Zn + S8 = ZnS

Zn zinc + S_8 rhombic sulfur ⟶ ZnS zinc sulfide

Balance the chemical equation algebraically: Zn + S_8 ⟶ ZnS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 S_8 ⟶ c_3 ZnS Set the number of atoms in the reactants equal to the number of atoms in the products for Zn and S: Zn: | 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 Zn + S_8 ⟶ 8 ZnS

+ ⟶

zinc + rhombic sulfur ⟶ zinc sulfide

| zinc | rhombic sulfur | zinc sulfide molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -206 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -1648 kJ/mol | H_initial = 0 kJ/mol | | H_final = -1648 kJ/mol ΔH_rxn^0 | -1648 kJ/mol - 0 kJ/mol = -1648 kJ/mol (exothermic) | |

| zinc | rhombic sulfur | zinc sulfide molecular entropy | 42 J/(mol K) | 32.1 J/(mol K) | 58 J/(mol K) total entropy | 336 J/(mol K) | 32.1 J/(mol K) | 464 J/(mol K) | S_initial = 368.1 J/(mol K) | | S_final = 464 J/(mol K) ΔS_rxn^0 | 464 J/(mol K) - 368.1 J/(mol K) = 95.9 J/(mol K) (endoentropic) | |

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

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

| zinc | rhombic sulfur | zinc sulfide formula | Zn | S_8 | ZnS Hill formula | Zn | S_8 | SZn name | zinc | rhombic sulfur | zinc sulfide IUPAC name | zinc | octathiocane | thioxozinc

| zinc | rhombic sulfur | zinc sulfide molar mass | 65.38 g/mol | 256.5 g/mol | 97.44 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 420 °C | | 1064 °C boiling point | 907 °C | | density | 7.14 g/cm^3 | 2.07 g/cm^3 | 4.1 g/cm^3 solubility in water | insoluble | | odor | odorless | |