CuS + HNO2 = H2O + NO + CuSO4

CuS cupric sulfide + HNO_2 nitrous acid ⟶ H_2O water + NO nitric oxide + CuSO_4 copper(II) sulfate

Balance the chemical equation algebraically: CuS + HNO_2 ⟶ H_2O + NO + CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuS + c_2 HNO_2 ⟶ c_3 H_2O + c_4 NO + c_5 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, S, H, N and O: Cu: | c_1 = c_5 S: | c_1 = c_5 H: | c_2 = 2 c_3 N: | c_2 = c_4 O: | 2 c_2 = c_3 + c_4 + 4 c_5 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 = 8 c_3 = 4 c_4 = 8 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CuS + 8 HNO_2 ⟶ 4 H_2O + 8 NO + CuSO_4

+ ⟶ + +

cupric sulfide + nitrous acid ⟶ water + nitric oxide + copper(II) sulfate

Construct the equilibrium constant, K, expression for: CuS + HNO_2 ⟶ H_2O + NO + 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: CuS + 8 HNO_2 ⟶ 4 H_2O + 8 NO + 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 CuS | 1 | -1 HNO_2 | 8 | -8 H_2O | 4 | 4 NO | 8 | 8 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 CuS | 1 | -1 | ([CuS])^(-1) HNO_2 | 8 | -8 | ([HNO2])^(-8) H_2O | 4 | 4 | ([H2O])^4 NO | 8 | 8 | ([NO])^8 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 = ([CuS])^(-1) ([HNO2])^(-8) ([H2O])^4 ([NO])^8 [CuSO4] = (([H2O])^4 ([NO])^8 [CuSO4])/([CuS] ([HNO2])^8)

Construct the rate of reaction expression for: CuS + HNO_2 ⟶ H_2O + NO + 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: CuS + 8 HNO_2 ⟶ 4 H_2O + 8 NO + 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 CuS | 1 | -1 HNO_2 | 8 | -8 H_2O | 4 | 4 NO | 8 | 8 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 CuS | 1 | -1 | -(Δ[CuS])/(Δt) HNO_2 | 8 | -8 | -1/8 (Δ[HNO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO | 8 | 8 | 1/8 (Δ[NO])/(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 = -(Δ[CuS])/(Δt) = -1/8 (Δ[HNO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/8 (Δ[NO])/(Δt) = (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| cupric sulfide | nitrous acid | water | nitric oxide | copper(II) sulfate formula | CuS | HNO_2 | H_2O | NO | CuSO_4 Hill formula | CuS | HNO_2 | H_2O | NO | CuO_4S name | cupric sulfide | nitrous acid | water | nitric oxide | copper(II) sulfate IUPAC name | | nitrous acid | water | nitric oxide | copper sulfate