Br2 + C2H6 = HBr + C2H5Br

Br_2 bromine + CH_3CH_3 ethane ⟶ HBr hydrogen bromide + CH_3CH_2Br bromoethane

Balance the chemical equation algebraically: Br_2 + CH_3CH_3 ⟶ HBr + CH_3CH_2Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 CH_3CH_3 ⟶ c_3 HBr + c_4 CH_3CH_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 = c_3 + c_4 C: | 2 c_2 = 2 c_4 H: | 6 c_2 = c_3 + 5 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Br_2 + CH_3CH_3 ⟶ HBr + CH_3CH_2Br

+ ⟶ +

bromine + ethane ⟶ hydrogen bromide + bromoethane

Construct the equilibrium constant, K, expression for: Br_2 + CH_3CH_3 ⟶ HBr + CH_3CH_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_3CH_3 ⟶ HBr + CH_3CH_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_3CH_3 | 1 | -1 HBr | 1 | 1 CH_3CH_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_3CH_3 | 1 | -1 | ([CH3CH3])^(-1) HBr | 1 | 1 | [HBr] CH_3CH_2Br | 1 | 1 | [CH3CH2Br] 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) ([CH3CH3])^(-1) [HBr] [CH3CH2Br] = ([HBr] [CH3CH2Br])/([Br2] [CH3CH3])

Construct the rate of reaction expression for: Br_2 + CH_3CH_3 ⟶ HBr + CH_3CH_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_3CH_3 ⟶ HBr + CH_3CH_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_3CH_3 | 1 | -1 HBr | 1 | 1 CH_3CH_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_3CH_3 | 1 | -1 | -(Δ[CH3CH3])/(Δt) HBr | 1 | 1 | (Δ[HBr])/(Δt) CH_3CH_2Br | 1 | 1 | (Δ[CH3CH2Br])/(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[CH3CH3])/(Δt) = (Δ[HBr])/(Δt) = (Δ[CH3CH2Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | ethane | hydrogen bromide | bromoethane formula | Br_2 | CH_3CH_3 | HBr | CH_3CH_2Br Hill formula | Br_2 | C_2H_6 | BrH | C_2H_5Br name | bromine | ethane | hydrogen bromide | bromoethane IUPAC name | molecular bromine | ethane | hydrogen bromide | bromoethane