Input interpretation
![Cl_2 chlorine + Cr chromium ⟶ CrCl_3 chromic chloride](../image_source/f819294ea3c9d0b96905a6bd8dbe9344.png)
Cl_2 chlorine + Cr chromium ⟶ CrCl_3 chromic chloride
Balanced equation
![Balance the chemical equation algebraically: Cl_2 + Cr ⟶ CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 Cr ⟶ c_3 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl and Cr: Cl: | 2 c_1 = 3 c_3 Cr: | 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 = 3/2 c_2 = 1 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 2 Cr ⟶ 2 CrCl_3](../image_source/9f823653748b8294eff7ea45db18a005.png)
Balance the chemical equation algebraically: Cl_2 + Cr ⟶ CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 Cr ⟶ c_3 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl and Cr: Cl: | 2 c_1 = 3 c_3 Cr: | 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 = 3/2 c_2 = 1 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 2 Cr ⟶ 2 CrCl_3
Structures
![+ ⟶](../image_source/2ce38a1358e5204ed68dca87e57b3e7a.png)
+ ⟶
Names
![chlorine + chromium ⟶ chromic chloride](../image_source/094eaec20e8635b42a489cb787a69218.png)
chlorine + chromium ⟶ chromic chloride
Reaction thermodynamics
Enthalpy
![| chlorine | chromium | chromic chloride molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -556.5 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -1113 kJ/mol | H_initial = 0 kJ/mol | | H_final = -1113 kJ/mol ΔH_rxn^0 | -1113 kJ/mol - 0 kJ/mol = -1113 kJ/mol (exothermic) | |](../image_source/bbe657e616d893e0bf1889fc44661e25.png)
| chlorine | chromium | chromic chloride molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -556.5 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -1113 kJ/mol | H_initial = 0 kJ/mol | | H_final = -1113 kJ/mol ΔH_rxn^0 | -1113 kJ/mol - 0 kJ/mol = -1113 kJ/mol (exothermic) | |
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Cl_2 + Cr ⟶ 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 Cl_2 + 2 Cr ⟶ 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 Cl_2 | 3 | -3 Cr | 2 | -2 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 Cl_2 | 3 | -3 | ([Cl2])^(-3) Cr | 2 | -2 | ([Cr])^(-2) 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 = ([Cl2])^(-3) ([Cr])^(-2) ([CrCl3])^2 = ([CrCl3])^2/(([Cl2])^3 ([Cr])^2)](../image_source/5c5e710ee21aef1fa478022fc379286a.png)
Construct the equilibrium constant, K, expression for: Cl_2 + Cr ⟶ 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 Cl_2 + 2 Cr ⟶ 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 Cl_2 | 3 | -3 Cr | 2 | -2 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 Cl_2 | 3 | -3 | ([Cl2])^(-3) Cr | 2 | -2 | ([Cr])^(-2) 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 = ([Cl2])^(-3) ([Cr])^(-2) ([CrCl3])^2 = ([CrCl3])^2/(([Cl2])^3 ([Cr])^2)
Rate of reaction
![Construct the rate of reaction expression for: Cl_2 + Cr ⟶ 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 Cl_2 + 2 Cr ⟶ 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 Cl_2 | 3 | -3 Cr | 2 | -2 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(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 = -1/3 (Δ[Cl2])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/729ae55e2d58981f70f47f6ca4a3195d.png)
Construct the rate of reaction expression for: Cl_2 + Cr ⟶ 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 Cl_2 + 2 Cr ⟶ 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 Cl_2 | 3 | -3 Cr | 2 | -2 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 Cl_2 | 3 | -3 | -1/3 (Δ[Cl2])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(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 = -1/3 (Δ[Cl2])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| chlorine | chromium | chromic chloride formula | Cl_2 | Cr | CrCl_3 Hill formula | Cl_2 | Cr | Cl_3Cr name | chlorine | chromium | chromic chloride IUPAC name | molecular chlorine | chromium | trichlorochromium](../image_source/ed1a5dd58cb18301c5849b5395d6779d.png)
| chlorine | chromium | chromic chloride formula | Cl_2 | Cr | CrCl_3 Hill formula | Cl_2 | Cr | Cl_3Cr name | chlorine | chromium | chromic chloride IUPAC name | molecular chlorine | chromium | trichlorochromium
Substance properties
![| chlorine | chromium | chromic chloride molar mass | 70.9 g/mol | 51.9961 g/mol | 158.3 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | 1857 °C | 1152 °C boiling point | -34 °C | 2672 °C | density | 0.003214 g/cm^3 (at 0 °C) | 7.14 g/cm^3 | 2.87 g/cm^3 solubility in water | | insoluble | slightly soluble odor | | odorless |](../image_source/dc7f26f3f9ca4920eb77a7166412a007.png)
| chlorine | chromium | chromic chloride molar mass | 70.9 g/mol | 51.9961 g/mol | 158.3 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -101 °C | 1857 °C | 1152 °C boiling point | -34 °C | 2672 °C | density | 0.003214 g/cm^3 (at 0 °C) | 7.14 g/cm^3 | 2.87 g/cm^3 solubility in water | | insoluble | slightly soluble odor | | odorless |
Units