Cr + S8 = CrS2

Cr chromium + S_8 rhombic sulfur ⟶ CrS2

Balance the chemical equation algebraically: Cr + S_8 ⟶ CrS2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr + c_2 S_8 ⟶ c_3 CrS2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr and S: Cr: | c_1 = c_3 S: | 8 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Cr + S_8 ⟶ 4 CrS2

+ ⟶ CrS2

chromium + rhombic sulfur ⟶ CrS2

Construct the equilibrium constant, K, expression for: Cr + S_8 ⟶ CrS2 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: 4 Cr + S_8 ⟶ 4 CrS2 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 | 4 | -4 S_8 | 1 | -1 CrS2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr | 4 | -4 | ([Cr])^(-4) S_8 | 1 | -1 | ([S8])^(-1) CrS2 | 4 | 4 | ([CrS2])^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 = ([Cr])^(-4) ([S8])^(-1) ([CrS2])^4 = ([CrS2])^4/(([Cr])^4 [S8])

Construct the rate of reaction expression for: Cr + S_8 ⟶ CrS2 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: 4 Cr + S_8 ⟶ 4 CrS2 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 | 4 | -4 S_8 | 1 | -1 CrS2 | 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 Cr | 4 | -4 | -1/4 (Δ[Cr])/(Δt) S_8 | 1 | -1 | -(Δ[S8])/(Δt) CrS2 | 4 | 4 | 1/4 (Δ[CrS2])/(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 = -1/4 (Δ[Cr])/(Δt) = -(Δ[S8])/(Δt) = 1/4 (Δ[CrS2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium | rhombic sulfur | CrS2 formula | Cr | S_8 | CrS2 name | chromium | rhombic sulfur | IUPAC name | chromium | octathiocane |

| chromium | rhombic sulfur | CrS2 molar mass | 51.9961 g/mol | 256.5 g/mol | 116.1 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 | solubility in water | insoluble | | odor | odorless | |