S + NO2 = SO2 + N2

S mixed sulfur + NO_2 nitrogen dioxide ⟶ SO_2 sulfur dioxide + N_2 nitrogen

Balance the chemical equation algebraically: S + NO_2 ⟶ SO_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 NO_2 ⟶ 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: | c_2 = 2 c_4 O: | 2 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_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 S + 2 NO_2 ⟶ 2 SO_2 + N_2

+ ⟶ +

mixed sulfur + nitrogen dioxide ⟶ sulfur dioxide + nitrogen

Construct the equilibrium constant, K, expression for: S + NO_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: 2 S + 2 NO_2 ⟶ 2 SO_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 | 2 | -2 NO_2 | 2 | -2 SO_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 S | 2 | -2 | ([S])^(-2) NO_2 | 2 | -2 | ([NO2])^(-2) SO_2 | 2 | 2 | ([SO2])^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 = ([S])^(-2) ([NO2])^(-2) ([SO2])^2 [N2] = (([SO2])^2 [N2])/(([S])^2 ([NO2])^2)

Construct the rate of reaction expression for: S + NO_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: 2 S + 2 NO_2 ⟶ 2 SO_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 | 2 | -2 NO_2 | 2 | -2 SO_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 S | 2 | -2 | -1/2 (Δ[S])/(Δt) NO_2 | 2 | -2 | -1/2 (Δ[NO2])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(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[S])/(Δt) = -1/2 (Δ[NO2])/(Δt) = 1/2 (Δ[SO2])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | nitrogen dioxide | sulfur dioxide | nitrogen formula | S | NO_2 | SO_2 | N_2 Hill formula | S | NO_2 | O_2S | N_2 name | mixed sulfur | nitrogen dioxide | sulfur dioxide | nitrogen IUPAC name | sulfur | Nitrogen dioxide | sulfur dioxide | molecular nitrogen

| mixed sulfur | nitrogen dioxide | sulfur dioxide | nitrogen molar mass | 32.06 g/mol | 46.005 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 | -11 °C | -73 °C | -210 °C boiling point | 444.7 °C | 21 °C | -10 °C | -195.79 °C density | 2.07 g/cm^3 | 0.00188 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 | | reacts | | insoluble surface tension | | | 0.02859 N/m | 0.0066 N/m dynamic viscosity | | 4.02×10^-4 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