NO + C = CO2 + N2

NO nitric oxide + C activated charcoal ⟶ CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: NO + C ⟶ CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NO + 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: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NO + C ⟶ CO_2 + N_2

+ ⟶ +

nitric oxide + activated charcoal ⟶ carbon dioxide + nitrogen

Construct the equilibrium constant, K, expression for: NO + 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 + C ⟶ 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 C | 1 | -1 CO_2 | 1 | 1 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 | ([NO])^(-2) C | 1 | -1 | ([C])^(-1) CO_2 | 1 | 1 | [CO2] 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 = ([NO])^(-2) ([C])^(-1) [CO2] [N2] = ([CO2] [N2])/(([NO])^2 [C])

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

| nitric oxide | activated charcoal | carbon dioxide | nitrogen formula | NO | C | CO_2 | N_2 name | nitric oxide | activated charcoal | carbon dioxide | nitrogen IUPAC name | nitric oxide | carbon | carbon dioxide | molecular nitrogen