Cr + S8 = Cr2S3

Cr chromium + S_8 rhombic sulfur ⟶ Cr_2S_3 chromium(III) sulfide

Balance the chemical equation algebraically: Cr + S_8 ⟶ Cr_2S_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr + c_2 S_8 ⟶ c_3 Cr_2S_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr and S: Cr: | c_1 = 2 c_3 S: | 8 c_2 = 3 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 = 16/3 c_2 = 1 c_3 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 16 c_2 = 3 c_3 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 Cr + 3 S_8 ⟶ 8 Cr_2S_3

+ ⟶

chromium + rhombic sulfur ⟶ chromium(III) sulfide

Construct the equilibrium constant, K, expression for: Cr + S_8 ⟶ 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: 16 Cr + 3 S_8 ⟶ 8 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 Cr | 16 | -16 S_8 | 3 | -3 Cr_2S_3 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr | 16 | -16 | ([Cr])^(-16) S_8 | 3 | -3 | ([S8])^(-3) Cr_2S_3 | 8 | 8 | ([Cr2S3])^8 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 = ([Cr])^(-16) ([S8])^(-3) ([Cr2S3])^8 = ([Cr2S3])^8/(([Cr])^16 ([S8])^3)

Construct the rate of reaction expression for: Cr + S_8 ⟶ 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: 16 Cr + 3 S_8 ⟶ 8 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 Cr | 16 | -16 S_8 | 3 | -3 Cr_2S_3 | 8 | 8 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 Cr | 16 | -16 | -1/16 (Δ[Cr])/(Δt) S_8 | 3 | -3 | -1/3 (Δ[S8])/(Δt) Cr_2S_3 | 8 | 8 | 1/8 (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 = -1/16 (Δ[Cr])/(Δt) = -1/3 (Δ[S8])/(Δt) = 1/8 (Δ[Cr2S3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium | rhombic sulfur | chromium(III) sulfide formula | Cr | S_8 | Cr_2S_3 name | chromium | rhombic sulfur | chromium(III) sulfide IUPAC name | chromium | octathiocane | chromium(+3) cation trisulfide

| chromium | rhombic sulfur | chromium(III) sulfide molar mass | 51.9961 g/mol | 256.5 g/mol | 200.2 g/mol phase | solid (at STP) | solid (at STP) | melting point | 1857 °C | | boiling point | 2672 °C | | density | 7.14 g/cm^3 | 2.07 g/cm^3 | 3.77 g/cm^3 solubility in water | insoluble | | odor | odorless | |