O2 + ZnS = ZnO + SO3

O_2 oxygen + ZnS zinc sulfide ⟶ ZnO zinc oxide + SO_3 sulfur trioxide

Balance the chemical equation algebraically: O_2 + ZnS ⟶ ZnO + SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 ZnS ⟶ c_3 ZnO + c_4 SO_3 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_3 + 3 c_4 S: | c_2 = c_4 Zn: | 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + ZnS ⟶ ZnO + SO_3

+ ⟶ +

oxygen + zinc sulfide ⟶ zinc oxide + sulfur trioxide

| oxygen | zinc sulfide | zinc oxide | sulfur trioxide molecular free energy | 231.7 kJ/mol | -201 kJ/mol | -320.5 kJ/mol | -373.8 kJ/mol total free energy | 463.4 kJ/mol | -201 kJ/mol | -320.5 kJ/mol | -373.8 kJ/mol | G_initial = 262.4 kJ/mol | | G_final = -694.3 kJ/mol | ΔG_rxn^0 | -694.3 kJ/mol - 262.4 kJ/mol = -956.7 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: O_2 + ZnS ⟶ ZnO + SO_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: 2 O_2 + ZnS ⟶ ZnO + SO_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 O_2 | 2 | -2 ZnS | 1 | -1 ZnO | 1 | 1 SO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 2 | -2 | ([O2])^(-2) ZnS | 1 | -1 | ([ZnS])^(-1) ZnO | 1 | 1 | [ZnO] SO_3 | 1 | 1 | [SO3] 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])^(-2) ([ZnS])^(-1) [ZnO] [SO3] = ([ZnO] [SO3])/(([O2])^2 [ZnS])

Construct the rate of reaction expression for: O_2 + ZnS ⟶ ZnO + SO_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: 2 O_2 + ZnS ⟶ ZnO + SO_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 O_2 | 2 | -2 ZnS | 1 | -1 ZnO | 1 | 1 SO_3 | 1 | 1 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 | 2 | -2 | -1/2 (Δ[O2])/(Δt) ZnS | 1 | -1 | -(Δ[ZnS])/(Δt) ZnO | 1 | 1 | (Δ[ZnO])/(Δt) SO_3 | 1 | 1 | (Δ[SO3])/(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 = -1/2 (Δ[O2])/(Δt) = -(Δ[ZnS])/(Δt) = (Δ[ZnO])/(Δt) = (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | zinc sulfide | zinc oxide | sulfur trioxide formula | O_2 | ZnS | ZnO | SO_3 Hill formula | O_2 | SZn | OZn | O_3S name | oxygen | zinc sulfide | zinc oxide | sulfur trioxide IUPAC name | molecular oxygen | thioxozinc | oxozinc | sulfur trioxide

| oxygen | zinc sulfide | zinc oxide | sulfur trioxide molar mass | 31.998 g/mol | 97.44 g/mol | 81.38 g/mol | 80.06 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) melting point | -218 °C | 1064 °C | 1975 °C | 16.8 °C boiling point | -183 °C | | 2360 °C | 44.7 °C density | 0.001429 g/cm^3 (at 0 °C) | 4.1 g/cm^3 | 5.6 g/cm^3 | 1.97 g/cm^3 solubility in water | | | | reacts surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | 0.00159 Pa s (at 30 °C) odor | odorless | | odorless |