SO2 + C = S + CO

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

Balance the chemical equation algebraically: SO_2 + C ⟶ S + CO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 C ⟶ c_3 S + c_4 CO 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 C: | 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_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: | | SO_2 + 2 C ⟶ S + 2 CO

+ ⟶ +

sulfur dioxide + activated charcoal ⟶ mixed sulfur + carbon monoxide

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

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

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