C + CaSO4 = CO2 + CaS

C activated charcoal + CaSO_4 calcium sulfate ⟶ CO_2 carbon dioxide + CaS calcium sulfide

Balance the chemical equation algebraically: C + CaSO_4 ⟶ CO_2 + CaS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 CaSO_4 ⟶ c_3 CO_2 + c_4 CaS 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_3 Ca: | c_2 = c_4 O: | 4 c_2 = 2 c_3 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 C + CaSO_4 ⟶ 2 CO_2 + CaS

+ ⟶ +

activated charcoal + calcium sulfate ⟶ carbon dioxide + calcium sulfide

Construct the equilibrium constant, K, expression for: C + CaSO_4 ⟶ CO_2 + CaS 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: 2 C + CaSO_4 ⟶ 2 CO_2 + CaS 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 | 2 | -2 CaSO_4 | 1 | -1 CO_2 | 2 | 2 CaS | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 2 | -2 | ([C])^(-2) CaSO_4 | 1 | -1 | ([CaSO4])^(-1) CO_2 | 2 | 2 | ([CO2])^2 CaS | 1 | 1 | [CaS] 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])^(-2) ([CaSO4])^(-1) ([CO2])^2 [CaS] = (([CO2])^2 [CaS])/(([C])^2 [CaSO4])

Construct the rate of reaction expression for: C + CaSO_4 ⟶ CO_2 + CaS 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: 2 C + CaSO_4 ⟶ 2 CO_2 + CaS 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 | 2 | -2 CaSO_4 | 1 | -1 CO_2 | 2 | 2 CaS | 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 | 2 | -2 | -1/2 (Δ[C])/(Δt) CaSO_4 | 1 | -1 | -(Δ[CaSO4])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) CaS | 1 | 1 | (Δ[CaS])/(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 = -1/2 (Δ[C])/(Δt) = -(Δ[CaSO4])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[CaS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | calcium sulfate | carbon dioxide | calcium sulfide formula | C | CaSO_4 | CO_2 | CaS Hill formula | C | CaO_4S | CO_2 | CaS name | activated charcoal | calcium sulfate | carbon dioxide | calcium sulfide IUPAC name | carbon | calcium sulfate | carbon dioxide | thioxocalcium

| activated charcoal | calcium sulfate | carbon dioxide | calcium sulfide molar mass | 12.011 g/mol | 136.13 g/mol | 44.009 g/mol | 72.14 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) melting point | 3550 °C | | -56.56 °C (at triple point) | 2450 °C boiling point | 4027 °C | | -78.5 °C (at sublimation point) | density | 2.26 g/cm^3 | | 0.00184212 g/cm^3 (at 20 °C) | 2.5 g/cm^3 solubility in water | insoluble | slightly soluble | | decomposes dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | odorless | odorless |