S + Li = LiS

S mixed sulfur + Li lithium ⟶ LiS

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

+ ⟶ LiS

mixed sulfur + lithium ⟶ LiS

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

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

| mixed sulfur | lithium | LiS formula | S | Li | LiS name | mixed sulfur | lithium | IUPAC name | sulfur | lithium |

| mixed sulfur | lithium | LiS molar mass | 32.06 g/mol | 6.94 g/mol | 39 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 180 °C | boiling point | 444.7 °C | 1342 °C | density | 2.07 g/cm^3 | 0.534 g/cm^3 | solubility in water | | decomposes | surface tension | | 0.3975 N/m |