HNO3 + CuS2 = H2O + H2SO4 + NO + Cu(NO3)2

HNO_3 nitric acid + CuS2 ⟶ H_2O water + H_2SO_4 sulfuric acid + NO nitric oxide + Cu(NO_3)_2 copper(II) nitrate

Balance the chemical equation algebraically: HNO_3 + CuS2 ⟶ H_2O + H_2SO_4 + NO + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CuS2 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO + c_6 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 + 2 c_4 N: | c_1 = c_5 + 2 c_6 O: | 3 c_1 = c_3 + 4 c_4 + c_5 + 6 c_6 Cu: | c_2 = c_6 S: | 2 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 = 20/3 c_2 = 1 c_3 = 4/3 c_4 = 2 c_5 = 14/3 c_6 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 20 c_2 = 3 c_3 = 4 c_4 = 6 c_5 = 14 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 20 HNO_3 + 3 CuS2 ⟶ 4 H_2O + 6 H_2SO_4 + 14 NO + 3 Cu(NO_3)_2

+ CuS2 ⟶ + + +

nitric acid + CuS2 ⟶ water + sulfuric acid + nitric oxide + copper(II) nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + CuS2 ⟶ H_2O + H_2SO_4 + NO + 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: 20 HNO_3 + 3 CuS2 ⟶ 4 H_2O + 6 H_2SO_4 + 14 NO + 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 | 20 | -20 CuS2 | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 6 | 6 NO | 14 | 14 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 | 20 | -20 | ([HNO3])^(-20) CuS2 | 3 | -3 | ([CuS2])^(-3) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 6 | 6 | ([H2SO4])^6 NO | 14 | 14 | ([NO])^14 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])^(-20) ([CuS2])^(-3) ([H2O])^4 ([H2SO4])^6 ([NO])^14 ([Cu(NO3)2])^3 = (([H2O])^4 ([H2SO4])^6 ([NO])^14 ([Cu(NO3)2])^3)/(([HNO3])^20 ([CuS2])^3)

Construct the rate of reaction expression for: HNO_3 + CuS2 ⟶ H_2O + H_2SO_4 + NO + 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: 20 HNO_3 + 3 CuS2 ⟶ 4 H_2O + 6 H_2SO_4 + 14 NO + 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 | 20 | -20 CuS2 | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 6 | 6 NO | 14 | 14 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 | 20 | -20 | -1/20 (Δ[HNO3])/(Δt) CuS2 | 3 | -3 | -1/3 (Δ[CuS2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 6 | 6 | 1/6 (Δ[H2SO4])/(Δt) NO | 14 | 14 | 1/14 (Δ[NO])/(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 = -1/20 (Δ[HNO3])/(Δt) = -1/3 (Δ[CuS2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/6 (Δ[H2SO4])/(Δt) = 1/14 (Δ[NO])/(Δt) = 1/3 (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | CuS2 | water | sulfuric acid | nitric oxide | copper(II) nitrate formula | HNO_3 | CuS2 | H_2O | H_2SO_4 | NO | Cu(NO_3)_2 Hill formula | HNO_3 | CuS2 | H_2O | H_2O_4S | NO | CuN_2O_6 name | nitric acid | | water | sulfuric acid | nitric oxide | copper(II) nitrate