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Cu + HNO3 -> Cu(NO3)2 + NO2 + H2O

Input interpretation

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

Balanced equation

Balance the chemical equation algebraically: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 HNO_3 ⟶ c_3 Cu(NO_3)_2 + c_4 NO_2 + c_5 H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, H, N and O: Cu: | c_1 = c_3 H: | c_2 = 2 c_5 N: | c_2 = 2 c_3 + c_4 O: | 3 c_2 = 6 c_3 + 2 c_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 = 4 c_3 = 1 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O
Balance the chemical equation algebraically: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 HNO_3 ⟶ c_3 Cu(NO_3)_2 + c_4 NO_2 + c_5 H_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, H, N and O: Cu: | c_1 = c_3 H: | c_2 = 2 c_5 N: | c_2 = 2 c_3 + c_4 O: | 3 c_2 = 6 c_3 + 2 c_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 = 4 c_3 = 1 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O

Structures

+ ⟶ + +
+ ⟶ + +

Names

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

Equilibrium constant

Construct the equilibrium constant, K, expression for: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O 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: Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O 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 Cu | 1 | -1 HNO_3 | 4 | -4 Cu(NO_3)_2 | 1 | 1 NO_2 | 2 | 2 H_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) HNO_3 | 4 | -4 | ([HNO3])^(-4) Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] NO_2 | 2 | 2 | ([NO2])^2 H_2O | 2 | 2 | ([H2O])^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 = ([Cu])^(-1) ([HNO3])^(-4) [Cu(NO3)2] ([NO2])^2 ([H2O])^2 = ([Cu(NO3)2] ([NO2])^2 ([H2O])^2)/([Cu] ([HNO3])^4)
Construct the equilibrium constant, K, expression for: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O 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: Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O 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 Cu | 1 | -1 HNO_3 | 4 | -4 Cu(NO_3)_2 | 1 | 1 NO_2 | 2 | 2 H_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) HNO_3 | 4 | -4 | ([HNO3])^(-4) Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] NO_2 | 2 | 2 | ([NO2])^2 H_2O | 2 | 2 | ([H2O])^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 = ([Cu])^(-1) ([HNO3])^(-4) [Cu(NO3)2] ([NO2])^2 ([H2O])^2 = ([Cu(NO3)2] ([NO2])^2 ([H2O])^2)/([Cu] ([HNO3])^4)

Rate of reaction

Construct the rate of reaction expression for: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O 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: Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O 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 Cu | 1 | -1 HNO_3 | 4 | -4 Cu(NO_3)_2 | 1 | 1 NO_2 | 2 | 2 H_2O | 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 Cu | 1 | -1 | -(Δ[Cu])/(Δt) HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(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[Cu])/(Δt) = -1/4 (Δ[HNO3])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[NO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Cu + HNO_3 ⟶ Cu(NO_3)_2 + NO_2 + H_2O 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: Cu + 4 HNO_3 ⟶ Cu(NO_3)_2 + 2 NO_2 + 2 H_2O 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 Cu | 1 | -1 HNO_3 | 4 | -4 Cu(NO_3)_2 | 1 | 1 NO_2 | 2 | 2 H_2O | 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 Cu | 1 | -1 | -(Δ[Cu])/(Δt) HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(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[Cu])/(Δt) = -1/4 (Δ[HNO3])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[NO2])/(Δt) = 1/2 (Δ[H2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

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

Substance properties

| copper | nitric acid | copper(II) nitrate | nitrogen dioxide | water molar mass | 63.546 g/mol | 63.012 g/mol | 187.55 g/mol | 46.005 g/mol | 18.015 g/mol phase | solid (at STP) | liquid (at STP) | | gas (at STP) | liquid (at STP) melting point | 1083 °C | -41.6 °C | | -11 °C | 0 °C boiling point | 2567 °C | 83 °C | | 21 °C | 99.9839 °C density | 8.96 g/cm^3 | 1.5129 g/cm^3 | | 0.00188 g/cm^3 (at 25 °C) | 1 g/cm^3 solubility in water | insoluble | miscible | | reacts | surface tension | | | | | 0.0728 N/m dynamic viscosity | | 7.6×10^-4 Pa s (at 25 °C) | | 4.02×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) odor | odorless | | | | odorless
| copper | nitric acid | copper(II) nitrate | nitrogen dioxide | water molar mass | 63.546 g/mol | 63.012 g/mol | 187.55 g/mol | 46.005 g/mol | 18.015 g/mol phase | solid (at STP) | liquid (at STP) | | gas (at STP) | liquid (at STP) melting point | 1083 °C | -41.6 °C | | -11 °C | 0 °C boiling point | 2567 °C | 83 °C | | 21 °C | 99.9839 °C density | 8.96 g/cm^3 | 1.5129 g/cm^3 | | 0.00188 g/cm^3 (at 25 °C) | 1 g/cm^3 solubility in water | insoluble | miscible | | reacts | surface tension | | | | | 0.0728 N/m dynamic viscosity | | 7.6×10^-4 Pa s (at 25 °C) | | 4.02×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) odor | odorless | | | | odorless

Units

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