C + BaSO4 = CO2 + BaS

C activated charcoal + BaSO_4 barium sulfate ⟶ CO_2 carbon dioxide + BaS barium sulfide

Balance the chemical equation algebraically: C + BaSO_4 ⟶ CO_2 + BaS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 BaSO_4 ⟶ c_3 CO_2 + c_4 BaS Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ba, O and S: C: | c_1 = c_3 Ba: | 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 + BaSO_4 ⟶ 2 CO_2 + BaS

+ ⟶ +

activated charcoal + barium sulfate ⟶ carbon dioxide + barium sulfide

Construct the equilibrium constant, K, expression for: C + BaSO_4 ⟶ CO_2 + BaS 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 + BaSO_4 ⟶ 2 CO_2 + BaS 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 BaSO_4 | 1 | -1 CO_2 | 2 | 2 BaS | 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) BaSO_4 | 1 | -1 | ([BaSO4])^(-1) CO_2 | 2 | 2 | ([CO2])^2 BaS | 1 | 1 | [BaS] 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) ([BaSO4])^(-1) ([CO2])^2 [BaS] = (([CO2])^2 [BaS])/(([C])^2 [BaSO4])

Construct the rate of reaction expression for: C + BaSO_4 ⟶ CO_2 + BaS 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 + BaSO_4 ⟶ 2 CO_2 + BaS 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 BaSO_4 | 1 | -1 CO_2 | 2 | 2 BaS | 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) BaSO_4 | 1 | -1 | -(Δ[BaSO4])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) BaS | 1 | 1 | (Δ[BaS])/(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[BaSO4])/(Δt) = 1/2 (Δ[CO2])/(Δt) = (Δ[BaS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | barium sulfate | carbon dioxide | barium sulfide formula | C | BaSO_4 | CO_2 | BaS Hill formula | C | BaO_4S | CO_2 | BaS name | activated charcoal | barium sulfate | carbon dioxide | barium sulfide IUPAC name | carbon | barium(+2) cation sulfate | carbon dioxide | thioxobarium

| activated charcoal | barium sulfate | carbon dioxide | barium sulfide molar mass | 12.011 g/mol | 233.38 g/mol | 44.009 g/mol | 169.39 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 1345 °C | -56.56 °C (at triple point) | 1999.85 °C boiling point | 4027 °C | | -78.5 °C (at sublimation point) | density | 2.26 g/cm^3 | 4.5 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 4.25 g/cm^3 solubility in water | insoluble | insoluble | | dynamic viscosity | | | 1.491×10^-5 Pa s (at 25 °C) | odor | | | odorless |