S + Cr = Cr2S3

S mixed sulfur + Cr chromium ⟶ Cr_2S_3 chromium(III) sulfide

Balance the chemical equation algebraically: S + Cr ⟶ Cr_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 Cr ⟶ c_3 Cr_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for S and Cr: S: | c_1 = 3 c_3 Cr: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 S + 2 Cr ⟶ Cr_2S_3

+ ⟶

mixed sulfur + chromium ⟶ chromium(III) sulfide

Construct the equilibrium constant, K, expression for: S + Cr ⟶ Cr_2S_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: 3 S + 2 Cr ⟶ Cr_2S_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 S | 3 | -3 Cr | 2 | -2 Cr_2S_3 | 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) Cr | 2 | -2 | ([Cr])^(-2) Cr_2S_3 | 1 | 1 | [Cr2S3] 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) ([Cr])^(-2) [Cr2S3] = ([Cr2S3])/(([S])^3 ([Cr])^2)

Construct the rate of reaction expression for: S + Cr ⟶ Cr_2S_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: 3 S + 2 Cr ⟶ Cr_2S_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 S | 3 | -3 Cr | 2 | -2 Cr_2S_3 | 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) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) Cr_2S_3 | 1 | 1 | (Δ[Cr2S3])/(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) = -1/2 (Δ[Cr])/(Δt) = (Δ[Cr2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | chromium | chromium(III) sulfide formula | S | Cr | Cr_2S_3 name | mixed sulfur | chromium | chromium(III) sulfide IUPAC name | sulfur | chromium | chromium(+3) cation trisulfide

| mixed sulfur | chromium | chromium(III) sulfide molar mass | 32.06 g/mol | 51.9961 g/mol | 200.2 g/mol phase | solid (at STP) | solid (at STP) | melting point | 112.8 °C | 1857 °C | boiling point | 444.7 °C | 2672 °C | density | 2.07 g/cm^3 | 7.14 g/cm^3 | 3.77 g/cm^3 solubility in water | | insoluble | odor | | odorless |