O2 + CuS = CuSO4

O_2 oxygen + CuS cupric sulfide ⟶ CuSO_4 copper(II) sulfate

Balance the chemical equation algebraically: O_2 + CuS ⟶ CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 CuS ⟶ c_3 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cu and S: O: | 2 c_1 = 4 c_3 Cu: | c_2 = c_3 S: | 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 O_2 + CuS ⟶ CuSO_4

+ ⟶

oxygen + cupric sulfide ⟶ copper(II) sulfate

| oxygen | cupric sulfide | copper(II) sulfate molecular enthalpy | 0 kJ/mol | -53.1 kJ/mol | -771.4 kJ/mol total enthalpy | 0 kJ/mol | -53.1 kJ/mol | -771.4 kJ/mol | H_initial = -53.1 kJ/mol | | H_final = -771.4 kJ/mol ΔH_rxn^0 | -771.4 kJ/mol - -53.1 kJ/mol = -718.3 kJ/mol (exothermic) | |

| oxygen | cupric sulfide | copper(II) sulfate molecular free energy | 231.7 kJ/mol | -53.6 kJ/mol | -662.2 kJ/mol total free energy | 463.4 kJ/mol | -53.6 kJ/mol | -662.2 kJ/mol | G_initial = 409.8 kJ/mol | | G_final = -662.2 kJ/mol ΔG_rxn^0 | -662.2 kJ/mol - 409.8 kJ/mol = -1072 kJ/mol (exergonic) | |

Construct the equilibrium constant, K, expression for: O_2 + CuS ⟶ CuSO_4 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 + CuS ⟶ CuSO_4 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 CuS | 1 | -1 CuSO_4 | 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) CuS | 1 | -1 | ([CuS])^(-1) CuSO_4 | 1 | 1 | [CuSO4] 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) ([CuS])^(-1) [CuSO4] = ([CuSO4])/(([O2])^2 [CuS])

Construct the rate of reaction expression for: O_2 + CuS ⟶ CuSO_4 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 + CuS ⟶ CuSO_4 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 CuS | 1 | -1 CuSO_4 | 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) CuS | 1 | -1 | -(Δ[CuS])/(Δt) CuSO_4 | 1 | 1 | (Δ[CuSO4])/(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[CuS])/(Δt) = (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | cupric sulfide | copper(II) sulfate formula | O_2 | CuS | CuSO_4 Hill formula | O_2 | CuS | CuO_4S name | oxygen | cupric sulfide | copper(II) sulfate IUPAC name | molecular oxygen | | copper sulfate

| oxygen | cupric sulfide | copper(II) sulfate molar mass | 31.998 g/mol | 95.61 g/mol | 159.6 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -218 °C | 220 °C | 200 °C boiling point | -183 °C | | density | 0.001429 g/cm^3 (at 0 °C) | 4.6 g/cm^3 | 3.603 g/cm^3 surface tension | 0.01347 N/m | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 3.68×10^-5 Pa s (at 1250 °C) | odor | odorless | |