/(Δt) = -1/2 (Δ[C])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen dioxide | activated charcoal | carbon dioxide | nitrogen formula | NO_2 | C | CO_2 | N_2 name | nitrogen dioxide | activated charcoal | carbon dioxide | nitrogen IUPAC name | Nitrogen dioxide | carbon | carbon dioxide | molecular nitrogen

| nitrogen dioxide | activated charcoal | carbon dioxide | nitrogen molar mass | 46.005 g/mol | 12.011 g/mol | 44.009 g/mol | 28.014 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | gas (at STP) melting point | -11 °C | 3550 °C | -56.56 °C (at triple point) | -210 °C boiling point | 21 °C | 4027 °C | -78.5 °C (at sublimation point) | -195.79 °C density | 0.00188 g/cm^3 (at 25 °C) | 2.26 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.001251 g/cm^3 (at 0 °C) solubility in water | reacts | insoluble | | insoluble surface tension | | | | 0.0066 N/m dynamic viscosity | 4.02×10^-4 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) odor | | | odorless | odorless