Input interpretation
HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + H_2O_2 hydrogen peroxide ⟶ H_2O water + O_2 oxygen + KCl potassium chloride + CrCl_3 chromic chloride
Balanced equation
Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + KCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 H_2O_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 KCl + 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 and O: Cl: | c_1 = c_6 + 3 c_7 H: | c_1 + 2 c_3 = 2 c_4 Cr: | 2 c_2 = c_7 K: | 2 c_2 = c_6 O: | 7 c_2 + 2 c_3 = c_4 + 2 c_5 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_4 = c_3 + 4 c_5 = c_3/2 + 3/2 c_6 = 2 c_7 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_3 = 1 and solve for the remaining coefficients: c_1 = 8 c_2 = 1 c_3 = 1 c_4 = 5 c_5 = 2 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2Cr_2O_7 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + 2 KCl + 2 CrCl_3
Structures
+ + ⟶ + + +
Names
hydrogen chloride + potassium dichromate + hydrogen peroxide ⟶ water + oxygen + potassium chloride + chromic chloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + KCl + 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 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + 2 KCl + 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 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 KCl | 2 | 2 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) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 5 | 5 | ([H2O])^5 O_2 | 2 | 2 | ([O2])^2 KCl | 2 | 2 | ([KCl])^2 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) ([H2O2])^(-1) ([H2O])^5 ([O2])^2 ([KCl])^2 ([CrCl3])^2 = (([H2O])^5 ([O2])^2 ([KCl])^2 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] [H2O2])](../image_source/683e4c734f99bcfb9e87e2321ed36f3b.png)
Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + KCl + 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 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + 2 KCl + 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 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 KCl | 2 | 2 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) H_2O_2 | 1 | -1 | ([H2O2])^(-1) H_2O | 5 | 5 | ([H2O])^5 O_2 | 2 | 2 | ([O2])^2 KCl | 2 | 2 | ([KCl])^2 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) ([H2O2])^(-1) ([H2O])^5 ([O2])^2 ([KCl])^2 ([CrCl3])^2 = (([H2O])^5 ([O2])^2 ([KCl])^2 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] [H2O2])
Rate of reaction
![Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + KCl + 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 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + 2 KCl + 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 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 KCl | 2 | 2 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) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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) = -(Δ[H2O2])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/7709146d68feb886f133589bf7e43247.png)
Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + H_2O_2 ⟶ H_2O + O_2 + KCl + 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 + H_2O_2 ⟶ 5 H_2O + 2 O_2 + 2 KCl + 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 H_2O_2 | 1 | -1 H_2O | 5 | 5 O_2 | 2 | 2 KCl | 2 | 2 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) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(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) = -(Δ[H2O2])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[O2])/(Δt) = 1/2 (Δ[KCl])/(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 | hydrogen peroxide | water | oxygen | potassium chloride | chromic chloride formula | HCl | K_2Cr_2O_7 | H_2O_2 | H_2O | O_2 | KCl | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | H_2O_2 | H_2O | O_2 | ClK | Cl_3Cr name | hydrogen chloride | potassium dichromate | hydrogen peroxide | water | oxygen | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | hydrogen peroxide | water | molecular oxygen | potassium chloride | trichlorochromium