Input interpretation
HCl hydrogen chloride + K_2Cr_2O_7 potassium dichromate + Na_2SO_3 sodium sulfite ⟶ H_2O water + KCl potassium chloride + Na_2SO_4 sodium sulfate + CrCl_3 chromic chloride
Balanced equation
Balance the chemical equation algebraically: HCl + K_2Cr_2O_7 + Na_2SO_3 ⟶ H_2O + KCl + Na_2SO_4 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K_2Cr_2O_7 + c_3 Na_2SO_3 ⟶ c_4 H_2O + c_5 KCl + c_6 Na_2SO_4 + 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, Na and S: 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_5 O: | 7 c_2 + 3 c_3 = c_4 + 4 c_6 Na: | 2 c_3 = 2 c_6 S: | 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 Na_2SO_3 ⟶ 4 H_2O + 2 KCl + 3 Na_2SO_4 + 2 CrCl_3
Structures
+ + ⟶ + + +
Names
hydrogen chloride + potassium dichromate + sodium sulfite ⟶ water + potassium chloride + sodium sulfate + chromic chloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + Na_2SO_3 ⟶ H_2O + KCl + Na_2SO_4 + 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 Na_2SO_3 ⟶ 4 H_2O + 2 KCl + 3 Na_2SO_4 + 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 Na_2SO_3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 Na_2SO_4 | 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) Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^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) ([Na2SO3])^(-3) ([H2O])^4 ([KCl])^2 ([Na2SO4])^3 ([CrCl3])^2 = (([H2O])^4 ([KCl])^2 ([Na2SO4])^3 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] ([Na2SO3])^3)](../image_source/63e168852ad5a2e699c31fb0e2aa1f2d.png)
Construct the equilibrium constant, K, expression for: HCl + K_2Cr_2O_7 + Na_2SO_3 ⟶ H_2O + KCl + Na_2SO_4 + 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 Na_2SO_3 ⟶ 4 H_2O + 2 KCl + 3 Na_2SO_4 + 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 Na_2SO_3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 Na_2SO_4 | 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) Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 Na_2SO_4 | 3 | 3 | ([Na2SO4])^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) ([Na2SO3])^(-3) ([H2O])^4 ([KCl])^2 ([Na2SO4])^3 ([CrCl3])^2 = (([H2O])^4 ([KCl])^2 ([Na2SO4])^3 ([CrCl3])^2)/(([HCl])^8 [K2Cr2O7] ([Na2SO3])^3)
Rate of reaction
![Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + Na_2SO_3 ⟶ H_2O + KCl + Na_2SO_4 + 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 Na_2SO_3 ⟶ 4 H_2O + 2 KCl + 3 Na_2SO_4 + 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 Na_2SO_3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 Na_2SO_4 | 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) Na_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(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[Na2SO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/c91cb0eb62d3ce54014fde52b1fee05e.png)
Construct the rate of reaction expression for: HCl + K_2Cr_2O_7 + Na_2SO_3 ⟶ H_2O + KCl + Na_2SO_4 + 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 Na_2SO_3 ⟶ 4 H_2O + 2 KCl + 3 Na_2SO_4 + 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 Na_2SO_3 | 3 | -3 H_2O | 4 | 4 KCl | 2 | 2 Na_2SO_4 | 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) Na_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(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[Na2SO3])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = 1/3 (Δ[Na2SO4])/(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 | sodium sulfite | water | potassium chloride | sodium sulfate | chromic chloride formula | HCl | K_2Cr_2O_7 | Na_2SO_3 | H_2O | KCl | Na_2SO_4 | CrCl_3 Hill formula | ClH | Cr_2K_2O_7 | Na_2O_3S | H_2O | ClK | Na_2O_4S | Cl_3Cr name | hydrogen chloride | potassium dichromate | sodium sulfite | water | potassium chloride | sodium sulfate | chromic chloride IUPAC name | hydrogen chloride | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | disodium sulfite | water | potassium chloride | disodium sulfate | trichlorochromium