Br2 + Cr = CrBr3

Br_2 bromine + Cr chromium ⟶ Br_3Cr chromium tribromide

Balance the chemical equation algebraically: Br_2 + Cr ⟶ Br_3Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 Cr ⟶ c_3 Br_3Cr Set the number of atoms in the reactants equal to the number of atoms in the products for Br and Cr: Br: | 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 Br_2 + 2 Cr ⟶ 2 Br_3Cr

+ ⟶

bromine + chromium ⟶ chromium tribromide

Construct the equilibrium constant, K, expression for: Br_2 + Cr ⟶ Br_3Cr 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 Br_2 + 2 Cr ⟶ 2 Br_3Cr 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 Br_2 | 3 | -3 Cr | 2 | -2 Br_3Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Br_2 | 3 | -3 | ([Br2])^(-3) Cr | 2 | -2 | ([Cr])^(-2) Br_3Cr | 2 | 2 | ([Br3Cr])^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 = ([Br2])^(-3) ([Cr])^(-2) ([Br3Cr])^2 = ([Br3Cr])^2/(([Br2])^3 ([Cr])^2)

Construct the rate of reaction expression for: Br_2 + Cr ⟶ Br_3Cr 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 Br_2 + 2 Cr ⟶ 2 Br_3Cr 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 Br_2 | 3 | -3 Cr | 2 | -2 Br_3Cr | 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 Br_2 | 3 | -3 | -1/3 (Δ[Br2])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) Br_3Cr | 2 | 2 | 1/2 (Δ[Br3Cr])/(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[Br2])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/2 (Δ[Br3Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | chromium | chromium tribromide formula | Br_2 | Cr | Br_3Cr name | bromine | chromium | chromium tribromide IUPAC name | molecular bromine | chromium | chromium(+3) cation tribromide

| bromine | chromium | chromium tribromide molar mass | 159.81 g/mol | 51.9961 g/mol | 291.71 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -7.2 °C | 1857 °C | 1130 °C boiling point | 58.8 °C | 2672 °C | density | 3.119 g/cm^3 | 7.14 g/cm^3 | 4.68 g/cm^3 solubility in water | insoluble | insoluble | slightly soluble surface tension | 0.0409 N/m | | dynamic viscosity | 9.44×10^-4 Pa s (at 25 °C) | | odor | | odorless |