C + CaSO4 = SO2 + CO + CaO

C activated charcoal + CaSO_4 calcium sulfate ⟶ SO_2 sulfur dioxide + CO carbon monoxide + CaO lime

Balance the chemical equation algebraically: C + CaSO_4 ⟶ SO_2 + CO + CaO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 CaSO_4 ⟶ c_3 SO_2 + c_4 CO + c_5 CaO Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca, O and S: C: | c_1 = c_4 Ca: | c_2 = c_5 O: | 4 c_2 = 2 c_3 + c_4 + c_5 S: | c_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 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C + CaSO_4 ⟶ SO_2 + CO + CaO

+ ⟶ + +

activated charcoal + calcium sulfate ⟶ sulfur dioxide + carbon monoxide + lime

Construct the equilibrium constant, K, expression for: C + CaSO_4 ⟶ SO_2 + CO + CaO 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: C + CaSO_4 ⟶ SO_2 + CO + CaO 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 C | 1 | -1 CaSO_4 | 1 | -1 SO_2 | 1 | 1 CO | 1 | 1 CaO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 1 | -1 | ([C])^(-1) CaSO_4 | 1 | -1 | ([CaSO4])^(-1) SO_2 | 1 | 1 | [SO2] CO | 1 | 1 | [CO] CaO | 1 | 1 | [CaO] 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 = ([C])^(-1) ([CaSO4])^(-1) [SO2] [CO] [CaO] = ([SO2] [CO] [CaO])/([C] [CaSO4])

Construct the rate of reaction expression for: C + CaSO_4 ⟶ SO_2 + CO + CaO 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: C + CaSO_4 ⟶ SO_2 + CO + CaO 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 C | 1 | -1 CaSO_4 | 1 | -1 SO_2 | 1 | 1 CO | 1 | 1 CaO | 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 C | 1 | -1 | -(Δ[C])/(Δt) CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) CO | 1 | 1 | (Δ[CO])/(Δt) CaO | 1 | 1 | (Δ[CaO])/(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[C])/(Δt) = -(Δ[CaSO4])/(Δt) = (Δ[SO2])/(Δt) = (Δ[CO])/(Δt) = (Δ[CaO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | calcium sulfate | sulfur dioxide | carbon monoxide | lime formula | C | CaSO_4 | SO_2 | CO | CaO Hill formula | C | CaO_4S | O_2S | CO | CaO name | activated charcoal | calcium sulfate | sulfur dioxide | carbon monoxide | lime IUPAC name | carbon | calcium sulfate | sulfur dioxide | carbon monoxide |