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HCl + Zn + K2Cr2O7 = H2O + KCl + CrCl3 + ZnCl2

Input interpretation

HCl hydrogen chloride + Zn zinc + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride + ZnCl_2 zinc chloride
HCl hydrogen chloride + Zn zinc + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride + ZnCl_2 zinc chloride

Balanced equation

Balance the chemical equation algebraically: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Zn + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 + c_7 ZnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Zn, Cr, K and O: Cl: | c_1 = c_5 + 3 c_6 + 2 c_7 H: | c_1 = 2 c_4 Zn: | c_2 = c_7 Cr: | 2 c_3 = c_6 K: | 2 c_3 = c_5 O: | 7 c_3 = c_4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14 c_2 = 3 c_3 = 1 c_4 = 7 c_5 = 2 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2
Balance the chemical equation algebraically: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Zn + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 + c_7 ZnCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Zn, Cr, K and O: Cl: | c_1 = c_5 + 3 c_6 + 2 c_7 H: | c_1 = 2 c_4 Zn: | c_2 = c_7 Cr: | 2 c_3 = c_6 K: | 2 c_3 = c_5 O: | 7 c_3 = c_4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14 c_2 = 3 c_3 = 1 c_4 = 7 c_5 = 2 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

hydrogen chloride + zinc + potassium dichromate ⟶ water + potassium chloride + chromic chloride + zinc chloride
hydrogen chloride + zinc + potassium dichromate ⟶ water + potassium chloride + chromic chloride + zinc chloride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 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: 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2 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 | 14 | -14 Zn | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 ZnCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 14 | -14 | ([HCl])^(-14) Zn | 3 | -3 | ([Zn])^(-3) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^2 ZnCl_2 | 3 | 3 | ([ZnCl2])^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])^(-14) ([Zn])^(-3) ([K2Cr2O7])^(-1) ([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([ZnCl2])^3 = (([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([ZnCl2])^3)/(([HCl])^14 ([Zn])^3 [K2Cr2O7])
Construct the equilibrium constant, K, expression for: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 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: 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2 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 | 14 | -14 Zn | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 ZnCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 14 | -14 | ([HCl])^(-14) Zn | 3 | -3 | ([Zn])^(-3) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^2 ZnCl_2 | 3 | 3 | ([ZnCl2])^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])^(-14) ([Zn])^(-3) ([K2Cr2O7])^(-1) ([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([ZnCl2])^3 = (([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([ZnCl2])^3)/(([HCl])^14 ([Zn])^3 [K2Cr2O7])

Rate of reaction

Construct the rate of reaction expression for: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 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: 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2 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 | 14 | -14 Zn | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 ZnCl_2 | 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 | 14 | -14 | -1/14 (Δ[HCl])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(Δt) ZnCl_2 | 3 | 3 | 1/3 (Δ[ZnCl2])/(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 = -1/14 (Δ[HCl])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[ZnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + Zn + K_2Cr_2O_7 ⟶ H_2O + KCl + CrCl_3 + ZnCl_2 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: 14 HCl + 3 Zn + K_2Cr_2O_7 ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 ZnCl_2 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 | 14 | -14 Zn | 3 | -3 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 ZnCl_2 | 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 | 14 | -14 | -1/14 (Δ[HCl])/(Δt) Zn | 3 | -3 | -1/3 (Δ[Zn])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) CrCl_3 | 2 | 2 | 1/2 (Δ[CrCl3])/(Δt) ZnCl_2 | 3 | 3 | 1/3 (Δ[ZnCl2])/(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 = -1/14 (Δ[HCl])/(Δt) = -1/3 (Δ[Zn])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[ZnCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | zinc | potassium dichromate | water | potassium chloride | chromic chloride | zinc chloride formula | HCl | Zn | K_2Cr_2O_7 | H_2O | KCl | CrCl_3 | ZnCl_2 Hill formula | ClH | Zn | Cr_2K_2O_7 | H_2O | ClK | Cl_3Cr | Cl_2Zn name | hydrogen chloride | zinc | potassium dichromate | water | potassium chloride | chromic chloride | zinc chloride IUPAC name | hydrogen chloride | zinc | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | potassium chloride | trichlorochromium | zinc dichloride
| hydrogen chloride | zinc | potassium dichromate | water | potassium chloride | chromic chloride | zinc chloride formula | HCl | Zn | K_2Cr_2O_7 | H_2O | KCl | CrCl_3 | ZnCl_2 Hill formula | ClH | Zn | Cr_2K_2O_7 | H_2O | ClK | Cl_3Cr | Cl_2Zn name | hydrogen chloride | zinc | potassium dichromate | water | potassium chloride | chromic chloride | zinc chloride IUPAC name | hydrogen chloride | zinc | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | potassium chloride | trichlorochromium | zinc dichloride

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