Input interpretation
![HCl hydrogen chloride + HNO_3 nitric acid + Au gold ⟶ H_2O water + NO nitric oxide + HAuCl3](../image_source/57a7926c5a42fcc561ba44d28b1d9597.png)
HCl hydrogen chloride + HNO_3 nitric acid + Au gold ⟶ H_2O water + NO nitric oxide + HAuCl3
Balanced equation
![Balance the chemical equation algebraically: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 + c_3 Au ⟶ c_4 H_2O + c_5 NO + c_6 HAuCl3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, O and Au: Cl: | c_1 = 3 c_6 H: | c_1 + c_2 = 2 c_4 + c_6 N: | c_2 = c_5 O: | 3 c_2 = c_4 + c_5 Au: | 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 = 9/2 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 = 9 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: | | 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3](../image_source/d79371c17705b97a1f0dfeff56b9f4ce.png)
Balance the chemical equation algebraically: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 + c_3 Au ⟶ c_4 H_2O + c_5 NO + c_6 HAuCl3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, O and Au: Cl: | c_1 = 3 c_6 H: | c_1 + c_2 = 2 c_4 + c_6 N: | c_2 = c_5 O: | 3 c_2 = c_4 + c_5 Au: | 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 = 9/2 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 = 9 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: | | 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3
Structures
![+ + ⟶ + + HAuCl3](../image_source/a70c0f323aa22991f95a481508e648df.png)
+ + ⟶ + + HAuCl3
Names
![hydrogen chloride + nitric acid + gold ⟶ water + nitric oxide + HAuCl3](../image_source/043afce8900798956df2a3dd7f29b87d.png)
hydrogen chloride + nitric acid + gold ⟶ water + nitric oxide + HAuCl3
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 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: 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3 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 HCl | 9 | -9 HNO_3 | 2 | -2 Au | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 HAuCl3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 9 | -9 | ([HCl])^(-9) HNO_3 | 2 | -2 | ([HNO3])^(-2) Au | 3 | -3 | ([Au])^(-3) H_2O | 4 | 4 | ([H2O])^4 NO | 2 | 2 | ([NO])^2 HAuCl3 | 3 | 3 | ([HAuCl3])^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 = ([HCl])^(-9) ([HNO3])^(-2) ([Au])^(-3) ([H2O])^4 ([NO])^2 ([HAuCl3])^3 = (([H2O])^4 ([NO])^2 ([HAuCl3])^3)/(([HCl])^9 ([HNO3])^2 ([Au])^3)](../image_source/36ed807c38ed99fb986916f602fd24ab.png)
Construct the equilibrium constant, K, expression for: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 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: 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3 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 HCl | 9 | -9 HNO_3 | 2 | -2 Au | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 HAuCl3 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 9 | -9 | ([HCl])^(-9) HNO_3 | 2 | -2 | ([HNO3])^(-2) Au | 3 | -3 | ([Au])^(-3) H_2O | 4 | 4 | ([H2O])^4 NO | 2 | 2 | ([NO])^2 HAuCl3 | 3 | 3 | ([HAuCl3])^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 = ([HCl])^(-9) ([HNO3])^(-2) ([Au])^(-3) ([H2O])^4 ([NO])^2 ([HAuCl3])^3 = (([H2O])^4 ([NO])^2 ([HAuCl3])^3)/(([HCl])^9 ([HNO3])^2 ([Au])^3)
Rate of reaction
![Construct the rate of reaction expression for: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 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: 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3 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 HCl | 9 | -9 HNO_3 | 2 | -2 Au | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 HAuCl3 | 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 HCl | 9 | -9 | -1/9 (Δ[HCl])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Au | 3 | -3 | -1/3 (Δ[Au])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) HAuCl3 | 3 | 3 | 1/3 (Δ[HAuCl3])/(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 = -1/9 (Δ[HCl])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/3 (Δ[Au])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/3 (Δ[HAuCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/7397b83020ca00b591e0c02349be253f.png)
Construct the rate of reaction expression for: HCl + HNO_3 + Au ⟶ H_2O + NO + HAuCl3 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: 9 HCl + 2 HNO_3 + 3 Au ⟶ 4 H_2O + 2 NO + 3 HAuCl3 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 HCl | 9 | -9 HNO_3 | 2 | -2 Au | 3 | -3 H_2O | 4 | 4 NO | 2 | 2 HAuCl3 | 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 HCl | 9 | -9 | -1/9 (Δ[HCl])/(Δt) HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Au | 3 | -3 | -1/3 (Δ[Au])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) NO | 2 | 2 | 1/2 (Δ[NO])/(Δt) HAuCl3 | 3 | 3 | 1/3 (Δ[HAuCl3])/(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 = -1/9 (Δ[HCl])/(Δt) = -1/2 (Δ[HNO3])/(Δt) = -1/3 (Δ[Au])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[NO])/(Δt) = 1/3 (Δ[HAuCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| hydrogen chloride | nitric acid | gold | water | nitric oxide | HAuCl3 formula | HCl | HNO_3 | Au | H_2O | NO | HAuCl3 Hill formula | ClH | HNO_3 | Au | H_2O | NO | HAuCl3 name | hydrogen chloride | nitric acid | gold | water | nitric oxide |](../image_source/bd0bc2bcefa0c4f86a193549c7942999.png)
| hydrogen chloride | nitric acid | gold | water | nitric oxide | HAuCl3 formula | HCl | HNO_3 | Au | H_2O | NO | HAuCl3 Hill formula | ClH | HNO_3 | Au | H_2O | NO | HAuCl3 name | hydrogen chloride | nitric acid | gold | water | nitric oxide |