O2 + ZnS = S + ZnO

O_2 oxygen + ZnS zinc sulfide ⟶ S mixed sulfur + ZnO zinc oxide

Balance the chemical equation algebraically: O_2 + ZnS ⟶ S + ZnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 ZnS ⟶ c_3 S + c_4 ZnO Set the number of atoms in the reactants equal to the number of atoms in the products for O, S and Zn: O: | 2 c_1 = c_4 S: | c_2 = c_3 Zn: | c_2 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 2 ZnS ⟶ 2 S + 2 ZnO

+ ⟶ +

oxygen + zinc sulfide ⟶ mixed sulfur + zinc oxide

Construct the equilibrium constant, K, expression for: O_2 + ZnS ⟶ S + ZnO 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: O_2 + 2 ZnS ⟶ 2 S + 2 ZnO 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 O_2 | 1 | -1 ZnS | 2 | -2 S | 2 | 2 ZnO | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) ZnS | 2 | -2 | ([ZnS])^(-2) S | 2 | 2 | ([S])^2 ZnO | 2 | 2 | ([ZnO])^2 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 = ([O2])^(-1) ([ZnS])^(-2) ([S])^2 ([ZnO])^2 = (([S])^2 ([ZnO])^2)/([O2] ([ZnS])^2)

Construct the rate of reaction expression for: O_2 + ZnS ⟶ S + ZnO 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: O_2 + 2 ZnS ⟶ 2 S + 2 ZnO 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 O_2 | 1 | -1 ZnS | 2 | -2 S | 2 | 2 ZnO | 2 | 2 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) ZnS | 2 | -2 | -1/2 (Δ[ZnS])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) ZnO | 2 | 2 | 1/2 (Δ[ZnO])/(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 = -(Δ[O2])/(Δt) = -1/2 (Δ[ZnS])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/2 (Δ[ZnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | zinc sulfide | mixed sulfur | zinc oxide formula | O_2 | ZnS | S | ZnO Hill formula | O_2 | SZn | S | OZn name | oxygen | zinc sulfide | mixed sulfur | zinc oxide IUPAC name | molecular oxygen | thioxozinc | sulfur | oxozinc

| oxygen | zinc sulfide | mixed sulfur | zinc oxide molar mass | 31.998 g/mol | 97.44 g/mol | 32.06 g/mol | 81.38 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | -218 °C | 1064 °C | 112.8 °C | 1975 °C boiling point | -183 °C | | 444.7 °C | 2360 °C density | 0.001429 g/cm^3 (at 0 °C) | 4.1 g/cm^3 | 2.07 g/cm^3 | 5.6 g/cm^3 surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | odor | odorless | | | odorless