Cu + S8 = CuS

Cu copper + S_8 rhombic sulfur ⟶ CuS cupric sulfide

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

+ ⟶

copper + rhombic sulfur ⟶ cupric sulfide

| copper | rhombic sulfur | cupric sulfide molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -53.1 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -424.8 kJ/mol | H_initial = 0 kJ/mol | | H_final = -424.8 kJ/mol ΔH_rxn^0 | -424.8 kJ/mol - 0 kJ/mol = -424.8 kJ/mol (exothermic) | |

| copper | rhombic sulfur | cupric sulfide molecular entropy | 33 J/(mol K) | 32.1 J/(mol K) | 67 J/(mol K) total entropy | 264 J/(mol K) | 32.1 J/(mol K) | 536 J/(mol K) | S_initial = 296.1 J/(mol K) | | S_final = 536 J/(mol K) ΔS_rxn^0 | 536 J/(mol K) - 296.1 J/(mol K) = 239.9 J/(mol K) (endoentropic) | |

Construct the equilibrium constant, K, expression for: Cu + S_8 ⟶ CuS 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: 8 Cu + S_8 ⟶ 8 CuS 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 Cu | 8 | -8 S_8 | 1 | -1 CuS | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 8 | -8 | ([Cu])^(-8) S_8 | 1 | -1 | ([S8])^(-1) CuS | 8 | 8 | ([CuS])^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 = ([Cu])^(-8) ([S8])^(-1) ([CuS])^8 = ([CuS])^8/(([Cu])^8 [S8])

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

| copper | rhombic sulfur | cupric sulfide formula | Cu | S_8 | CuS name | copper | rhombic sulfur | cupric sulfide IUPAC name | copper | octathiocane |

| copper | rhombic sulfur | cupric sulfide molar mass | 63.546 g/mol | 256.5 g/mol | 95.61 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1083 °C | | 220 °C boiling point | 2567 °C | | density | 8.96 g/cm^3 | 2.07 g/cm^3 | 4.6 g/cm^3 solubility in water | insoluble | | dynamic viscosity | | | 3.68×10^-5 Pa s (at 1250 °C) odor | odorless | |