Cl2 + Cr = CrCl4

Cl_2 chlorine + Cr chromium ⟶ Cl_4Cr_1 chromium(IV) chloride

Balance the chemical equation algebraically: Cl_2 + Cr ⟶ Cl_4Cr_1 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 Cr ⟶ c_3 Cl_4Cr_1 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 = 4 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 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + Cr ⟶ Cl_4Cr_1

+ ⟶

chlorine + chromium ⟶ chromium(IV) chloride

Construct the equilibrium constant, K, expression for: Cl_2 + Cr ⟶ Cl_4Cr_1 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: 2 Cl_2 + Cr ⟶ Cl_4Cr_1 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 | 2 | -2 Cr | 1 | -1 Cl_4Cr_1 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 2 | -2 | ([Cl2])^(-2) Cr | 1 | -1 | ([Cr])^(-1) Cl_4Cr_1 | 1 | 1 | [Cl4Cr1] 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])^(-2) ([Cr])^(-1) [Cl4Cr1] = ([Cl4Cr1])/(([Cl2])^2 [Cr])

Construct the rate of reaction expression for: Cl_2 + Cr ⟶ Cl_4Cr_1 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: 2 Cl_2 + Cr ⟶ Cl_4Cr_1 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 | 2 | -2 Cr | 1 | -1 Cl_4Cr_1 | 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 Cl_2 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) Cr | 1 | -1 | -(Δ[Cr])/(Δt) Cl_4Cr_1 | 1 | 1 | (Δ[Cl4Cr1])/(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 = -1/2 (Δ[Cl2])/(Δt) = -(Δ[Cr])/(Δt) = (Δ[Cl4Cr1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | chromium | chromium(IV) chloride formula | Cl_2 | Cr | Cl_4Cr_1 Hill formula | Cl_2 | Cr | Cl_4Cr name | chlorine | chromium | chromium(IV) chloride IUPAC name | molecular chlorine | chromium | tetrachlorochromium

| chlorine | chromium | chromium(IV) chloride molar mass | 70.9 g/mol | 51.9961 g/mol | 193.8 g/mol phase | gas (at STP) | solid (at STP) | melting point | -101 °C | 1857 °C | boiling point | -34 °C | 2672 °C | density | 0.003214 g/cm^3 (at 0 °C) | 7.14 g/cm^3 | solubility in water | | insoluble | odor | | odorless |