S + Si = SiS2

S mixed sulfur + Si silicon ⟶ S_2Si silicon disulfide

Balance the chemical equation algebraically: S + Si ⟶ S_2Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Si ⟶ c_3 S_2Si Set the number of atoms in the reactants equal to the number of atoms in the products for S and Si: S: | c_1 = 2 c_3 Si: | 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 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 S + Si ⟶ S_2Si

+ ⟶

mixed sulfur + silicon ⟶ silicon disulfide

Construct the equilibrium constant, K, expression for: S + Si ⟶ S_2Si 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 S + Si ⟶ S_2Si 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 | 2 | -2 Si | 1 | -1 S_2Si | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 2 | -2 | ([S])^(-2) Si | 1 | -1 | ([Si])^(-1) S_2Si | 1 | 1 | [S2Si] 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])^(-2) ([Si])^(-1) [S2Si] = ([S2Si])/(([S])^2 [Si])

Construct the rate of reaction expression for: S + Si ⟶ S_2Si 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 S + Si ⟶ S_2Si 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 | 2 | -2 Si | 1 | -1 S_2Si | 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 | 2 | -2 | -1/2 (Δ[S])/(Δt) Si | 1 | -1 | -(Δ[Si])/(Δt) S_2Si | 1 | 1 | (Δ[S2Si])/(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[S])/(Δt) = -(Δ[Si])/(Δt) = (Δ[S2Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | silicon | silicon disulfide formula | S | Si | S_2Si name | mixed sulfur | silicon | silicon disulfide IUPAC name | sulfur | silicon | disulfanylidenesilane

| mixed sulfur | silicon | silicon disulfide molar mass | 32.06 g/mol | 28.085 g/mol | 92.21 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 112.8 °C | 1410 °C | 1090 °C boiling point | 444.7 °C | 2355 °C | density | 2.07 g/cm^3 | 2.33 g/cm^3 | 2.02 g/cm^3 solubility in water | | insoluble |