SO2 + C = S + CO + CS2

SO_2 sulfur dioxide + C activated charcoal ⟶ S mixed sulfur + CO carbon monoxide + CS_2 carbon disulfide

Balance the chemical equation algebraically: SO_2 + C ⟶ S + CO + CS_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 C ⟶ c_3 S + c_4 CO + c_5 CS_2 Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and C: O: | 2 c_1 = c_4 S: | c_1 = c_3 + 2 c_5 C: | c_2 = c_4 + c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (5 c_1)/2 - 1/2 c_3 = 1 c_4 = 2 c_1 c_5 = c_1/2 - 1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 7 c_3 = 1 c_4 = 6 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 SO_2 + 7 C ⟶ S + 6 CO + CS_2

+ ⟶ + +

sulfur dioxide + activated charcoal ⟶ mixed sulfur + carbon monoxide + carbon disulfide

Construct the equilibrium constant, K, expression for: SO_2 + C ⟶ S + CO + CS_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: 3 SO_2 + 7 C ⟶ S + 6 CO + CS_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 SO_2 | 3 | -3 C | 7 | -7 S | 1 | 1 CO | 6 | 6 CS_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression SO_2 | 3 | -3 | ([SO2])^(-3) C | 7 | -7 | ([C])^(-7) S | 1 | 1 | [S] CO | 6 | 6 | ([CO])^6 CS_2 | 1 | 1 | [CS2] 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 = ([SO2])^(-3) ([C])^(-7) [S] ([CO])^6 [CS2] = ([S] ([CO])^6 [CS2])/(([SO2])^3 ([C])^7)

Construct the rate of reaction expression for: SO_2 + C ⟶ S + CO + CS_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: 3 SO_2 + 7 C ⟶ S + 6 CO + CS_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 SO_2 | 3 | -3 C | 7 | -7 S | 1 | 1 CO | 6 | 6 CS_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 SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) C | 7 | -7 | -1/7 (Δ[C])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) CO | 6 | 6 | 1/6 (Δ[CO])/(Δt) CS_2 | 1 | 1 | (Δ[CS2])/(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 = -1/3 (Δ[SO2])/(Δt) = -1/7 (Δ[C])/(Δt) = (Δ[S])/(Δt) = 1/6 (Δ[CO])/(Δt) = (Δ[CS2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfur dioxide | activated charcoal | mixed sulfur | carbon monoxide | carbon disulfide formula | SO_2 | C | S | CO | CS_2 Hill formula | O_2S | C | S | CO | CS_2 name | sulfur dioxide | activated charcoal | mixed sulfur | carbon monoxide | carbon disulfide IUPAC name | sulfur dioxide | carbon | sulfur | carbon monoxide | methanedithione

| sulfur dioxide | activated charcoal | mixed sulfur | carbon monoxide | carbon disulfide molar mass | 64.06 g/mol | 12.011 g/mol | 32.06 g/mol | 28.01 g/mol | 76.13 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) melting point | -73 °C | 3550 °C | 112.8 °C | -205 °C | -111.5 °C boiling point | -10 °C | 4027 °C | 444.7 °C | -191.5 °C | 46 °C density | 0.002619 g/cm^3 (at 25 °C) | 2.26 g/cm^3 | 2.07 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 1.266 g/cm^3 solubility in water | | insoluble | | | slightly soluble surface tension | 0.02859 N/m | | | | 0.03225 N/m dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | | | 1.772×10^-5 Pa s (at 25 °C) | 3.52×10^-4 Pa s (at 25 °C) odor | | | | odorless |