HNO3 + Cu2S2 = H2O + H2SO4 + NO2 + Cu(NO3)2

HNO_3 nitric acid + Cu2S2 ⟶ H_2O water + H_2SO_4 sulfuric acid + NO_2 nitrogen dioxide + Cu(NO_3)_2 copper(II) nitrate

Balance the chemical equation algebraically: HNO_3 + Cu2S2 ⟶ H_2O + H_2SO_4 + NO_2 + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Cu2S2 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 + 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 + 2 c_5 + 6 c_6 Cu: | 2 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 c_2 = 1 c_3 = 8 c_4 = 2 c_5 = 16 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 20 HNO_3 + Cu2S2 ⟶ 8 H_2O + 2 H_2SO_4 + 16 NO_2 + 2 Cu(NO_3)_2

+ Cu2S2 ⟶ + + +

nitric acid + Cu2S2 ⟶ water + sulfuric acid + nitrogen dioxide + copper(II) nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Cu2S2 ⟶ H_2O + H_2SO_4 + 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: 20 HNO_3 + Cu2S2 ⟶ 8 H_2O + 2 H_2SO_4 + 16 NO_2 + 2 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 Cu2S2 | 1 | -1 H_2O | 8 | 8 H_2SO_4 | 2 | 2 NO_2 | 16 | 16 Cu(NO_3)_2 | 2 | 2 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) Cu2S2 | 1 | -1 | ([Cu2S2])^(-1) H_2O | 8 | 8 | ([H2O])^8 H_2SO_4 | 2 | 2 | ([H2SO4])^2 NO_2 | 16 | 16 | ([NO2])^16 Cu(NO_3)_2 | 2 | 2 | ([Cu(NO3)2])^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 = ([HNO3])^(-20) ([Cu2S2])^(-1) ([H2O])^8 ([H2SO4])^2 ([NO2])^16 ([Cu(NO3)2])^2 = (([H2O])^8 ([H2SO4])^2 ([NO2])^16 ([Cu(NO3)2])^2)/(([HNO3])^20 [Cu2S2])

Construct the rate of reaction expression for: HNO_3 + Cu2S2 ⟶ H_2O + H_2SO_4 + 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: 20 HNO_3 + Cu2S2 ⟶ 8 H_2O + 2 H_2SO_4 + 16 NO_2 + 2 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 Cu2S2 | 1 | -1 H_2O | 8 | 8 H_2SO_4 | 2 | 2 NO_2 | 16 | 16 Cu(NO_3)_2 | 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 HNO_3 | 20 | -20 | -1/20 (Δ[HNO3])/(Δt) Cu2S2 | 1 | -1 | -(Δ[Cu2S2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) NO_2 | 16 | 16 | 1/16 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 2 | 2 | 1/2 (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) = -(Δ[Cu2S2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = 1/16 (Δ[NO2])/(Δt) = 1/2 (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | Cu2S2 | water | sulfuric acid | nitrogen dioxide | copper(II) nitrate formula | HNO_3 | Cu2S2 | H_2O | H_2SO_4 | NO_2 | Cu(NO_3)_2 Hill formula | HNO_3 | Cu2S2 | H_2O | H_2O_4S | NO_2 | CuN_2O_6 name | nitric acid | | water | sulfuric acid | nitrogen dioxide | copper(II) nitrate IUPAC name | nitric acid | | water | sulfuric acid | Nitrogen dioxide | copper(II) nitrate

| nitric acid | Cu2S2 | water | sulfuric acid | nitrogen dioxide | copper(II) nitrate molar mass | 63.012 g/mol | 191.2 g/mol | 18.015 g/mol | 98.07 g/mol | 46.005 g/mol | 187.55 g/mol phase | liquid (at STP) | | liquid (at STP) | liquid (at STP) | gas (at STP) | melting point | -41.6 °C | | 0 °C | 10.371 °C | -11 °C | boiling point | 83 °C | | 99.9839 °C | 279.6 °C | 21 °C | density | 1.5129 g/cm^3 | | 1 g/cm^3 | 1.8305 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | solubility in water | miscible | | | very soluble | reacts | surface tension | | | 0.0728 N/m | 0.0735 N/m | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | odor | | | odorless | odorless | |