Br2 + CH4 = HBr + CH3Br

Br_2 bromine + CH_4 methane ⟶ HBr hydrogen bromide + CH_3Br methyl bromide

Balance the chemical equation algebraically: Br_2 + CH_4 ⟶ HBr + CH_3Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 CH_4 ⟶ c_3 HBr + c_4 CH_3Br 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: | c_2 = c_4 H: | 4 c_2 = c_3 + 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_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_4 ⟶ HBr + CH_3Br

+ ⟶ +

bromine + methane ⟶ hydrogen bromide + methyl bromide

| bromine | methane | hydrogen bromide | methyl bromide molecular enthalpy | 0 kJ/mol | -74.6 kJ/mol | -36.3 kJ/mol | -35.4 kJ/mol total enthalpy | 0 kJ/mol | -74.6 kJ/mol | -36.3 kJ/mol | -35.4 kJ/mol | H_initial = -74.6 kJ/mol | | H_final = -71.7 kJ/mol | ΔH_rxn^0 | -71.7 kJ/mol - -74.6 kJ/mol = 2.9 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: Br_2 + CH_4 ⟶ HBr + CH_3Br 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_4 ⟶ HBr + CH_3Br 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_4 | 1 | -1 HBr | 1 | 1 CH_3Br | 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_4 | 1 | -1 | ([CH4])^(-1) HBr | 1 | 1 | [HBr] CH_3Br | 1 | 1 | [CH3Br] 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) ([CH4])^(-1) [HBr] [CH3Br] = ([HBr] [CH3Br])/([Br2] [CH4])

Construct the rate of reaction expression for: Br_2 + CH_4 ⟶ HBr + CH_3Br 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_4 ⟶ HBr + CH_3Br 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_4 | 1 | -1 HBr | 1 | 1 CH_3Br | 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_4 | 1 | -1 | -(Δ[CH4])/(Δt) HBr | 1 | 1 | (Δ[HBr])/(Δt) CH_3Br | 1 | 1 | (Δ[CH3Br])/(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[CH4])/(Δt) = (Δ[HBr])/(Δt) = (Δ[CH3Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | methane | hydrogen bromide | methyl bromide formula | Br_2 | CH_4 | HBr | CH_3Br Hill formula | Br_2 | CH_4 | BrH | CH_3Br name | bromine | methane | hydrogen bromide | methyl bromide IUPAC name | molecular bromine | methane | hydrogen bromide | bromomethane

| bromine | methane | hydrogen bromide | methyl bromide molar mass | 159.81 g/mol | 16.04 g/mol | 80.912 g/mol | 94.94 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) | gas (at STP) melting point | -7.2 °C | -182.47 °C | -86.8 °C | -93.68 °C boiling point | 58.8 °C | -161.48 °C | -66.38 °C | 3.5 °C density | 3.119 g/cm^3 | 6.67151×10^-4 g/cm^3 (at 20 °C) | 0.003307 g/cm^3 (at 25 °C) | 1.6755 g/cm^3 (at 20 °C) solubility in water | insoluble | soluble | miscible | surface tension | 0.0409 N/m | 0.0137 N/m | 0.0271 N/m | 0.0245 N/m dynamic viscosity | 9.44×10^-4 Pa s (at 25 °C) | 1.114×10^-5 Pa s (at 25 °C) | 8.4×10^-4 Pa s (at -75 °C) | 3.97×10^-4 Pa s (at 0 °C) odor | | odorless | | odorless