O2 + Cu2S = SO2 + Cu2O

O_2 (oxygen) + Cu_2S (copper(I) sulfide) ⟶ SO_2 (sulfur dioxide) + Cu_2O (copper(I) oxide)

Balance the chemical equation algebraically: O_2 + Cu_2S ⟶ SO_2 + Cu_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 Cu_2S ⟶ c_3 SO_2 + c_4 Cu_2O Set the number of atoms and the charges in the reactants equal to the number of atoms and the charges in the products for O, Cu and S: O: | 2 c_1 = 2 c_3 + c_4 Cu: | c_2 = c_4 S: | c_2 = c_3 Charges: | -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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 1 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 2 Cu_2S ⟶ 2 SO_2 + 2 Cu_2O

+ ⟶ +

oxygen + copper(I) sulfide ⟶ sulfur dioxide + copper(I) oxide

Construct the equilibrium constant, K, expression for: O_2 + Cu_2S ⟶ SO_2 + Cu_2O 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: 3 O_2 + 2 Cu_2S ⟶ 2 SO_2 + 2 Cu_2O 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 | 3 | -3 Cu_2S | 2 | -2 SO_2 | 2 | 2 Cu_2O | 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 | 3 | -3 | ([O2])^(-3) Cu_2S | 2 | -2 | ([Cu2S])^(-2) SO_2 | 2 | 2 | ([SO2])^2 Cu_2O | 2 | 2 | ([Cu2O])^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])^(-3) ([Cu2S])^(-2) ([SO2])^2 ([Cu2O])^2 = (([SO2])^2 ([Cu2O])^2)/(([O2])^3 ([Cu2S])^2)

Construct the rate of reaction expression for: O_2 + Cu_2S ⟶ SO_2 + Cu_2O 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: 3 O_2 + 2 Cu_2S ⟶ 2 SO_2 + 2 Cu_2O 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 | 3 | -3 Cu_2S | 2 | -2 SO_2 | 2 | 2 Cu_2O | 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 | 3 | -3 | -1/3 (Δ[O2])/(Δt) Cu_2S | 2 | -2 | -1/2 (Δ[Cu2S])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) Cu_2O | 2 | 2 | 1/2 (Δ[Cu2O])/(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 = -1/3 (Δ[O2])/(Δt) = -1/2 (Δ[Cu2S])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/2 (Δ[Cu2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | copper(I) sulfide | sulfur dioxide | copper(I) oxide formula | O_2 | Cu_2S | SO_2 | Cu_2O Hill formula | O_2 | Cu_2S_1 | O_2S | Cu_2O_1 name | oxygen | copper(I) sulfide | sulfur dioxide | copper(I) oxide IUPAC name | molecular oxygen | | sulfur dioxide |

| oxygen | copper(I) sulfide | sulfur dioxide | copper(I) oxide molar mass | 31.998 g/mol | 95.61 g/mol | 64.06 g/mol | 79.545 g/mol phase | gas (at STP) | | gas (at STP) | melting point | -218 °C | | -73 °C | boiling point | -183 °C | | -10 °C | density | 0.001429 g/cm^3 (at 0 °C) | 5.6 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 6 g/cm^3 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 | | |