Br2 + HN3 = N2 + NH4Br

Br_2 bromine + HNN congruent N hydrazoic acid ⟶ N_2 nitrogen + NH_4Br ammonium bromide

Balance the chemical equation algebraically: Br_2 + HNN congruent N ⟶ N_2 + NH_4Br Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Br_2 + c_2 HNN congruent N ⟶ c_3 N_2 + c_4 NH_4Br Set the number of atoms in the reactants equal to the number of atoms in the products for Br, H and N: Br: | 2 c_1 = c_4 H: | c_2 = 4 c_4 N: | 3 c_2 = 2 c_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 = 8 c_3 = 11 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Br_2 + 8 HNN congruent N ⟶ 11 N_2 + 2 NH_4Br

+ ⟶ +

bromine + hydrazoic acid ⟶ nitrogen + ammonium bromide

Construct the equilibrium constant, K, expression for: Br_2 + HNN congruent N ⟶ N_2 + NH_4Br 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 + 8 HNN congruent N ⟶ 11 N_2 + 2 NH_4Br 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 HNN congruent N | 8 | -8 N_2 | 11 | 11 NH_4Br | 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 | 1 | -1 | ([Br2])^(-1) HNN congruent N | 8 | -8 | ([HNN congruent N])^(-8) N_2 | 11 | 11 | ([N2])^11 NH_4Br | 2 | 2 | ([NH4Br])^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])^(-1) ([HNN congruent N])^(-8) ([N2])^11 ([NH4Br])^2 = (([N2])^11 ([NH4Br])^2)/([Br2] ([HNN congruent N])^8)

Construct the rate of reaction expression for: Br_2 + HNN congruent N ⟶ N_2 + NH_4Br 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 + 8 HNN congruent N ⟶ 11 N_2 + 2 NH_4Br 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 HNN congruent N | 8 | -8 N_2 | 11 | 11 NH_4Br | 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 | 1 | -1 | -(Δ[Br2])/(Δt) HNN congruent N | 8 | -8 | -1/8 (Δ[HNN congruent N])/(Δt) N_2 | 11 | 11 | 1/11 (Δ[N2])/(Δt) NH_4Br | 2 | 2 | 1/2 (Δ[NH4Br])/(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) = -1/8 (Δ[HNN congruent N])/(Δt) = 1/11 (Δ[N2])/(Δt) = 1/2 (Δ[NH4Br])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| bromine | hydrazoic acid | nitrogen | ammonium bromide formula | Br_2 | HNN congruent N | N_2 | NH_4Br Hill formula | Br_2 | HN_3 | N_2 | BrH_4N name | bromine | hydrazoic acid | nitrogen | ammonium bromide IUPAC name | molecular bromine | diazonioazanide | molecular nitrogen |

| bromine | hydrazoic acid | nitrogen | ammonium bromide molar mass | 159.81 g/mol | 43.029 g/mol | 28.014 g/mol | 97.94 g/mol phase | liquid (at STP) | | gas (at STP) | solid (at STP) melting point | -7.2 °C | | -210 °C | 452 °C boiling point | 58.8 °C | | -195.79 °C | density | 3.119 g/cm^3 | | 0.001251 g/cm^3 (at 0 °C) | 2.43 g/cm^3 solubility in water | insoluble | | insoluble | surface tension | 0.0409 N/m | | 0.0066 N/m | dynamic viscosity | 9.44×10^-4 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless |