N2O + CS2 = CO2 + SO2 + N2

N_2O nitrous oxide + CS_2 carbon disulfide ⟶ CO_2 carbon dioxide + SO_2 sulfur dioxide + N_2 nitrogen

Balance the chemical equation algebraically: N_2O + CS_2 ⟶ CO_2 + SO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2O + c_2 CS_2 ⟶ c_3 CO_2 + c_4 SO_2 + c_5 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N, O, C and S: N: | 2 c_1 = 2 c_5 O: | c_1 = 2 c_3 + 2 c_4 C: | c_2 = c_3 S: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 N_2O + CS_2 ⟶ CO_2 + 2 SO_2 + 6 N_2

+ ⟶ + +

nitrous oxide + carbon disulfide ⟶ carbon dioxide + sulfur dioxide + nitrogen

| nitrous oxide | carbon disulfide | carbon dioxide | sulfur dioxide | nitrogen molecular free energy | 104 kJ/mol | 64.6 kJ/mol | -394.4 kJ/mol | -300.1 kJ/mol | 0 kJ/mol total free energy | 624 kJ/mol | 64.6 kJ/mol | -394.4 kJ/mol | -600.2 kJ/mol | 0 kJ/mol | G_initial = 688.6 kJ/mol | | G_final = -994.6 kJ/mol | | ΔG_rxn^0 | -994.6 kJ/mol - 688.6 kJ/mol = -1683 kJ/mol (exergonic) | | | |

Construct the equilibrium constant, K, expression for: N_2O + CS_2 ⟶ CO_2 + SO_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: 6 N_2O + CS_2 ⟶ CO_2 + 2 SO_2 + 6 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 N_2O | 6 | -6 CS_2 | 1 | -1 CO_2 | 1 | 1 SO_2 | 2 | 2 N_2 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression N_2O | 6 | -6 | ([N2O])^(-6) CS_2 | 1 | -1 | ([CS2])^(-1) CO_2 | 1 | 1 | [CO2] SO_2 | 2 | 2 | ([SO2])^2 N_2 | 6 | 6 | ([N2])^6 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 = ([N2O])^(-6) ([CS2])^(-1) [CO2] ([SO2])^2 ([N2])^6 = ([CO2] ([SO2])^2 ([N2])^6)/(([N2O])^6 [CS2])

Construct the rate of reaction expression for: N_2O + CS_2 ⟶ CO_2 + SO_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: 6 N_2O + CS_2 ⟶ CO_2 + 2 SO_2 + 6 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 N_2O | 6 | -6 CS_2 | 1 | -1 CO_2 | 1 | 1 SO_2 | 2 | 2 N_2 | 6 | 6 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 N_2O | 6 | -6 | -1/6 (Δ[N2O])/(Δt) CS_2 | 1 | -1 | -(Δ[CS2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) N_2 | 6 | 6 | 1/6 (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 = -1/6 (Δ[N2O])/(Δt) = -(Δ[CS2])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/6 (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrous oxide | carbon disulfide | carbon dioxide | sulfur dioxide | nitrogen formula | N_2O | CS_2 | CO_2 | SO_2 | N_2 Hill formula | N_2O | CS_2 | CO_2 | O_2S | N_2 name | nitrous oxide | carbon disulfide | carbon dioxide | sulfur dioxide | nitrogen IUPAC name | nitrous oxide | methanedithione | carbon dioxide | sulfur dioxide | molecular nitrogen