Al + N2 = AlN2

Al aluminum + N_2 nitrogen ⟶ AlN2

Balance the chemical equation algebraically: Al + N_2 ⟶ AlN2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 N_2 ⟶ c_3 AlN2 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and N: Al: | c_1 = c_3 N: | 2 c_2 = 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_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: | | Al + N_2 ⟶ AlN2

+ ⟶ AlN2

aluminum + nitrogen ⟶ AlN2

Construct the equilibrium constant, K, expression for: Al + N_2 ⟶ AlN2 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: Al + N_2 ⟶ AlN2 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 Al | 1 | -1 N_2 | 1 | -1 AlN2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 1 | -1 | ([Al])^(-1) N_2 | 1 | -1 | ([N2])^(-1) AlN2 | 1 | 1 | [AlN2] 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 = ([Al])^(-1) ([N2])^(-1) [AlN2] = ([AlN2])/([Al] [N2])

Construct the rate of reaction expression for: Al + N_2 ⟶ AlN2 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: Al + N_2 ⟶ AlN2 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 Al | 1 | -1 N_2 | 1 | -1 AlN2 | 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 Al | 1 | -1 | -(Δ[Al])/(Δt) N_2 | 1 | -1 | -(Δ[N2])/(Δt) AlN2 | 1 | 1 | (Δ[AlN2])/(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[Al])/(Δt) = -(Δ[N2])/(Δt) = (Δ[AlN2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | nitrogen | AlN2 formula | Al | N_2 | AlN2 name | aluminum | nitrogen | IUPAC name | aluminum | molecular nitrogen |

| aluminum | nitrogen | AlN2 molar mass | 26.9815385 g/mol | 28.014 g/mol | 54.996 g/mol phase | solid (at STP) | gas (at STP) | melting point | 660.4 °C | -210 °C | boiling point | 2460 °C | -195.79 °C | density | 2.7 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | insoluble | insoluble | surface tension | 0.817 N/m | 0.0066 N/m | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | odorless | odorless |