Mg + N2 = Mg3N

Mg magnesium + N_2 nitrogen ⟶ Mg3N

Balance the chemical equation algebraically: Mg + N_2 ⟶ Mg3N Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 N_2 ⟶ c_3 Mg3N Set the number of atoms in the reactants equal to the number of atoms in the products for Mg and N: Mg: | c_1 = 3 c_3 N: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 Mg + N_2 ⟶ 2 Mg3N

+ ⟶ Mg3N

magnesium + nitrogen ⟶ Mg3N

Construct the equilibrium constant, K, expression for: Mg + N_2 ⟶ Mg3N 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: 6 Mg + N_2 ⟶ 2 Mg3N 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 Mg | 6 | -6 N_2 | 1 | -1 Mg3N | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 6 | -6 | ([Mg])^(-6) N_2 | 1 | -1 | ([N2])^(-1) Mg3N | 2 | 2 | ([Mg3N])^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 = ([Mg])^(-6) ([N2])^(-1) ([Mg3N])^2 = ([Mg3N])^2/(([Mg])^6 [N2])

Construct the rate of reaction expression for: Mg + N_2 ⟶ Mg3N 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: 6 Mg + N_2 ⟶ 2 Mg3N 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 Mg | 6 | -6 N_2 | 1 | -1 Mg3N | 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 Mg | 6 | -6 | -1/6 (Δ[Mg])/(Δt) N_2 | 1 | -1 | -(Δ[N2])/(Δt) Mg3N | 2 | 2 | 1/2 (Δ[Mg3N])/(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 = -1/6 (Δ[Mg])/(Δt) = -(Δ[N2])/(Δt) = 1/2 (Δ[Mg3N])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | nitrogen | Mg3N formula | Mg | N_2 | Mg3N name | magnesium | nitrogen | IUPAC name | magnesium | molecular nitrogen |

| magnesium | nitrogen | Mg3N molar mass | 24.305 g/mol | 28.014 g/mol | 86.922 g/mol phase | solid (at STP) | gas (at STP) | melting point | 648 °C | -210 °C | boiling point | 1090 °C | -195.79 °C | density | 1.738 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | reacts | insoluble | surface tension | | 0.0066 N/m | dynamic viscosity | | 1.78×10^-5 Pa s (at 25 °C) | odor | | odorless |