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HNO3 + AgCuS = H2O + H2SO4 + NO2 + CuSO4 + Cu(NO3)2 + AgNO3

Input interpretation

HNO_3 nitric acid + AgCuS ⟶ H_2O water + H_2SO_4 sulfuric acid + NO_2 nitrogen dioxide + CuSO_4 copper(II) sulfate + Cu(NO_3)_2 copper(II) nitrate + AgNO_3 silver nitrate
HNO_3 nitric acid + AgCuS ⟶ H_2O water + H_2SO_4 sulfuric acid + NO_2 nitrogen dioxide + CuSO_4 copper(II) sulfate + Cu(NO_3)_2 copper(II) nitrate + AgNO_3 silver nitrate

Balanced equation

Balance the chemical equation algebraically: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 AgCuS ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 + c_6 CuSO_4 + c_7 Cu(NO_3)_2 + c_8 AgNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Ag, Cu and S: H: | c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_5 + 2 c_7 + c_8 O: | 3 c_1 = c_3 + 4 c_4 + 2 c_5 + 4 c_6 + 6 c_7 + 3 c_8 Ag: | c_2 = c_8 Cu: | c_2 = c_6 + c_7 S: | c_2 = c_4 + 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/10 - 1/5 c_3 = c_1/2 - 1 c_4 = 1 c_5 = (9 c_1)/10 - 9/5 c_6 = c_1/10 - 6/5 c_7 = 1 c_8 = c_1/10 - 1/5 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 22 and solve for the remaining coefficients: c_1 = 22 c_2 = 2 c_3 = 10 c_4 = 1 c_5 = 18 c_6 = 1 c_7 = 1 c_8 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3
Balance the chemical equation algebraically: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 AgCuS ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 NO_2 + c_6 CuSO_4 + c_7 Cu(NO_3)_2 + c_8 AgNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Ag, Cu and S: H: | c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_5 + 2 c_7 + c_8 O: | 3 c_1 = c_3 + 4 c_4 + 2 c_5 + 4 c_6 + 6 c_7 + 3 c_8 Ag: | c_2 = c_8 Cu: | c_2 = c_6 + c_7 S: | c_2 = c_4 + 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/10 - 1/5 c_3 = c_1/2 - 1 c_4 = 1 c_5 = (9 c_1)/10 - 9/5 c_6 = c_1/10 - 6/5 c_7 = 1 c_8 = c_1/10 - 1/5 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 22 and solve for the remaining coefficients: c_1 = 22 c_2 = 2 c_3 = 10 c_4 = 1 c_5 = 18 c_6 = 1 c_7 = 1 c_8 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3

Structures

+ AgCuS ⟶ + + + + +
+ AgCuS ⟶ + + + + +

Names

nitric acid + AgCuS ⟶ water + sulfuric acid + nitrogen dioxide + copper(II) sulfate + copper(II) nitrate + silver nitrate
nitric acid + AgCuS ⟶ water + sulfuric acid + nitrogen dioxide + copper(II) sulfate + copper(II) nitrate + silver nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 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: 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3 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 | 22 | -22 AgCuS | 2 | -2 H_2O | 10 | 10 H_2SO_4 | 1 | 1 NO_2 | 18 | 18 CuSO_4 | 1 | 1 Cu(NO_3)_2 | 1 | 1 AgNO_3 | 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 | 22 | -22 | ([HNO3])^(-22) AgCuS | 2 | -2 | ([AgCuS])^(-2) H_2O | 10 | 10 | ([H2O])^10 H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 18 | 18 | ([NO2])^18 CuSO_4 | 1 | 1 | [CuSO4] Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] AgNO_3 | 2 | 2 | ([AgNO3])^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])^(-22) ([AgCuS])^(-2) ([H2O])^10 [H2SO4] ([NO2])^18 [CuSO4] [Cu(NO3)2] ([AgNO3])^2 = (([H2O])^10 [H2SO4] ([NO2])^18 [CuSO4] [Cu(NO3)2] ([AgNO3])^2)/(([HNO3])^22 ([AgCuS])^2)
Construct the equilibrium constant, K, expression for: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 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: 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3 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 | 22 | -22 AgCuS | 2 | -2 H_2O | 10 | 10 H_2SO_4 | 1 | 1 NO_2 | 18 | 18 CuSO_4 | 1 | 1 Cu(NO_3)_2 | 1 | 1 AgNO_3 | 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 | 22 | -22 | ([HNO3])^(-22) AgCuS | 2 | -2 | ([AgCuS])^(-2) H_2O | 10 | 10 | ([H2O])^10 H_2SO_4 | 1 | 1 | [H2SO4] NO_2 | 18 | 18 | ([NO2])^18 CuSO_4 | 1 | 1 | [CuSO4] Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] AgNO_3 | 2 | 2 | ([AgNO3])^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])^(-22) ([AgCuS])^(-2) ([H2O])^10 [H2SO4] ([NO2])^18 [CuSO4] [Cu(NO3)2] ([AgNO3])^2 = (([H2O])^10 [H2SO4] ([NO2])^18 [CuSO4] [Cu(NO3)2] ([AgNO3])^2)/(([HNO3])^22 ([AgCuS])^2)

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 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: 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3 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 | 22 | -22 AgCuS | 2 | -2 H_2O | 10 | 10 H_2SO_4 | 1 | 1 NO_2 | 18 | 18 CuSO_4 | 1 | 1 Cu(NO_3)_2 | 1 | 1 AgNO_3 | 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 | 22 | -22 | -1/22 (Δ[HNO3])/(Δt) AgCuS | 2 | -2 | -1/2 (Δ[AgCuS])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 18 | 18 | 1/18 (Δ[NO2])/(Δt) CuSO_4 | 1 | 1 | (Δ[CuSO4])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) AgNO_3 | 2 | 2 | 1/2 (Δ[AgNO3])/(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 = -1/22 (Δ[HNO3])/(Δt) = -1/2 (Δ[AgCuS])/(Δt) = 1/10 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/18 (Δ[NO2])/(Δt) = (Δ[CuSO4])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[AgNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + AgCuS ⟶ H_2O + H_2SO_4 + NO_2 + CuSO_4 + Cu(NO_3)_2 + AgNO_3 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: 22 HNO_3 + 2 AgCuS ⟶ 10 H_2O + H_2SO_4 + 18 NO_2 + CuSO_4 + Cu(NO_3)_2 + 2 AgNO_3 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 | 22 | -22 AgCuS | 2 | -2 H_2O | 10 | 10 H_2SO_4 | 1 | 1 NO_2 | 18 | 18 CuSO_4 | 1 | 1 Cu(NO_3)_2 | 1 | 1 AgNO_3 | 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 | 22 | -22 | -1/22 (Δ[HNO3])/(Δt) AgCuS | 2 | -2 | -1/2 (Δ[AgCuS])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NO_2 | 18 | 18 | 1/18 (Δ[NO2])/(Δt) CuSO_4 | 1 | 1 | (Δ[CuSO4])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) AgNO_3 | 2 | 2 | 1/2 (Δ[AgNO3])/(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 = -1/22 (Δ[HNO3])/(Δt) = -1/2 (Δ[AgCuS])/(Δt) = 1/10 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/18 (Δ[NO2])/(Δt) = (Δ[CuSO4])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = 1/2 (Δ[AgNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | AgCuS | water | sulfuric acid | nitrogen dioxide | copper(II) sulfate | copper(II) nitrate | silver nitrate formula | HNO_3 | AgCuS | H_2O | H_2SO_4 | NO_2 | CuSO_4 | Cu(NO_3)_2 | AgNO_3 Hill formula | HNO_3 | AgCuS | H_2O | H_2O_4S | NO_2 | CuO_4S | CuN_2O_6 | AgNO_3 name | nitric acid | | water | sulfuric acid | nitrogen dioxide | copper(II) sulfate | copper(II) nitrate | silver nitrate IUPAC name | nitric acid | | water | sulfuric acid | Nitrogen dioxide | copper sulfate | copper(II) nitrate | silver nitrate
| nitric acid | AgCuS | water | sulfuric acid | nitrogen dioxide | copper(II) sulfate | copper(II) nitrate | silver nitrate formula | HNO_3 | AgCuS | H_2O | H_2SO_4 | NO_2 | CuSO_4 | Cu(NO_3)_2 | AgNO_3 Hill formula | HNO_3 | AgCuS | H_2O | H_2O_4S | NO_2 | CuO_4S | CuN_2O_6 | AgNO_3 name | nitric acid | | water | sulfuric acid | nitrogen dioxide | copper(II) sulfate | copper(II) nitrate | silver nitrate IUPAC name | nitric acid | | water | sulfuric acid | Nitrogen dioxide | copper sulfate | copper(II) nitrate | silver nitrate

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