S + Al = AlS3

S mixed sulfur + Al aluminum ⟶ AlS3

Balance the chemical equation algebraically: S + Al ⟶ AlS3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Al ⟶ c_3 AlS3 Set the number of atoms in the reactants equal to the number of atoms in the products for S and Al: S: | c_1 = 3 c_3 Al: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 S + Al ⟶ AlS3

+ ⟶ AlS3

mixed sulfur + aluminum ⟶ AlS3

Construct the equilibrium constant, K, expression for: S + Al ⟶ AlS3 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: 3 S + Al ⟶ AlS3 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 S | 3 | -3 Al | 1 | -1 AlS3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 3 | -3 | ([S])^(-3) Al | 1 | -1 | ([Al])^(-1) AlS3 | 1 | 1 | [AlS3] 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 = ([S])^(-3) ([Al])^(-1) [AlS3] = ([AlS3])/(([S])^3 [Al])

Construct the rate of reaction expression for: S + Al ⟶ AlS3 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: 3 S + Al ⟶ AlS3 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 S | 3 | -3 Al | 1 | -1 AlS3 | 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 S | 3 | -3 | -1/3 (Δ[S])/(Δt) Al | 1 | -1 | -(Δ[Al])/(Δt) AlS3 | 1 | 1 | (Δ[AlS3])/(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 = -1/3 (Δ[S])/(Δt) = -(Δ[Al])/(Δt) = (Δ[AlS3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | aluminum | AlS3 formula | S | Al | AlS3 name | mixed sulfur | aluminum | IUPAC name | sulfur | aluminum |

| mixed sulfur | aluminum | AlS3 molar mass | 32.06 g/mol | 26.9815385 g/mol | 123.2 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 660.4 °C | boiling point | 444.7 °C | 2460 °C | density | 2.07 g/cm^3 | 2.7 g/cm^3 | solubility in water | | insoluble | surface tension | | 0.817 N/m | dynamic viscosity | | 1.5×10^-4 Pa s (at 760 °C) | odor | | odorless |