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HCl + K2Cr2O7 + KNO2 = H2O + KCl + KNO3 + CrCl3

Input interpretation

HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + KNO_2 potassium nitrite ⟶ H_2O water + KCl potassium chloride + KNO_3 potassium nitrate + CrCl_3 chromic chloride
HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + KNO_2 potassium nitrite ⟶ H_2O water + KCl potassium chloride + KNO_3 potassium nitrate + CrCl_3 chromic chloride

Balanced equation

Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 KNO_2 ⟶ c_4 H_2O + c_5 KCl + c_6 KNO_3 + c_7 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K, O and N: Cl: | c_1 = c_5 + 3 c_7 H: | c_1 = 2 c_4 Cr: | 2 c_2 = c_7 K: | 2 c_2 + c_3 = c_5 + c_6 O: | 7 c_2 + 2 c_3 = c_4 + 3 c_6 N: | 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 = 8 c_2 = 1 c_3 = 3 c_4 = 4 c_5 = 2 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_3
Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 KNO_2 ⟶ c_4 H_2O + c_5 KCl + c_6 KNO_3 + c_7 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K, O and N: Cl: | c_1 = c_5 + 3 c_7 H: | c_1 = 2 c_4 Cr: | 2 c_2 = c_7 K: | 2 c_2 + c_3 = c_5 + c_6 O: | 7 c_2 + 2 c_3 = c_4 + 3 c_6 N: | 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 = 8 c_2 = 1 c_3 = 3 c_4 = 4 c_5 = 2 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_3

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

hydrogen chloride + potassium dichromate + potassium nitrite ⟶ water + potassium chloride + potassium nitrate + chromic chloride
hydrogen chloride + potassium dichromate + potassium nitrite ⟶ water + potassium chloride + potassium nitrate + chromic chloride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_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: 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_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 HCl | 8 | -8 K_2Cr_2O_7 | 1 | -1 KNO_2 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 KNO_3 | 3 | 3 CrCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KNO_2 | 3 | -3 | ([KNO2])^(-3) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 KNO_3 | 3 | 3 | ([KNO3])^3 CrCl_3 | 2 | 2 | ([CrCl3])^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 = ([HCl])^(-8) ([K2Cr2O7])^(-1) ([KNO2])^(-3) ([H2O])^4 ([KCl])^2 ([KNO3])^3 ([CrCl3])^2 = (([H2O])^4 ([KCl])^2 ([KNO3])^3 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] ([KNO2])^3)
Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_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: 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_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 HCl | 8 | -8 K_2Cr_2O_7 | 1 | -1 KNO_2 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 KNO_3 | 3 | 3 CrCl_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KNO_2 | 3 | -3 | ([KNO2])^(-3) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 KNO_3 | 3 | 3 | ([KNO3])^3 CrCl_3 | 2 | 2 | ([CrCl3])^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 = ([HCl])^(-8) ([K2Cr2O7])^(-1) ([KNO2])^(-3) ([H2O])^4 ([KCl])^2 ([KNO3])^3 ([CrCl3])^2 = (([H2O])^4 ([KCl])^2 ([KNO3])^3 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] ([KNO2])^3)

Rate of reaction

Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_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: 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_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 HCl | 8 | -8 K_2Cr_2O_7 | 1 | -1 KNO_2 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 KNO_3 | 3 | 3 CrCl_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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KNO_2 | 3 | -3 | -1/3 (Δ[KNO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(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 = -1/8 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[KNO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + KNO_2 ⟶ H_2O + KCl + KNO_3 + CrCl_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: 8 HCl + K_2Cr_2O_7 + 3 KNO_2 ⟶ 4 H_2O + 2 KCl + 3 KNO_3 + 2 CrCl_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 HCl | 8 | -8 K_2Cr_2O_7 | 1 | -1 KNO_2 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 KNO_3 | 3 | 3 CrCl_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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KNO_2 | 3 | -3 | -1/3 (Δ[KNO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) KNO_3 | 3 | 3 | 1/3 (Δ[KNO3])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(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 = -1/8 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/3 (Δ[KNO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/3 (Δ[KNO3])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | potassium dichromate | potassium nitrite | water | potassium chloride | potassium nitrate | chromic chloride formula | HCl | K_2Cr_2O_7 | KNO_2 | H_2O | KCl | KNO_3 | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | KNO_2 | H_2O | ClK | KNO_3 | Cl_3Cr name | hydrogen chloride | potassium dichromate | potassium nitrite | water | potassium chloride | potassium nitrate | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium nitrite | water | potassium chloride | potassium nitrate | trichlorochromium
| hydrogen chloride | potassium dichromate | potassium nitrite | water | potassium chloride | potassium nitrate | chromic chloride formula | HCl | K_2Cr_2O_7 | KNO_2 | H_2O | KCl | KNO_3 | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | KNO_2 | H_2O | ClK | KNO_3 | Cl_3Cr name | hydrogen chloride | potassium dichromate | potassium nitrite | water | potassium chloride | potassium nitrate | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium nitrite | water | potassium chloride | potassium nitrate | trichlorochromium

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