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CuS + NHO3 = H2O + H2SO4 + NO2 + Cu(NO3)2

Input interpretation

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

Balanced equation

Balance the chemical equation algebraically: CuS + HNO_3 ⟶ H_2O + H_2SO_4 + NO_2 + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuS + c_2 HNO_3 ⟶ 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 Cu, S, H, N and O: Cu: | c_1 = c_6 S: | c_1 = c_4 H: | c_2 = 2 c_3 + 2 c_4 N: | c_2 = c_5 + 2 c_6 O: | 3 c_2 = c_3 + 4 c_4 + 2 c_5 + 6 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 10 c_3 = 4 c_4 = 1 c_5 = 8 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_2 + Cu(NO_3)_2
Balance the chemical equation algebraically: CuS + HNO_3 ⟶ H_2O + H_2SO_4 + NO_2 + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuS + c_2 HNO_3 ⟶ 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 Cu, S, H, N and O: Cu: | c_1 = c_6 S: | c_1 = c_4 H: | c_2 = 2 c_3 + 2 c_4 N: | c_2 = c_5 + 2 c_6 O: | 3 c_2 = c_3 + 4 c_4 + 2 c_5 + 6 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 10 c_3 = 4 c_4 = 1 c_5 = 8 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_2 + Cu(NO_3)_2

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

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

Equilibrium constant

Construct the equilibrium constant, K, expression for: CuS + HNO_3 ⟶ 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: CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_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 CuS | 1 | -1 HNO_3 | 10 | -10 H_2O | 4 | 4 H_2SO_4 | 1 | 1 NO_2 | 8 | 8 Cu(NO_3)_2 | 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_3 | 10 | -10 | ([HNO3])^(-10) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 8 | 8 | ([NO2])^8 Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)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 = ([CuS])^(-1) ([HNO3])^(-10) ([H2O])^4 [H2SO4] ([NO2])^8 [Cu(NO3)2] = (([H2O])^4 [H2SO4] ([NO2])^8 [Cu(NO3)2])/([CuS] ([HNO3])^10)
Construct the equilibrium constant, K, expression for: CuS + HNO_3 ⟶ 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: CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_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 CuS | 1 | -1 HNO_3 | 10 | -10 H_2O | 4 | 4 H_2SO_4 | 1 | 1 NO_2 | 8 | 8 Cu(NO_3)_2 | 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_3 | 10 | -10 | ([HNO3])^(-10) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 8 | 8 | ([NO2])^8 Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)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 = ([CuS])^(-1) ([HNO3])^(-10) ([H2O])^4 [H2SO4] ([NO2])^8 [Cu(NO3)2] = (([H2O])^4 [H2SO4] ([NO2])^8 [Cu(NO3)2])/([CuS] ([HNO3])^10)

Rate of reaction

Construct the rate of reaction expression for: CuS + HNO_3 ⟶ 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: CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_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 CuS | 1 | -1 HNO_3 | 10 | -10 H_2O | 4 | 4 H_2SO_4 | 1 | 1 NO_2 | 8 | 8 Cu(NO_3)_2 | 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_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 8 | 8 | 1/8 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 1 | 1 | (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 = -(Δ[CuS])/(Δt) = -1/10 (Δ[HNO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/8 (Δ[NO2])/(Δt) = (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: CuS + HNO_3 ⟶ 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: CuS + 10 HNO_3 ⟶ 4 H_2O + H_2SO_4 + 8 NO_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 CuS | 1 | -1 HNO_3 | 10 | -10 H_2O | 4 | 4 H_2SO_4 | 1 | 1 NO_2 | 8 | 8 Cu(NO_3)_2 | 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_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 8 | 8 | 1/8 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 1 | 1 | (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 = -(Δ[CuS])/(Δt) = -1/10 (Δ[HNO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/8 (Δ[NO2])/(Δt) = (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

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

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