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HCl + Na2Cr2O7 + CrCl2 = H2O + NaCl + CrCl3

Input interpretation

HCl hydrogen chloride + Na_2Cr_2O_7 sodium bichromate + CrCl_2 chromous chloride ⟶ H_2O water + NaCl sodium chloride + CrCl_3 chromic chloride
HCl hydrogen chloride + Na_2Cr_2O_7 sodium bichromate + CrCl_2 chromous chloride ⟶ H_2O water + NaCl sodium chloride + CrCl_3 chromic chloride

Balanced equation

Balance the chemical equation algebraically: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Na_2Cr_2O_7 + c_3 CrCl_2 ⟶ c_4 H_2O + c_5 NaCl + 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, Na and O: Cl: | c_1 + 2 c_3 = c_5 + 3 c_6 H: | c_1 = 2 c_4 Cr: | 2 c_2 + c_3 = c_6 Na: | 2 c_2 = c_5 O: | 7 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14 c_2 = 1 c_3 = 6 c_4 = 7 c_5 = 2 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 CrCl_3
Balance the chemical equation algebraically: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Na_2Cr_2O_7 + c_3 CrCl_2 ⟶ c_4 H_2O + c_5 NaCl + 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, Na and O: Cl: | c_1 + 2 c_3 = c_5 + 3 c_6 H: | c_1 = 2 c_4 Cr: | 2 c_2 + c_3 = c_6 Na: | 2 c_2 = c_5 O: | 7 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 14 c_2 = 1 c_3 = 6 c_4 = 7 c_5 = 2 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HCl + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 CrCl_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

hydrogen chloride + sodium bichromate + chromous chloride ⟶ water + sodium chloride + chromic chloride
hydrogen chloride + sodium bichromate + chromous chloride ⟶ water + sodium chloride + chromic chloride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + 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 + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 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 Na_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 NaCl | 2 | 2 CrCl_3 | 8 | 8 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) Na_2Cr_2O_7 | 1 | -1 | ([Na2Cr2O7])^(-1) CrCl_2 | 6 | -6 | ([CrCl2])^(-6) H_2O | 7 | 7 | ([H2O])^7 NaCl | 2 | 2 | ([NaCl])^2 CrCl_3 | 8 | 8 | ([CrCl3])^8 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) ([Na2Cr2O7])^(-1) ([CrCl2])^(-6) ([H2O])^7 ([NaCl])^2 ([CrCl3])^8 = (([H2O])^7 ([NaCl])^2 ([CrCl3])^8)/(([HCl])^14 [Na2Cr2O7] ([CrCl2])^6)
Construct the equilibrium constant, K, expression for: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + 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 + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 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 Na_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 NaCl | 2 | 2 CrCl_3 | 8 | 8 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) Na_2Cr_2O_7 | 1 | -1 | ([Na2Cr2O7])^(-1) CrCl_2 | 6 | -6 | ([CrCl2])^(-6) H_2O | 7 | 7 | ([H2O])^7 NaCl | 2 | 2 | ([NaCl])^2 CrCl_3 | 8 | 8 | ([CrCl3])^8 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) ([Na2Cr2O7])^(-1) ([CrCl2])^(-6) ([H2O])^7 ([NaCl])^2 ([CrCl3])^8 = (([H2O])^7 ([NaCl])^2 ([CrCl3])^8)/(([HCl])^14 [Na2Cr2O7] ([CrCl2])^6)

Rate of reaction

Construct the rate of reaction expression for: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + 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 + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 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 Na_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 NaCl | 2 | 2 CrCl_3 | 8 | 8 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) Na_2Cr_2O_7 | 1 | -1 | -(Δ[Na2Cr2O7])/(Δt) CrCl_2 | 6 | -6 | -1/6 (Δ[CrCl2])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) CrCl_3 | 8 | 8 | 1/8 (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[Na2Cr2O7])/(Δt) = -1/6 (Δ[CrCl2])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/8 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + Na_2Cr_2O_7 + CrCl_2 ⟶ H_2O + NaCl + 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 + Na_2Cr_2O_7 + 6 CrCl_2 ⟶ 7 H_2O + 2 NaCl + 8 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 Na_2Cr_2O_7 | 1 | -1 CrCl_2 | 6 | -6 H_2O | 7 | 7 NaCl | 2 | 2 CrCl_3 | 8 | 8 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) Na_2Cr_2O_7 | 1 | -1 | -(Δ[Na2Cr2O7])/(Δt) CrCl_2 | 6 | -6 | -1/6 (Δ[CrCl2])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) CrCl_3 | 8 | 8 | 1/8 (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[Na2Cr2O7])/(Δt) = -1/6 (Δ[CrCl2])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = 1/8 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | sodium bichromate | chromous chloride | water | sodium chloride | chromic chloride formula | HCl | Na_2Cr_2O_7 | CrCl_2 | H_2O | NaCl | CrCl_3 Hill formula | ClH | Cr_2Na_2O_7 | Cl_2Cr | H_2O | ClNa | Cl_3Cr name | hydrogen chloride | sodium bichromate | chromous chloride | water | sodium chloride | chromic chloride IUPAC name | hydrogen chloride | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | dichlorochromium | water | sodium chloride | trichlorochromium
| hydrogen chloride | sodium bichromate | chromous chloride | water | sodium chloride | chromic chloride formula | HCl | Na_2Cr_2O_7 | CrCl_2 | H_2O | NaCl | CrCl_3 Hill formula | ClH | Cr_2Na_2O_7 | Cl_2Cr | H_2O | ClNa | Cl_3Cr name | hydrogen chloride | sodium bichromate | chromous chloride | water | sodium chloride | chromic chloride IUPAC name | hydrogen chloride | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | dichlorochromium | water | sodium chloride | trichlorochromium

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