Br2 + C2H4 = C2H4Br2

Br_2 (bromine) + CH_2=CH_2 (ethylene) ⟶ BrCH_2CH_2Br (ethylene dibromide)

Balance the chemical equation algebraically: Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 CH_2=CH_2 ⟶ c_3 BrCH_2CH_2Br Set the number of atoms in the reactants equal to the number of atoms in the products for Br, C and H: Br: | 2 c_1 = 2 c_3 C: | 2 c_2 = 2 c_3 H: | 4 c_2 = 4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br

+ ⟶

bromine + ethylene ⟶ ethylene dibromide

Construct the equilibrium constant, K, expression for: Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br 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: Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br 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 | 1 | -1 CH_2=CH_2 | 1 | -1 BrCH_2CH_2Br | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Br_2 | 1 | -1 | ([Br2])^(-1) CH_2=CH_2 | 1 | -1 | ([CH2=CH2])^(-1) BrCH_2CH_2Br | 1 | 1 | [BrCH2CH2Br] 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])^(-1) ([CH2=CH2])^(-1) [BrCH2CH2Br] = ([BrCH2CH2Br])/([Br2] [CH2=CH2])

Construct the rate of reaction expression for: Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br 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: Br_2 + CH_2=CH_2 ⟶ BrCH_2CH_2Br 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 | 1 | -1 CH_2=CH_2 | 1 | -1 BrCH_2CH_2Br | 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 Br_2 | 1 | -1 | -(Δ[Br2])/(Δt) CH_2=CH_2 | 1 | -1 | -(Δ[CH2=CH2])/(Δt) BrCH_2CH_2Br | 1 | 1 | (Δ[BrCH2CH2Br])/(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 = -(Δ[Br2])/(Δt) = -(Δ[CH2=CH2])/(Δt) = (Δ[BrCH2CH2Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | ethylene | ethylene dibromide formula | Br_2 | CH_2=CH_2 | BrCH_2CH_2Br Hill formula | Br_2 | C_2H_4 | C_2H_4Br_2 name | bromine | ethylene | ethylene dibromide IUPAC name | molecular bromine | ethylene | 1, 2-dibromoethane