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HNO3 + CuS = H2O + NO2 + Cu(NO3)2 + S8

Input interpretation

HNO_3 nitric acid + CuS cupric sulfide ⟶ H_2O water + NO_2 nitrogen dioxide + Cu(NO_3)_2 copper(II) nitrate + S_8 rhombic sulfur
HNO_3 nitric acid + CuS cupric sulfide ⟶ H_2O water + NO_2 nitrogen dioxide + Cu(NO_3)_2 copper(II) nitrate + S_8 rhombic sulfur

Balanced equation

Balance the chemical equation algebraically: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CuS ⟶ c_3 H_2O + c_4 NO_2 + c_5 Cu(NO_3)_2 + c_6 S_8 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 N: | c_1 = c_4 + 2 c_5 O: | 3 c_1 = c_3 + 2 c_4 + 6 c_5 Cu: | c_2 = c_5 S: | c_2 = 8 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 32 c_2 = 8 c_3 = 16 c_4 = 16 c_5 = 8 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8
Balance the chemical equation algebraically: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CuS ⟶ c_3 H_2O + c_4 NO_2 + c_5 Cu(NO_3)_2 + c_6 S_8 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 N: | c_1 = c_4 + 2 c_5 O: | 3 c_1 = c_3 + 2 c_4 + 6 c_5 Cu: | c_2 = c_5 S: | c_2 = 8 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 32 c_2 = 8 c_3 = 16 c_4 = 16 c_5 = 8 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

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

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 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: 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8 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 | 32 | -32 CuS | 8 | -8 H_2O | 16 | 16 NO_2 | 16 | 16 Cu(NO_3)_2 | 8 | 8 S_8 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 32 | -32 | ([HNO3])^(-32) CuS | 8 | -8 | ([CuS])^(-8) H_2O | 16 | 16 | ([H2O])^16 NO_2 | 16 | 16 | ([NO2])^16 Cu(NO_3)_2 | 8 | 8 | ([Cu(NO3)2])^8 S_8 | 1 | 1 | [S8] 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])^(-32) ([CuS])^(-8) ([H2O])^16 ([NO2])^16 ([Cu(NO3)2])^8 [S8] = (([H2O])^16 ([NO2])^16 ([Cu(NO3)2])^8 [S8])/(([HNO3])^32 ([CuS])^8)
Construct the equilibrium constant, K, expression for: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 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: 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8 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 | 32 | -32 CuS | 8 | -8 H_2O | 16 | 16 NO_2 | 16 | 16 Cu(NO_3)_2 | 8 | 8 S_8 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 32 | -32 | ([HNO3])^(-32) CuS | 8 | -8 | ([CuS])^(-8) H_2O | 16 | 16 | ([H2O])^16 NO_2 | 16 | 16 | ([NO2])^16 Cu(NO_3)_2 | 8 | 8 | ([Cu(NO3)2])^8 S_8 | 1 | 1 | [S8] 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])^(-32) ([CuS])^(-8) ([H2O])^16 ([NO2])^16 ([Cu(NO3)2])^8 [S8] = (([H2O])^16 ([NO2])^16 ([Cu(NO3)2])^8 [S8])/(([HNO3])^32 ([CuS])^8)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 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: 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8 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 | 32 | -32 CuS | 8 | -8 H_2O | 16 | 16 NO_2 | 16 | 16 Cu(NO_3)_2 | 8 | 8 S_8 | 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 HNO_3 | 32 | -32 | -1/32 (Δ[HNO3])/(Δt) CuS | 8 | -8 | -1/8 (Δ[CuS])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) NO_2 | 16 | 16 | 1/16 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 8 | 8 | 1/8 (Δ[Cu(NO3)2])/(Δt) S_8 | 1 | 1 | (Δ[S8])/(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 = -1/32 (Δ[HNO3])/(Δt) = -1/8 (Δ[CuS])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/16 (Δ[NO2])/(Δt) = 1/8 (Δ[Cu(NO3)2])/(Δt) = (Δ[S8])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + CuS ⟶ H_2O + NO_2 + Cu(NO_3)_2 + S_8 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: 32 HNO_3 + 8 CuS ⟶ 16 H_2O + 16 NO_2 + 8 Cu(NO_3)_2 + S_8 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 | 32 | -32 CuS | 8 | -8 H_2O | 16 | 16 NO_2 | 16 | 16 Cu(NO_3)_2 | 8 | 8 S_8 | 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 HNO_3 | 32 | -32 | -1/32 (Δ[HNO3])/(Δt) CuS | 8 | -8 | -1/8 (Δ[CuS])/(Δt) H_2O | 16 | 16 | 1/16 (Δ[H2O])/(Δt) NO_2 | 16 | 16 | 1/16 (Δ[NO2])/(Δt) Cu(NO_3)_2 | 8 | 8 | 1/8 (Δ[Cu(NO3)2])/(Δt) S_8 | 1 | 1 | (Δ[S8])/(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 = -1/32 (Δ[HNO3])/(Δt) = -1/8 (Δ[CuS])/(Δt) = 1/16 (Δ[H2O])/(Δt) = 1/16 (Δ[NO2])/(Δt) = 1/8 (Δ[Cu(NO3)2])/(Δt) = (Δ[S8])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | cupric sulfide | water | nitrogen dioxide | copper(II) nitrate | rhombic sulfur formula | HNO_3 | CuS | H_2O | NO_2 | Cu(NO_3)_2 | S_8 Hill formula | HNO_3 | CuS | H_2O | NO_2 | CuN_2O_6 | S_8 name | nitric acid | cupric sulfide | water | nitrogen dioxide | copper(II) nitrate | rhombic sulfur IUPAC name | nitric acid | | water | Nitrogen dioxide | copper(II) nitrate | octathiocane
| nitric acid | cupric sulfide | water | nitrogen dioxide | copper(II) nitrate | rhombic sulfur formula | HNO_3 | CuS | H_2O | NO_2 | Cu(NO_3)_2 | S_8 Hill formula | HNO_3 | CuS | H_2O | NO_2 | CuN_2O_6 | S_8 name | nitric acid | cupric sulfide | water | nitrogen dioxide | copper(II) nitrate | rhombic sulfur IUPAC name | nitric acid | | water | Nitrogen dioxide | copper(II) nitrate | octathiocane

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