H2SO4 + HNO3 + Cu = H2O + NO + CuSO4

H_2SO_4 sulfuric acid + HNO_3 nitric acid + Cu copper ⟶ H_2O water + NO nitric oxide + CuSO_4 copper(II) sulfate

Balance the chemical equation algebraically: H_2SO_4 + HNO_3 + Cu ⟶ H_2O + NO + CuSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 HNO_3 + c_3 Cu ⟶ c_4 H_2O + c_5 NO + c_6 CuSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, N and Cu: H: | 2 c_1 + c_2 = 2 c_4 O: | 4 c_1 + 3 c_2 = c_4 + c_5 + 4 c_6 S: | c_1 = c_6 N: | c_2 = c_5 Cu: | c_3 = c_6 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 = 3/2 c_4 = 2 c_5 = 1 c_6 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 4 c_5 = 2 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 HNO_3 + 3 Cu ⟶ 4 H_2O + 2 NO + 3 CuSO_4

+ + ⟶ + +

sulfuric acid + nitric acid + copper ⟶ water + nitric oxide + copper(II) sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + HNO_3 + Cu ⟶ 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: 3 H_2SO_4 + 2 HNO_3 + 3 Cu ⟶ 4 H_2O + 2 NO + 3 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 H_2SO_4 | 3 | -3 HNO_3 | 2 | -2 Cu | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 CuSO_4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) HNO_3 | 2 | -2 | ([HNO3])^(-2) Cu | 3 | -3 | ([Cu])^(-3) H_2O | 4 | 4 | ([H2O])^4 NO | 2 | 2 | ([NO])^2 CuSO_4 | 3 | 3 | ([CuSO4])^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 = ([H2SO4])^(-3) ([HNO3])^(-2) ([Cu])^(-3) ([H2O])^4 ([NO])^2 ([CuSO4])^3 = (([H2O])^4 ([NO])^2 ([CuSO4])^3)/(([H2SO4])^3 ([HNO3])^2 ([Cu])^3)

Construct the rate of reaction expression for: H_2SO_4 + HNO_3 + Cu ⟶ 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: 3 H_2SO_4 + 2 HNO_3 + 3 Cu ⟶ 4 H_2O + 2 NO + 3 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 H_2SO_4 | 3 | -3 HNO_3 | 2 | -2 Cu | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 CuSO_4 | 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 H_2SO_4 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Cu | 3 | -3 | -1/3 (Δ[Cu])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) CuSO_4 | 3 | 3 | 1/3 (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 = -1/3 (Δ[H2SO4])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/3 (Δ[Cu])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/3 (Δ[CuSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | nitric acid | copper | water | nitric oxide | copper(II) sulfate formula | H_2SO_4 | HNO_3 | Cu | H_2O | NO | CuSO_4 Hill formula | H_2O_4S | HNO_3 | Cu | H_2O | NO | CuO_4S name | sulfuric acid | nitric acid | copper | water | nitric oxide | copper(II) sulfate IUPAC name | sulfuric acid | nitric acid | copper | water | nitric oxide | copper sulfate

| sulfuric acid | nitric acid | copper | water | nitric oxide | copper(II) sulfate molar mass | 98.07 g/mol | 63.012 g/mol | 63.546 g/mol | 18.015 g/mol | 30.006 g/mol | 159.6 g/mol phase | liquid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 10.371 °C | -41.6 °C | 1083 °C | 0 °C | -163.6 °C | 200 °C boiling point | 279.6 °C | 83 °C | 2567 °C | 99.9839 °C | -151.7 °C | density | 1.8305 g/cm^3 | 1.5129 g/cm^3 | 8.96 g/cm^3 | 1 g/cm^3 | 0.001226 g/cm^3 (at 25 °C) | 3.603 g/cm^3 solubility in water | very soluble | miscible | insoluble | | | surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.911×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless | |