Input interpretation
HCl (hydrogen chloride) + K_2Cr_2O_7 (potassium dichromate) ⟶ H_2O (water) + Cl_2 (chlorine) + KCl (potassium chloride) + CrCl_3 (chromic chloride)
Balanced equation
Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 ⟶ H_2O + Cl_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 + c_4 Cl_2 + c_5 KCl + c_6 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 = 2 c_4 + c_5 + 3 c_6 H: | c_1 = 2 c_3 Cr: | 2 c_2 = c_6 K: | 2 c_2 = c_5 O: | 7 c_2 = c_3 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 = 14 c_2 = 1 c_3 = 7 c_4 = 3 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + K_2Cr_2O_7 ⟶ 7 H_2O + 3 Cl_2 + 2 KCl + 2 CrCl_3
Structures
+ ⟶ + + +
Names
hydrogen chloride + potassium dichromate ⟶ water + chlorine + potassium chloride + chromic chloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 ⟶ H_2O + Cl_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: 14 HCl + K_2Cr_2O_7 ⟶ 7 H_2O + 3 Cl_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 | 14 | -14 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Cl_2 | 3 | 3 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 | 14 | -14 | ([HCl])^(-14) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 Cl_2 | 3 | 3 | ([Cl2])^3 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])^(-14) ([K2Cr2O7])^(-1) ([H2O])^7 ([Cl2])^3 ([KCl])^2 ([CrCl3])^2 = (([H2O])^7 ([Cl2])^3 ([KCl])^2 ([CrCl3])^2)/(([HCl])^14 [K2Cr2O7])](../image_source/43d2c4347e670bccb8249dc431ff5b77.png)
Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 ⟶ H_2O + Cl_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: 14 HCl + K_2Cr_2O_7 ⟶ 7 H_2O + 3 Cl_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 | 14 | -14 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Cl_2 | 3 | 3 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 | 14 | -14 | ([HCl])^(-14) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 Cl_2 | 3 | 3 | ([Cl2])^3 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])^(-14) ([K2Cr2O7])^(-1) ([H2O])^7 ([Cl2])^3 ([KCl])^2 ([CrCl3])^2 = (([H2O])^7 ([Cl2])^3 ([KCl])^2 ([CrCl3])^2)/(([HCl])^14 [K2Cr2O7])
Rate of reaction
![Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 ⟶ H_2O + Cl_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: 14 HCl + K_2Cr_2O_7 ⟶ 7 H_2O + 3 Cl_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 | 14 | -14 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Cl_2 | 3 | 3 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 | 14 | -14 | -1/14 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(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 = -1/14 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/51857d963fd12f43909137fc53a19284.png)
Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 ⟶ H_2O + Cl_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: 14 HCl + K_2Cr_2O_7 ⟶ 7 H_2O + 3 Cl_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 | 14 | -14 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 Cl_2 | 3 | 3 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 | 14 | -14 | -1/14 (Δ[HCl])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) Cl_2 | 3 | 3 | 1/3 (Δ[Cl2])/(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 = -1/14 (Δ[HCl])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[Cl2])/(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 | water | chlorine | potassium chloride | chromic chloride formula | HCl | K_2Cr_2O_7 | H_2O | Cl_2 | KCl | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | H_2O | Cl_2 | ClK | Cl_3Cr name | hydrogen chloride | potassium dichromate | water | chlorine | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | molecular chlorine | potassium chloride | trichlorochromium