O2 + ZnS = SO2 + Zn

O_2 oxygen + ZnS zinc sulfide ⟶ SO_2 sulfur dioxide + Zn zinc

Balance the chemical equation algebraically: O_2 + ZnS ⟶ SO_2 + Zn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 ZnS ⟶ c_3 SO_2 + c_4 Zn 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 = 2 c_3 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + ZnS ⟶ SO_2 + Zn

+ ⟶ +

oxygen + zinc sulfide ⟶ sulfur dioxide + zinc

| oxygen | zinc sulfide | sulfur dioxide | zinc molecular enthalpy | 0 kJ/mol | -206 kJ/mol | -296.8 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -206 kJ/mol | -296.8 kJ/mol | 0 kJ/mol | H_initial = -206 kJ/mol | | H_final = -296.8 kJ/mol | ΔH_rxn^0 | -296.8 kJ/mol - -206 kJ/mol = -90.8 kJ/mol (exothermic) | | |

| oxygen | zinc sulfide | sulfur dioxide | zinc molecular entropy | 205 J/(mol K) | 58 J/(mol K) | 248 J/(mol K) | 42 J/(mol K) total entropy | 205 J/(mol K) | 58 J/(mol K) | 248 J/(mol K) | 42 J/(mol K) | S_initial = 263 J/(mol K) | | S_final = 290 J/(mol K) | ΔS_rxn^0 | 290 J/(mol K) - 263 J/(mol K) = 27 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: O_2 + ZnS ⟶ SO_2 + Zn 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 + ZnS ⟶ SO_2 + Zn 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 | 1 | -1 SO_2 | 1 | 1 Zn | 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 | 1 | -1 | ([O2])^(-1) ZnS | 1 | -1 | ([ZnS])^(-1) SO_2 | 1 | 1 | [SO2] Zn | 1 | 1 | [Zn] 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])^(-1) [SO2] [Zn] = ([SO2] [Zn])/([O2] [ZnS])

Construct the rate of reaction expression for: O_2 + ZnS ⟶ SO_2 + Zn 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 + ZnS ⟶ SO_2 + Zn 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 | 1 | -1 SO_2 | 1 | 1 Zn | 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 | 1 | -1 | -(Δ[O2])/(Δt) ZnS | 1 | -1 | -(Δ[ZnS])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) Zn | 1 | 1 | (Δ[Zn])/(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) = -(Δ[ZnS])/(Δt) = (Δ[SO2])/(Δt) = (Δ[Zn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | zinc sulfide | sulfur dioxide | zinc formula | O_2 | ZnS | SO_2 | Zn Hill formula | O_2 | SZn | O_2S | Zn name | oxygen | zinc sulfide | sulfur dioxide | zinc IUPAC name | molecular oxygen | thioxozinc | sulfur dioxide | zinc

| oxygen | zinc sulfide | sulfur dioxide | zinc molar mass | 31.998 g/mol | 97.44 g/mol | 64.06 g/mol | 65.38 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -218 °C | 1064 °C | -73 °C | 420 °C boiling point | -183 °C | | -10 °C | 907 °C density | 0.001429 g/cm^3 (at 0 °C) | 4.1 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 7.14 g/cm^3 solubility in water | | | | insoluble surface tension | 0.01347 N/m | | 0.02859 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 1.282×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless