HNO3 + CuS = H2O + S + NO + NO2 + Cu(NO3)2

HNO_3 nitric acid + CuS cupric sulfide ⟶ H_2O water + S mixed sulfur + NO nitric oxide + NO_2 nitrogen dioxide + Cu(NO_3)_2 copper(II) nitrate

Balance the chemical equation algebraically: HNO_3 + CuS ⟶ H_2O + S + NO + NO_2 + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CuS ⟶ c_3 H_2O + c_4 S + c_5 NO + c_6 NO_2 + c_7 Cu(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cu and S: H: | c_1 = 2 c_3 N: | c_1 = c_5 + c_6 + 2 c_7 O: | 3 c_1 = c_3 + c_5 + 2 c_6 + 6 c_7 Cu: | c_2 = c_7 S: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/4 + 1/2 c_3 = c_1/2 c_4 = c_1/4 + 1/2 c_5 = 1 c_6 = c_1/2 - 2 c_7 = c_1/4 + 1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 10 and solve for the remaining coefficients: c_1 = 10 c_2 = 3 c_3 = 5 c_4 = 3 c_5 = 1 c_6 = 3 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 3 CuS ⟶ 5 H_2O + 3 S + NO + 3 NO_2 + 3 Cu(NO_3)_2

+ ⟶ + + + +

nitric acid + cupric sulfide ⟶ water + mixed sulfur + nitric oxide + nitrogen dioxide + copper(II) nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + CuS ⟶ H_2O + S + NO + NO_2 + Cu(NO_3)_2 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: 10 HNO_3 + 3 CuS ⟶ 5 H_2O + 3 S + NO + 3 NO_2 + 3 Cu(NO_3)_2 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 HNO_3 | 10 | -10 CuS | 3 | -3 H_2O | 5 | 5 S | 3 | 3 NO | 1 | 1 NO_2 | 3 | 3 Cu(NO_3)_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 10 | -10 | ([HNO3])^(-10) CuS | 3 | -3 | ([CuS])^(-3) H_2O | 5 | 5 | ([H2O])^5 S | 3 | 3 | ([S])^3 NO | 1 | 1 | [NO] NO_2 | 3 | 3 | ([NO2])^3 Cu(NO_3)_2 | 3 | 3 | ([Cu(NO3)2])^3 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 = ([HNO3])^(-10) ([CuS])^(-3) ([H2O])^5 ([S])^3 [NO] ([NO2])^3 ([Cu(NO3)2])^3 = (([H2O])^5 ([S])^3 [NO] ([NO2])^3 ([Cu(NO3)2])^3)/(([HNO3])^10 ([CuS])^3)

Construct the rate of reaction expression for: HNO_3 + CuS ⟶ H_2O + S + NO + NO_2 + Cu(NO_3)_2 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: 10 HNO_3 + 3 CuS ⟶ 5 H_2O + 3 S + NO + 3 NO_2 + 3 Cu(NO_3)_2 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 HNO_3 | 10 | -10 CuS | 3 | -3 H_2O | 5 | 5 S | 3 | 3 NO | 1 | 1 NO_2 | 3 | 3 Cu(NO_3)_2 | 3 | 3 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) CuS | 3 | -3 | -1/3 (Δ[CuS])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NO | 1 | 1 | (Δ[NO])/(Δt) NO_2 | 3 | 3 | 1/3 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 3 | 3 | 1/3 (Δ[Cu(NO3)2])/(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 = -1/10 (Δ[HNO3])/(Δt) = -1/3 (Δ[CuS])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = (Δ[NO])/(Δt) = 1/3 (Δ[NO2])/(Δt) = 1/3 (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | cupric sulfide | water | mixed sulfur | nitric oxide | nitrogen dioxide | copper(II) nitrate formula | HNO_3 | CuS | H_2O | S | NO | NO_2 | Cu(NO_3)_2 Hill formula | HNO_3 | CuS | H_2O | S | NO | NO_2 | CuN_2O_6 name | nitric acid | cupric sulfide | water | mixed sulfur | nitric oxide | nitrogen dioxide | copper(II) nitrate IUPAC name | nitric acid | | water | sulfur | nitric oxide | Nitrogen dioxide | copper(II) nitrate