Cl2 + C + Cr2O3 = CO + CrCl3

Cl_2 chlorine + C activated charcoal + Cr_2O_3 chromium(III) oxide ⟶ CO carbon monoxide + CrCl_3 chromic chloride

Balance the chemical equation algebraically: Cl_2 + C + Cr_2O_3 ⟶ CO + CrCl_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 C + c_3 Cr_2O_3 ⟶ c_4 CO + c_5 CrCl_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, C, Cr and O: Cl: | 2 c_1 = 3 c_5 C: | c_2 = c_4 Cr: | 2 c_3 = c_5 O: | 3 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 Cl_2 + 3 C + Cr_2O_3 ⟶ 3 CO + 2 CrCl_3

+ + ⟶ +

chlorine + activated charcoal + chromium(III) oxide ⟶ carbon monoxide + chromic chloride

Construct the equilibrium constant, K, expression for: Cl_2 + C + Cr_2O_3 ⟶ CO + 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 + 3 C + Cr_2O_3 ⟶ 3 CO + 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 C | 3 | -3 Cr_2O_3 | 1 | -1 CO | 3 | 3 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) C | 3 | -3 | ([C])^(-3) Cr_2O_3 | 1 | -1 | ([Cr2O3])^(-1) CO | 3 | 3 | ([CO])^3 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) ([C])^(-3) ([Cr2O3])^(-1) ([CO])^3 ([CrCl3])^2 = (([CO])^3 ([CrCl3])^2)/(([Cl2])^3 ([C])^3 [Cr2O3])

Construct the rate of reaction expression for: Cl_2 + C + Cr_2O_3 ⟶ CO + 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 + 3 C + Cr_2O_3 ⟶ 3 CO + 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 C | 3 | -3 Cr_2O_3 | 1 | -1 CO | 3 | 3 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) C | 3 | -3 | -1/3 (Δ[C])/(Δt) Cr_2O_3 | 1 | -1 | -(Δ[Cr2O3])/(Δt) CO | 3 | 3 | 1/3 (Δ[CO])/(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) = -1/3 (Δ[C])/(Δt) = -(Δ[Cr2O3])/(Δt) = 1/3 (Δ[CO])/(Δt) = 1/2 (Δ[CrCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | activated charcoal | chromium(III) oxide | carbon monoxide | chromic chloride formula | Cl_2 | C | Cr_2O_3 | CO | CrCl_3 Hill formula | Cl_2 | C | Cr_2O_3 | CO | Cl_3Cr name | chlorine | activated charcoal | chromium(III) oxide | carbon monoxide | chromic chloride IUPAC name | molecular chlorine | carbon | | carbon monoxide | trichlorochromium

| chlorine | activated charcoal | chromium(III) oxide | carbon monoxide | chromic chloride molar mass | 70.9 g/mol | 12.011 g/mol | 151.99 g/mol | 28.01 g/mol | 158.3 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -101 °C | 3550 °C | 2435 °C | -205 °C | 1152 °C boiling point | -34 °C | 4027 °C | 4000 °C | -191.5 °C | density | 0.003214 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | 4.8 g/cm^3 | 0.001145 g/cm^3 (at 25 °C) | 2.87 g/cm^3 solubility in water | | insoluble | insoluble | | slightly soluble dynamic viscosity | | | | 1.772×10^-5 Pa s (at 25 °C) | odor | | | | odorless |