Input interpretation
HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + CH_3CH_2OH ethanol ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride + CH_3CHO acetaldehyde
Balanced equation
Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + KCl + CrCl_3 + CH_3CHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 CH_3CH_2OH ⟶ c_4 H_2O + c_5 KCl + c_6 CrCl_3 + c_7 CH_3CHO Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr, K, O and C: Cl: | c_1 = c_5 + 3 c_6 H: | c_1 + 6 c_3 = 2 c_4 + 4 c_7 Cr: | 2 c_2 = c_6 K: | 2 c_2 = c_5 O: | 7 c_2 + c_3 = c_4 + c_7 C: | 2 c_3 = 2 c_7 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 = 7 c_5 = 2 c_6 = 2 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + K_2Cr_2O_7 + 3 CH_3CH_2OH ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 CH_3CHO
Structures
+ + ⟶ + + +
Names
hydrogen chloride + potassium dichromate + ethanol ⟶ water + potassium chloride + chromic chloride + acetaldehyde
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + KCl + CrCl_3 + CH_3CHO 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 CH_3CH_2OH ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 CH_3CHO | 3 | 3 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) CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) H_2O | 7 | 7 | ([H2O])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^2 CH_3CHO | 3 | 3 | ([CH3CHO])^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])^(-8) ([K2Cr2O7])^(-1) ([CH3CH2OH])^(-3) ([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([CH3CHO])^3 = (([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([CH3CHO])^3)/(([HCl])^8 [K2Cr2O7] ([CH3CH2OH])^3)](../image_source/548ba2eb723d9f0ebb358337c5ea203f.png)
Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + KCl + CrCl_3 + CH_3CHO 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 CH_3CH_2OH ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 CH_3CHO | 3 | 3 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) CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) H_2O | 7 | 7 | ([H2O])^7 KCl | 2 | 2 | ([KCl])^2 CrCl_3 | 2 | 2 | ([CrCl3])^2 CH_3CHO | 3 | 3 | ([CH3CHO])^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])^(-8) ([K2Cr2O7])^(-1) ([CH3CH2OH])^(-3) ([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([CH3CHO])^3 = (([H2O])^7 ([KCl])^2 ([CrCl3])^2 ([CH3CHO])^3)/(([HCl])^8 [K2Cr2O7] ([CH3CH2OH])^3)
Rate of reaction
![Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + KCl + CrCl_3 + CH_3CHO 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 CH_3CH_2OH ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 CH_3CHO | 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(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) CH_3CHO | 3 | 3 | 1/3 (Δ[CH3CHO])/(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[CH3CH2OH])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[CH3CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/2b16438b19054f22c9e49cc9f43e4fb3.png)
Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + CH_3CH_2OH ⟶ H_2O + KCl + CrCl_3 + CH_3CHO 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 CH_3CH_2OH ⟶ 7 H_2O + 2 KCl + 2 CrCl_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2O | 7 | 7 KCl | 2 | 2 CrCl_3 | 2 | 2 CH_3CHO | 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 | 8 | -8 | -1/8 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(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) CH_3CHO | 3 | 3 | 1/3 (Δ[CH3CHO])/(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[CH3CH2OH])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) = 1/3 (Δ[CH3CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| hydrogen chloride | potassium dichromate | ethanol | water | potassium chloride | chromic chloride | acetaldehyde formula | HCl | K_2Cr_2O_7 | CH_3CH_2OH | H_2O | KCl | CrCl_3 | CH_3CHO Hill formula | ClH | Cr_2K_2O_7 | C_2H_6O | H_2O | ClK | Cl_3Cr | C_2H_4O name | hydrogen chloride | potassium dichromate | ethanol | water | potassium chloride | chromic chloride | acetaldehyde IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | ethanol | water | potassium chloride | trichlorochromium | acetaldehyde