O2 + Al2S3 = Al2O3 + SO3

Input interpretation

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O_2 oxygen + Al_2S_3 aluminum sulfide ⟶ Al_2O_3 aluminum oxide + SO_3 sulfur trioxide

Balanced equation

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Balance the chemical equation algebraically: O_2 + Al_2S_3 ⟶ Al_2O_3 + SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Al_2S_3 ⟶ c_3 Al_2O_3 + c_4 SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Al and S: O: | 2 c_1 = 3 c_3 + 3 c_4 Al: | 2 c_2 = 2 c_3 S: | 3 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 = 6 c_2 = 1 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 O_2 + Al_2S_3 ⟶ Al_2O_3 + 3 SO_3

+ ⟶ +

Names

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oxygen + aluminum sulfide ⟶ aluminum oxide + sulfur trioxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: O_2 + Al_2S_3 ⟶ Al_2O_3 + SO_3 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: 6 O_2 + Al_2S_3 ⟶ Al_2O_3 + 3 SO_3 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 O_2 | 6 | -6 Al_2S_3 | 1 | -1 Al_2O_3 | 1 | 1 SO_3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 6 | -6 | ([O2])^(-6) Al_2S_3 | 1 | -1 | ([Al2S3])^(-1) Al_2O_3 | 1 | 1 | [Al2O3] SO_3 | 3 | 3 | ([SO3])^3 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 = ([O2])^(-6) ([Al2S3])^(-1) [Al2O3] ([SO3])^3 = ([Al2O3] ([SO3])^3)/(([O2])^6 [Al2S3])

Rate of reaction

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Construct the rate of reaction expression for: O_2 + Al_2S_3 ⟶ Al_2O_3 + SO_3 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: 6 O_2 + Al_2S_3 ⟶ Al_2O_3 + 3 SO_3 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 O_2 | 6 | -6 Al_2S_3 | 1 | -1 Al_2O_3 | 1 | 1 SO_3 | 3 | 3 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 O_2 | 6 | -6 | -1/6 (Δ[O2])/(Δt) Al_2S_3 | 1 | -1 | -(Δ[Al2S3])/(Δt) Al_2O_3 | 1 | 1 | (Δ[Al2O3])/(Δt) SO_3 | 3 | 3 | 1/3 (Δ[SO3])/(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 = -1/6 (Δ[O2])/(Δt) = -(Δ[Al2S3])/(Δt) = (Δ[Al2O3])/(Δt) = 1/3 (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)