S + N2O = SO2 + N2

S mixed sulfur + N_2O nitrous oxide ⟶ SO_2 sulfur dioxide + N_2 nitrogen

Balance the chemical equation algebraically: S + N_2O ⟶ SO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 N_2O ⟶ c_3 SO_2 + c_4 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for S, N and O: S: | c_1 = c_3 N: | 2 c_2 = 2 c_4 O: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + 2 N_2O ⟶ SO_2 + 2 N_2

+ ⟶ +

mixed sulfur + nitrous oxide ⟶ sulfur dioxide + nitrogen

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

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

| mixed sulfur | nitrous oxide | sulfur dioxide | nitrogen formula | S | N_2O | SO_2 | N_2 Hill formula | S | N_2O | O_2S | N_2 name | mixed sulfur | nitrous oxide | sulfur dioxide | nitrogen IUPAC name | sulfur | nitrous oxide | sulfur dioxide | molecular nitrogen

| mixed sulfur | nitrous oxide | sulfur dioxide | nitrogen molar mass | 32.06 g/mol | 44.013 g/mol | 64.06 g/mol | 28.014 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | gas (at STP) melting point | 112.8 °C | -91 °C | -73 °C | -210 °C boiling point | 444.7 °C | -88 °C | -10 °C | -195.79 °C density | 2.07 g/cm^3 | 0.001799 g/cm^3 (at 25 °C) | 0.002619 g/cm^3 (at 25 °C) | 0.001251 g/cm^3 (at 0 °C) solubility in water | | | | insoluble surface tension | | 0.00175 N/m | 0.02859 N/m | 0.0066 N/m dynamic viscosity | | 1.491×10^-5 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) odor | | | | odorless