Input interpretation
![O_2 (oxygen) + HCl (hydrogen chloride) + Cr (chromium) ⟶ H_2O (water) + CrCl_3 (chromic chloride)](../image_source/fc898e27827139ce96c2219debd6b9ab.png)
O_2 (oxygen) + HCl (hydrogen chloride) + Cr (chromium) ⟶ H_2O (water) + CrCl_3 (chromic chloride)
Balanced equation
![Balance the chemical equation algebraically: O_2 + HCl + Cr ⟶ H_2O + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 HCl + c_3 Cr ⟶ c_4 H_2O + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cl, H and Cr: O: | 2 c_1 = c_4 Cl: | c_2 = 3 c_5 H: | c_2 = 2 c_4 Cr: | c_3 = c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4/3 c_4 = 2 c_5 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 3 c_2 = 12 c_3 = 4 c_4 = 6 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 CrCl_3](../image_source/dafa54f7236c43055745f8b186a80db2.png)
Balance the chemical equation algebraically: O_2 + HCl + Cr ⟶ H_2O + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 HCl + c_3 Cr ⟶ c_4 H_2O + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Cl, H and Cr: O: | 2 c_1 = c_4 Cl: | c_2 = 3 c_5 H: | c_2 = 2 c_4 Cr: | c_3 = c_5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4/3 c_4 = 2 c_5 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 3 c_2 = 12 c_3 = 4 c_4 = 6 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 CrCl_3
Structures
![+ + ⟶ +](../image_source/23510a56c8ef307e63382799c8066924.png)
+ + ⟶ +
Names
![oxygen + hydrogen chloride + chromium ⟶ water + chromic chloride](../image_source/f532ad52778607af98dc0ebf696cd9b5.png)
oxygen + hydrogen chloride + chromium ⟶ water + chromic chloride
Reaction thermodynamics
Enthalpy
![| oxygen | hydrogen chloride | chromium | water | chromic chloride molecular enthalpy | 0 kJ/mol | -92.3 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -556.5 kJ/mol total enthalpy | 0 kJ/mol | -1108 kJ/mol | 0 kJ/mol | -1715 kJ/mol | -2226 kJ/mol | H_initial = -1108 kJ/mol | | | H_final = -3941 kJ/mol | ΔH_rxn^0 | -3941 kJ/mol - -1108 kJ/mol = -2833 kJ/mol (exothermic) | | | |](../image_source/fc03a7dad35d626a093705ce360ea274.png)
| oxygen | hydrogen chloride | chromium | water | chromic chloride molecular enthalpy | 0 kJ/mol | -92.3 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -556.5 kJ/mol total enthalpy | 0 kJ/mol | -1108 kJ/mol | 0 kJ/mol | -1715 kJ/mol | -2226 kJ/mol | H_initial = -1108 kJ/mol | | | H_final = -3941 kJ/mol | ΔH_rxn^0 | -3941 kJ/mol - -1108 kJ/mol = -2833 kJ/mol (exothermic) | | | |
Equilibrium constant
![Construct the equilibrium constant, K, expression for: O_2 + HCl + Cr ⟶ H_2O + 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: 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 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 O_2 | 3 | -3 HCl | 12 | -12 Cr | 4 | -4 H_2O | 6 | 6 CrCl_3 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) HCl | 12 | -12 | ([HCl])^(-12) Cr | 4 | -4 | ([Cr])^(-4) H_2O | 6 | 6 | ([H2O])^6 CrCl_3 | 4 | 4 | ([CrCl3])^4 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 = ([O2])^(-3) ([HCl])^(-12) ([Cr])^(-4) ([H2O])^6 ([CrCl3])^4 = (([H2O])^6 ([CrCl3])^4)/(([O2])^3 ([HCl])^12 ([Cr])^4)](../image_source/f7305adc4fcb114590dbfaa546a8280f.png)
Construct the equilibrium constant, K, expression for: O_2 + HCl + Cr ⟶ H_2O + 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: 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 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 O_2 | 3 | -3 HCl | 12 | -12 Cr | 4 | -4 H_2O | 6 | 6 CrCl_3 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) HCl | 12 | -12 | ([HCl])^(-12) Cr | 4 | -4 | ([Cr])^(-4) H_2O | 6 | 6 | ([H2O])^6 CrCl_3 | 4 | 4 | ([CrCl3])^4 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 = ([O2])^(-3) ([HCl])^(-12) ([Cr])^(-4) ([H2O])^6 ([CrCl3])^4 = (([H2O])^6 ([CrCl3])^4)/(([O2])^3 ([HCl])^12 ([Cr])^4)
Rate of reaction
![Construct the rate of reaction expression for: O_2 + HCl + Cr ⟶ H_2O + 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: 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 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 O_2 | 3 | -3 HCl | 12 | -12 Cr | 4 | -4 H_2O | 6 | 6 CrCl_3 | 4 | 4 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) Cr | 4 | -4 | -1/4 (Δ[Cr])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CrCl_3 | 4 | 4 | 1/4 (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 = -1/3 (Δ[O2])/(Δt) = -1/12 (Δ[HCl])/(Δt) = -1/4 (Δ[Cr])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/2d2b47c27f044bc18e0b26a1649c1c2a.png)
Construct the rate of reaction expression for: O_2 + HCl + Cr ⟶ H_2O + 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: 3 O_2 + 12 HCl + 4 Cr ⟶ 6 H_2O + 4 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 O_2 | 3 | -3 HCl | 12 | -12 Cr | 4 | -4 H_2O | 6 | 6 CrCl_3 | 4 | 4 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) HCl | 12 | -12 | -1/12 (Δ[HCl])/(Δt) Cr | 4 | -4 | -1/4 (Δ[Cr])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(Δt) CrCl_3 | 4 | 4 | 1/4 (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 = -1/3 (Δ[O2])/(Δt) = -1/12 (Δ[HCl])/(Δt) = -1/4 (Δ[Cr])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/4 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| oxygen | hydrogen chloride | chromium | water | chromic chloride formula | O_2 | HCl | Cr | H_2O | CrCl_3 Hill formula | O_2 | ClH | Cr | H_2O | Cl_3Cr name | oxygen | hydrogen chloride | chromium | water | chromic chloride IUPAC name | molecular oxygen | hydrogen chloride | chromium | water | trichlorochromium](../image_source/686895878e6339dfc9c05a2a548d4564.png)
| oxygen | hydrogen chloride | chromium | water | chromic chloride formula | O_2 | HCl | Cr | H_2O | CrCl_3 Hill formula | O_2 | ClH | Cr | H_2O | Cl_3Cr name | oxygen | hydrogen chloride | chromium | water | chromic chloride IUPAC name | molecular oxygen | hydrogen chloride | chromium | water | trichlorochromium
Substance properties
![| oxygen | hydrogen chloride | chromium | water | chromic chloride molar mass | 31.998 g/mol | 36.46 g/mol | 51.9961 g/mol | 18.015 g/mol | 158.3 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -218 °C | -114.17 °C | 1857 °C | 0 °C | 1152 °C boiling point | -183 °C | -85 °C | 2672 °C | 99.9839 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.00149 g/cm^3 (at 25 °C) | 7.14 g/cm^3 | 1 g/cm^3 | 2.87 g/cm^3 solubility in water | | miscible | insoluble | | slightly soluble surface tension | 0.01347 N/m | | | 0.0728 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |](../image_source/5f1a1d37d7e7f954e3f555de0349b825.png)
| oxygen | hydrogen chloride | chromium | water | chromic chloride molar mass | 31.998 g/mol | 36.46 g/mol | 51.9961 g/mol | 18.015 g/mol | 158.3 g/mol phase | gas (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -218 °C | -114.17 °C | 1857 °C | 0 °C | 1152 °C boiling point | -183 °C | -85 °C | 2672 °C | 99.9839 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.00149 g/cm^3 (at 25 °C) | 7.14 g/cm^3 | 1 g/cm^3 | 2.87 g/cm^3 solubility in water | | miscible | insoluble | | slightly soluble surface tension | 0.01347 N/m | | | 0.0728 N/m | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |
Units