CO + N2O = CO2 + N2

CO carbon monoxide + N_2O nitrous oxide ⟶ CO_2 carbon dioxide + N_2 nitrogen

Balance the chemical equation algebraically: CO + N_2O ⟶ CO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 N_2O ⟶ 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 C, O and N: C: | c_1 = c_3 O: | c_1 + c_2 = 2 c_3 N: | 2 c_2 = 2 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CO + N_2O ⟶ CO_2 + N_2

+ ⟶ +

carbon monoxide + nitrous oxide ⟶ carbon dioxide + nitrogen

| carbon monoxide | nitrous oxide | carbon dioxide | nitrogen molecular enthalpy | -110.5 kJ/mol | 81.6 kJ/mol | -393.5 kJ/mol | 0 kJ/mol total enthalpy | -110.5 kJ/mol | 81.6 kJ/mol | -393.5 kJ/mol | 0 kJ/mol | H_initial = -28.9 kJ/mol | | H_final = -393.5 kJ/mol | ΔH_rxn^0 | -393.5 kJ/mol - -28.9 kJ/mol = -364.6 kJ/mol (exothermic) | | |

| carbon monoxide | nitrous oxide | carbon dioxide | nitrogen molecular free energy | -137 kJ/mol | 104 kJ/mol | -394.4 kJ/mol | 0 kJ/mol total free energy | -137 kJ/mol | 104 kJ/mol | -394.4 kJ/mol | 0 kJ/mol | G_initial = -33 kJ/mol | | G_final = -394.4 kJ/mol | ΔG_rxn^0 | -394.4 kJ/mol - -33 kJ/mol = -361.4 kJ/mol (exergonic) | | |

| carbon monoxide | nitrous oxide | carbon dioxide | nitrogen molecular entropy | 198 J/(mol K) | 220 J/(mol K) | 214 J/(mol K) | 192 J/(mol K) total entropy | 198 J/(mol K) | 220 J/(mol K) | 214 J/(mol K) | 192 J/(mol K) | S_initial = 418 J/(mol K) | | S_final = 406 J/(mol K) | ΔS_rxn^0 | 406 J/(mol K) - 418 J/(mol K) = -12 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: CO + N_2O ⟶ 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: CO + N_2O ⟶ 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 CO | 1 | -1 N_2O | 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 CO | 1 | -1 | ([CO])^(-1) N_2O | 1 | -1 | ([N2O])^(-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 = ([CO])^(-1) ([N2O])^(-1) [CO2] [N2] = ([CO2] [N2])/([CO] [N2O])

Construct the rate of reaction expression for: CO + N_2O ⟶ 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: CO + N_2O ⟶ 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 CO | 1 | -1 N_2O | 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 CO | 1 | -1 | -(Δ[CO])/(Δt) N_2O | 1 | -1 | -(Δ[N2O])/(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 = -(Δ[CO])/(Δt) = -(Δ[N2O])/(Δt) = (Δ[CO2])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | nitrous oxide | carbon dioxide | nitrogen formula | CO | N_2O | CO_2 | N_2 name | carbon monoxide | nitrous oxide | carbon dioxide | nitrogen IUPAC name | carbon monoxide | nitrous oxide | carbon dioxide | molecular nitrogen