SO2 + Ca = S + CaO

SO_2 sulfur dioxide + Ca calcium ⟶ S mixed sulfur + CaO lime

Balance the chemical equation algebraically: SO_2 + Ca ⟶ S + CaO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 SO_2 + c_2 Ca ⟶ c_3 S + c_4 CaO Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and Ca: O: | 2 c_1 = c_4 S: | c_1 = c_3 Ca: | 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 Ca ⟶ S + 2 CaO

+ ⟶ +

sulfur dioxide + calcium ⟶ mixed sulfur + lime

Construct the equilibrium constant, K, expression for: SO_2 + Ca ⟶ S + 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: SO_2 + 2 Ca ⟶ S + 2 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 SO_2 | 1 | -1 Ca | 2 | -2 S | 1 | 1 CaO | 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) Ca | 2 | -2 | ([Ca])^(-2) S | 1 | 1 | [S] CaO | 2 | 2 | ([CaO])^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) ([Ca])^(-2) [S] ([CaO])^2 = ([S] ([CaO])^2)/([SO2] ([Ca])^2)

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

| sulfur dioxide | calcium | mixed sulfur | lime formula | SO_2 | Ca | S | CaO Hill formula | O_2S | Ca | S | CaO name | sulfur dioxide | calcium | mixed sulfur | lime IUPAC name | sulfur dioxide | calcium | sulfur |

| sulfur dioxide | calcium | mixed sulfur | lime molar mass | 64.06 g/mol | 40.078 g/mol | 32.06 g/mol | 56.077 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -73 °C | 850 °C | 112.8 °C | 2580 °C boiling point | -10 °C | 1484 °C | 444.7 °C | 2850 °C density | 0.002619 g/cm^3 (at 25 °C) | 1.54 g/cm^3 | 2.07 g/cm^3 | 3.3 g/cm^3 solubility in water | | decomposes | | reacts surface tension | 0.02859 N/m | | | dynamic viscosity | 1.282×10^-5 Pa s (at 25 °C) | | |