S + NO2 = NO + SO3

S mixed sulfur + NO_2 nitrogen dioxide ⟶ NO nitric oxide + SO_3 sulfur trioxide

Balance the chemical equation algebraically: S + NO_2 ⟶ NO + SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 NO_2 ⟶ c_3 NO + c_4 SO_3 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_4 N: | c_2 = c_3 O: | 2 c_2 = c_3 + 3 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 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + 3 NO_2 ⟶ 3 NO + SO_3

+ ⟶ +

mixed sulfur + nitrogen dioxide ⟶ nitric oxide + sulfur trioxide

Construct the equilibrium constant, K, expression for: S + NO_2 ⟶ NO + SO_3 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 + 3 NO_2 ⟶ 3 NO + SO_3 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 NO_2 | 3 | -3 NO | 3 | 3 SO_3 | 1 | 1 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) NO_2 | 3 | -3 | ([NO2])^(-3) NO | 3 | 3 | ([NO])^3 SO_3 | 1 | 1 | [SO3] 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) ([NO2])^(-3) ([NO])^3 [SO3] = (([NO])^3 [SO3])/([S] ([NO2])^3)

Construct the rate of reaction expression for: S + NO_2 ⟶ NO + SO_3 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 + 3 NO_2 ⟶ 3 NO + SO_3 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 NO_2 | 3 | -3 NO | 3 | 3 SO_3 | 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 | 1 | -1 | -(Δ[S])/(Δt) NO_2 | 3 | -3 | -1/3 (Δ[NO2])/(Δt) NO | 3 | 3 | 1/3 (Δ[NO])/(Δt) SO_3 | 1 | 1 | (Δ[SO3])/(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) = -1/3 (Δ[NO2])/(Δt) = 1/3 (Δ[NO])/(Δt) = (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | nitrogen dioxide | nitric oxide | sulfur trioxide formula | S | NO_2 | NO | SO_3 Hill formula | S | NO_2 | NO | O_3S name | mixed sulfur | nitrogen dioxide | nitric oxide | sulfur trioxide IUPAC name | sulfur | Nitrogen dioxide | nitric oxide | sulfur trioxide

| mixed sulfur | nitrogen dioxide | nitric oxide | sulfur trioxide molar mass | 32.06 g/mol | 46.005 g/mol | 30.006 g/mol | 80.06 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) melting point | 112.8 °C | -11 °C | -163.6 °C | 16.8 °C boiling point | 444.7 °C | 21 °C | -151.7 °C | 44.7 °C density | 2.07 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 0.001226 g/cm^3 (at 25 °C) | 1.97 g/cm^3 solubility in water | | reacts | | reacts dynamic viscosity | | 4.02×10^-4 Pa s (at 25 °C) | 1.911×10^-5 Pa s (at 25 °C) | 0.00159 Pa s (at 30 °C)