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HCl + CrO = H2O + H2 + CrCl3

Input interpretation

HCl hydrogen chloride + CrO ⟶ H_2O water + H_2 hydrogen + CrCl_3 chromic chloride
HCl hydrogen chloride + CrO ⟶ H_2O water + H_2 hydrogen + CrCl_3 chromic chloride

Balanced equation

Balance the chemical equation algebraically: HCl + CrO ⟶ H_2O + H_2 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 CrO ⟶ c_3 H_2O + c_4 H_2 + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr and O: Cl: | c_1 = 3 c_5 H: | c_1 = 2 c_3 + 2 c_4 Cr: | c_2 = c_5 O: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 2 CrO ⟶ 2 H_2O + H_2 + 2 CrCl_3
Balance the chemical equation algebraically: HCl + CrO ⟶ H_2O + H_2 + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 CrO ⟶ c_3 H_2O + c_4 H_2 + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Cr and O: Cl: | c_1 = 3 c_5 H: | c_1 = 2 c_3 + 2 c_4 Cr: | c_2 = c_5 O: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 2 CrO ⟶ 2 H_2O + H_2 + 2 CrCl_3

Structures

+ CrO ⟶ + +
+ CrO ⟶ + +

Names

hydrogen chloride + CrO ⟶ water + hydrogen + chromic chloride
hydrogen chloride + CrO ⟶ water + hydrogen + chromic chloride

Equilibrium constant

Construct the equilibrium constant, K, expression for: HCl + CrO ⟶ H_2O + H_2 + 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 + 2 CrO ⟶ 2 H_2O + H_2 + 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 | 6 | -6 CrO | 2 | -2 H_2O | 2 | 2 H_2 | 1 | 1 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 | 6 | -6 | ([HCl])^(-6) CrO | 2 | -2 | ([CrO])^(-2) H_2O | 2 | 2 | ([H2O])^2 H_2 | 1 | 1 | [H2] 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])^(-6) ([CrO])^(-2) ([H2O])^2 [H2] ([CrCl3])^2 = (([H2O])^2 [H2] ([CrCl3])^2)/(([HCl])^6 ([CrO])^2)
Construct the equilibrium constant, K, expression for: HCl + CrO ⟶ H_2O + H_2 + 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 + 2 CrO ⟶ 2 H_2O + H_2 + 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 | 6 | -6 CrO | 2 | -2 H_2O | 2 | 2 H_2 | 1 | 1 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 | 6 | -6 | ([HCl])^(-6) CrO | 2 | -2 | ([CrO])^(-2) H_2O | 2 | 2 | ([H2O])^2 H_2 | 1 | 1 | [H2] 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])^(-6) ([CrO])^(-2) ([H2O])^2 [H2] ([CrCl3])^2 = (([H2O])^2 [H2] ([CrCl3])^2)/(([HCl])^6 ([CrO])^2)

Rate of reaction

Construct the rate of reaction expression for: HCl + CrO ⟶ H_2O + H_2 + 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 + 2 CrO ⟶ 2 H_2O + H_2 + 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 | 6 | -6 CrO | 2 | -2 H_2O | 2 | 2 H_2 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) CrO | 2 | -2 | -1/2 (Δ[CrO])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(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 = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[CrO])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: HCl + CrO ⟶ H_2O + H_2 + 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 + 2 CrO ⟶ 2 H_2O + H_2 + 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 | 6 | -6 CrO | 2 | -2 H_2O | 2 | 2 H_2 | 1 | 1 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) CrO | 2 | -2 | -1/2 (Δ[CrO])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(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 = -1/6 (Δ[HCl])/(Δt) = -1/2 (Δ[CrO])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| hydrogen chloride | CrO | water | hydrogen | chromic chloride formula | HCl | CrO | H_2O | H_2 | CrCl_3 Hill formula | ClH | CrO | H_2O | H_2 | Cl_3Cr name | hydrogen chloride | | water | hydrogen | chromic chloride IUPAC name | hydrogen chloride | | water | molecular hydrogen | trichlorochromium
| hydrogen chloride | CrO | water | hydrogen | chromic chloride formula | HCl | CrO | H_2O | H_2 | CrCl_3 Hill formula | ClH | CrO | H_2O | H_2 | Cl_3Cr name | hydrogen chloride | | water | hydrogen | chromic chloride IUPAC name | hydrogen chloride | | water | molecular hydrogen | trichlorochromium

Substance properties

| hydrogen chloride | CrO | water | hydrogen | chromic chloride molar mass | 36.46 g/mol | 67.995 g/mol | 18.015 g/mol | 2.016 g/mol | 158.3 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | -259.2 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | -252.8 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.87 g/cm^3 solubility in water | miscible | | | | slightly soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless | odorless |
| hydrogen chloride | CrO | water | hydrogen | chromic chloride molar mass | 36.46 g/mol | 67.995 g/mol | 18.015 g/mol | 2.016 g/mol | 158.3 g/mol phase | gas (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | -114.17 °C | | 0 °C | -259.2 °C | 1152 °C boiling point | -85 °C | | 99.9839 °C | -252.8 °C | density | 0.00149 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.87 g/cm^3 solubility in water | miscible | | | | slightly soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless | odorless |

Units

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