Al + N2 = Al2N3

Al aluminum + N_2 nitrogen ⟶ Al2N3

Balance the chemical equation algebraically: Al + N_2 ⟶ Al2N3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 N_2 ⟶ c_3 Al2N3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and N: Al: | c_1 = 2 c_3 N: | 2 c_2 = 3 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Al + 3 N_2 ⟶ 2 Al2N3

+ ⟶ Al2N3

aluminum + nitrogen ⟶ Al2N3

Construct the equilibrium constant, K, expression for: Al + N_2 ⟶ Al2N3 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: 4 Al + 3 N_2 ⟶ 2 Al2N3 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 | 4 | -4 N_2 | 3 | -3 Al2N3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 4 | -4 | ([Al])^(-4) N_2 | 3 | -3 | ([N2])^(-3) Al2N3 | 2 | 2 | ([Al2N3])^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 = ([Al])^(-4) ([N2])^(-3) ([Al2N3])^2 = ([Al2N3])^2/(([Al])^4 ([N2])^3)

Construct the rate of reaction expression for: Al + N_2 ⟶ Al2N3 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: 4 Al + 3 N_2 ⟶ 2 Al2N3 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 | 4 | -4 N_2 | 3 | -3 Al2N3 | 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 Al | 4 | -4 | -1/4 (Δ[Al])/(Δt) N_2 | 3 | -3 | -1/3 (Δ[N2])/(Δt) Al2N3 | 2 | 2 | 1/2 (Δ[Al2N3])/(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 = -1/4 (Δ[Al])/(Δt) = -1/3 (Δ[N2])/(Δt) = 1/2 (Δ[Al2N3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | nitrogen | Al2N3 formula | Al | N_2 | Al2N3 name | aluminum | nitrogen | IUPAC name | aluminum | molecular nitrogen |

| aluminum | nitrogen | Al2N3 molar mass | 26.9815385 g/mol | 28.014 g/mol | 95.984 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 |