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HCl + K3[Cr(OH)6] = H2O + KCl + CrCl3

Input interpretation

HCl hydrogen chloride + K3Cr(OH)6 ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride
HCl hydrogen chloride + K3Cr(OH)6 ⟶ H_2O water + KCl potassium chloride + CrCl_3 chromic chloride

Balanced equation

Balance the chemical equation algebraically: HCl + K3Cr(OH)6 ⟶ H_2O + KCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K3Cr(OH)6 ⟶ c_3 H_2O + c_4 KCl + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Cr and O: Cl: | c_1 = c_4 + 3 c_5 H: | c_1 + 6 c_2 = 2 c_3 K: | 3 c_2 = c_4 Cr: | c_2 = c_5 O: | 6 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 = 6 c_2 = 1 c_3 = 6 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + CrCl_3
Balance the chemical equation algebraically: HCl + K3Cr(OH)6 ⟶ H_2O + KCl + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 K3Cr(OH)6 ⟶ c_3 H_2O + c_4 KCl + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, K, Cr and O: Cl: | c_1 = c_4 + 3 c_5 H: | c_1 + 6 c_2 = 2 c_3 K: | 3 c_2 = c_4 Cr: | c_2 = c_5 O: | 6 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 = 6 c_2 = 1 c_3 = 6 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + CrCl_3

Structures

+ K3Cr(OH)6 ⟶ + +
+ K3Cr(OH)6 ⟶ + +

Names

hydrogen chloride + K3Cr(OH)6 ⟶ water + potassium chloride + chromic chloride
hydrogen chloride + K3Cr(OH)6 ⟶ water + potassium chloride + chromic chloride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + K3Cr(OH)6 ⟶ H_2O + 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: 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + 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 | 6 | -6 K3Cr(OH)6 | 1 | -1 H_2O | 6 | 6 KCl | 3 | 3 CrCl_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) K3Cr(OH)6 | 1 | -1 | ([K3Cr(OH)6])^(-1) H_2O | 6 | 6 | ([H2O])^6 KCl | 3 | 3 | ([KCl])^3 CrCl_3 | 1 | 1 | [CrCl3] 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])^(-6) ([K3Cr(OH)6])^(-1) ([H2O])^6 ([KCl])^3 [CrCl3] = (([H2O])^6 ([KCl])^3 [CrCl3])/(([HCl])^6 [K3Cr(OH)6])
Construct the equilibrium constant, K, expression for: HCl + K3Cr(OH)6 ⟶ H_2O + 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: 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + 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 | 6 | -6 K3Cr(OH)6 | 1 | -1 H_2O | 6 | 6 KCl | 3 | 3 CrCl_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) K3Cr(OH)6 | 1 | -1 | ([K3Cr(OH)6])^(-1) H_2O | 6 | 6 | ([H2O])^6 KCl | 3 | 3 | ([KCl])^3 CrCl_3 | 1 | 1 | [CrCl3] 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])^(-6) ([K3Cr(OH)6])^(-1) ([H2O])^6 ([KCl])^3 [CrCl3] = (([H2O])^6 ([KCl])^3 [CrCl3])/(([HCl])^6 [K3Cr(OH)6])

Rate of reaction

Construct the rate of reaction expression for: HCl + K3Cr(OH)6 ⟶ H_2O + 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: 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + 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 | 6 | -6 K3Cr(OH)6 | 1 | -1 H_2O | 6 | 6 KCl | 3 | 3 CrCl_3 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) K3Cr(OH)6 | 1 | -1 | -(Δ[K3Cr(OH)6])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) CrCl_3 | 1 | 1 | (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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[K3Cr(OH)6])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + K3Cr(OH)6 ⟶ H_2O + 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: 6 HCl + K3Cr(OH)6 ⟶ 6 H_2O + 3 KCl + 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 | 6 | -6 K3Cr(OH)6 | 1 | -1 H_2O | 6 | 6 KCl | 3 | 3 CrCl_3 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) K3Cr(OH)6 | 1 | -1 | -(Δ[K3Cr(OH)6])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) KCl | 3 | 3 | 1/3 (Δ[KCl])/(Δt) CrCl_3 | 1 | 1 | (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 = -1/6 (Δ[HCl])/(Δt) = -(Δ[K3Cr(OH)6])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/3 (Δ[KCl])/(Δt) = (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | K3Cr(OH)6 | water | potassium chloride | chromic chloride formula | HCl | K3Cr(OH)6 | H_2O | KCl | CrCl_3 Hill formula | ClH | H6CrK3O6 | H_2O | ClK | Cl_3Cr name | hydrogen chloride | | water | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | | water | potassium chloride | trichlorochromium
| hydrogen chloride | K3Cr(OH)6 | water | potassium chloride | chromic chloride formula | HCl | K3Cr(OH)6 | H_2O | KCl | CrCl_3 Hill formula | ClH | H6CrK3O6 | H_2O | ClK | Cl_3Cr name | hydrogen chloride | | water | potassium chloride | chromic chloride IUPAC name | hydrogen chloride | | water | potassium chloride | trichlorochromium

Substance properties

| hydrogen chloride | K3Cr(OH)6 | water | potassium chloride | chromic chloride molar mass | 36.46 g/mol | 271.33 g/mol | 18.015 g/mol | 74.55 g/mol | 158.3 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | 770 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 1.98 g/cm^3 | 2.87 g/cm^3 solubility in water | miscible | | | soluble | slightly soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | odorless |
| hydrogen chloride | K3Cr(OH)6 | water | potassium chloride | chromic chloride molar mass | 36.46 g/mol | 271.33 g/mol | 18.015 g/mol | 74.55 g/mol | 158.3 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | 770 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | 1420 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 1.98 g/cm^3 | 2.87 g/cm^3 solubility in water | miscible | | | soluble | slightly soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | odorless |

Units

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