S8 + Ti = TiS2

S_8 rhombic sulfur + Ti titanium ⟶ TiS_2 titanium disulfide

Balance the chemical equation algebraically: S_8 + Ti ⟶ TiS_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S_8 + c_2 Ti ⟶ c_3 TiS_2 Set the number of atoms in the reactants equal to the number of atoms in the products for S and Ti: S: | 8 c_1 = 2 c_3 Ti: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S_8 + 4 Ti ⟶ 4 TiS_2

+ ⟶

rhombic sulfur + titanium ⟶ titanium disulfide

Construct the equilibrium constant, K, expression for: S_8 + Ti ⟶ TiS_2 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: S_8 + 4 Ti ⟶ 4 TiS_2 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_8 | 1 | -1 Ti | 4 | -4 TiS_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S_8 | 1 | -1 | ([S8])^(-1) Ti | 4 | -4 | ([Ti])^(-4) TiS_2 | 4 | 4 | ([TiS2])^4 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 = ([S8])^(-1) ([Ti])^(-4) ([TiS2])^4 = ([TiS2])^4/([S8] ([Ti])^4)

Construct the rate of reaction expression for: S_8 + Ti ⟶ TiS_2 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: S_8 + 4 Ti ⟶ 4 TiS_2 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_8 | 1 | -1 Ti | 4 | -4 TiS_2 | 4 | 4 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_8 | 1 | -1 | -(Δ[S8])/(Δt) Ti | 4 | -4 | -1/4 (Δ[Ti])/(Δt) TiS_2 | 4 | 4 | 1/4 (Δ[TiS2])/(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 = -(Δ[S8])/(Δt) = -1/4 (Δ[Ti])/(Δt) = 1/4 (Δ[TiS2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| rhombic sulfur | titanium | titanium disulfide formula | S_8 | Ti | TiS_2 Hill formula | S_8 | Ti | S_2Ti name | rhombic sulfur | titanium | titanium disulfide IUPAC name | octathiocane | titanium | dithioxotitanium

| rhombic sulfur | titanium | titanium disulfide molar mass | 256.5 g/mol | 47.867 g/mol | 112 g/mol phase | solid (at STP) | solid (at STP) | melting point | | 1660 °C | boiling point | | 3287 °C | density | 2.07 g/cm^3 | 4.5 g/cm^3 | 3.22 g/cm^3 solubility in water | | insoluble | insoluble