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HNO3 + CrCl2 = H2O + HCl + NO2 + Cr(NO3)3

Input interpretation

HNO_3 nitric acid + CrCl_2 chromous chloride ⟶ H_2O water + HCl hydrogen chloride + NO_2 nitrogen dioxide + CrN_3O_9 chromium nitrate
HNO_3 nitric acid + CrCl_2 chromous chloride ⟶ H_2O water + HCl hydrogen chloride + NO_2 nitrogen dioxide + CrN_3O_9 chromium nitrate

Balanced equation

Balance the chemical equation algebraically: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CrCl_2 ⟶ c_3 H_2O + c_4 HCl + c_5 NO_2 + c_6 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cl and Cr: H: | c_1 = 2 c_3 + c_4 N: | c_1 = c_5 + 3 c_6 O: | 3 c_1 = c_3 + 2 c_5 + 9 c_6 Cl: | 2 c_2 = c_4 Cr: | c_2 = 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9
Balance the chemical equation algebraically: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 CrCl_2 ⟶ c_3 H_2O + c_4 HCl + c_5 NO_2 + c_6 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Cl and Cr: H: | c_1 = 2 c_3 + c_4 N: | c_1 = c_5 + 3 c_6 O: | 3 c_1 = c_3 + 2 c_5 + 9 c_6 Cl: | 2 c_2 = c_4 Cr: | c_2 = 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

nitric acid + chromous chloride ⟶ water + hydrogen chloride + nitrogen dioxide + chromium nitrate
nitric acid + chromous chloride ⟶ water + hydrogen chloride + nitrogen dioxide + chromium nitrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 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: 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9 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 | 4 | -4 CrCl_2 | 1 | -1 H_2O | 1 | 1 HCl | 2 | 2 NO_2 | 1 | 1 CrN_3O_9 | 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 | 4 | -4 | ([HNO3])^(-4) CrCl_2 | 1 | -1 | ([CrCl2])^(-1) H_2O | 1 | 1 | [H2O] HCl | 2 | 2 | ([HCl])^2 NO_2 | 1 | 1 | [NO2] CrN_3O_9 | 1 | 1 | [CrN3O9] 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])^(-4) ([CrCl2])^(-1) [H2O] ([HCl])^2 [NO2] [CrN3O9] = ([H2O] ([HCl])^2 [NO2] [CrN3O9])/(([HNO3])^4 [CrCl2])
Construct the equilibrium constant, K, expression for: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 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: 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9 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 | 4 | -4 CrCl_2 | 1 | -1 H_2O | 1 | 1 HCl | 2 | 2 NO_2 | 1 | 1 CrN_3O_9 | 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 | 4 | -4 | ([HNO3])^(-4) CrCl_2 | 1 | -1 | ([CrCl2])^(-1) H_2O | 1 | 1 | [H2O] HCl | 2 | 2 | ([HCl])^2 NO_2 | 1 | 1 | [NO2] CrN_3O_9 | 1 | 1 | [CrN3O9] 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])^(-4) ([CrCl2])^(-1) [H2O] ([HCl])^2 [NO2] [CrN3O9] = ([H2O] ([HCl])^2 [NO2] [CrN3O9])/(([HNO3])^4 [CrCl2])

Rate of reaction

Construct the rate of reaction expression for: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 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: 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9 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 | 4 | -4 CrCl_2 | 1 | -1 H_2O | 1 | 1 HCl | 2 | 2 NO_2 | 1 | 1 CrN_3O_9 | 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 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) CrCl_2 | 1 | -1 | -(Δ[CrCl2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) NO_2 | 1 | 1 | (Δ[NO2])/(Δt) CrN_3O_9 | 1 | 1 | (Δ[CrN3O9])/(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 = -1/4 (Δ[HNO3])/(Δt) = -(Δ[CrCl2])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[HCl])/(Δt) = (Δ[NO2])/(Δt) = (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HNO_3 + CrCl_2 ⟶ H_2O + HCl + NO_2 + CrN_3O_9 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: 4 HNO_3 + CrCl_2 ⟶ H_2O + 2 HCl + NO_2 + CrN_3O_9 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 | 4 | -4 CrCl_2 | 1 | -1 H_2O | 1 | 1 HCl | 2 | 2 NO_2 | 1 | 1 CrN_3O_9 | 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 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) CrCl_2 | 1 | -1 | -(Δ[CrCl2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) NO_2 | 1 | 1 | (Δ[NO2])/(Δt) CrN_3O_9 | 1 | 1 | (Δ[CrN3O9])/(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 = -1/4 (Δ[HNO3])/(Δt) = -(Δ[CrCl2])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[HCl])/(Δt) = (Δ[NO2])/(Δt) = (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| nitric acid | chromous chloride | water | hydrogen chloride | nitrogen dioxide | chromium nitrate formula | HNO_3 | CrCl_2 | H_2O | HCl | NO_2 | CrN_3O_9 Hill formula | HNO_3 | Cl_2Cr | H_2O | ClH | NO_2 | CrN_3O_9 name | nitric acid | chromous chloride | water | hydrogen chloride | nitrogen dioxide | chromium nitrate IUPAC name | nitric acid | dichlorochromium | water | hydrogen chloride | Nitrogen dioxide | chromium(+3) cation trinitrate
| nitric acid | chromous chloride | water | hydrogen chloride | nitrogen dioxide | chromium nitrate formula | HNO_3 | CrCl_2 | H_2O | HCl | NO_2 | CrN_3O_9 Hill formula | HNO_3 | Cl_2Cr | H_2O | ClH | NO_2 | CrN_3O_9 name | nitric acid | chromous chloride | water | hydrogen chloride | nitrogen dioxide | chromium nitrate IUPAC name | nitric acid | dichlorochromium | water | hydrogen chloride | Nitrogen dioxide | chromium(+3) cation trinitrate

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