NH3 + Mg = H2 + Mg3N

NH_3 ammonia + Mg magnesium ⟶ H_2 hydrogen + Mg3N

Balance the chemical equation algebraically: NH_3 + Mg ⟶ H_2 + Mg3N Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 Mg ⟶ c_3 H_2 + c_4 Mg3N Set the number of atoms in the reactants equal to the number of atoms in the products for H, N and Mg: H: | 3 c_1 = 2 c_3 N: | c_1 = c_4 Mg: | c_2 = 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 = 3 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 6 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + 6 Mg ⟶ 3 H_2 + 2 Mg3N

+ ⟶ + Mg3N

ammonia + magnesium ⟶ hydrogen + Mg3N

Construct the equilibrium constant, K, expression for: NH_3 + Mg ⟶ H_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: 2 NH_3 + 6 Mg ⟶ 3 H_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 NH_3 | 2 | -2 Mg | 6 | -6 H_2 | 3 | 3 Mg3N | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 2 | -2 | ([NH3])^(-2) Mg | 6 | -6 | ([Mg])^(-6) H_2 | 3 | 3 | ([H2])^3 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 = ([NH3])^(-2) ([Mg])^(-6) ([H2])^3 ([Mg3N])^2 = (([H2])^3 ([Mg3N])^2)/(([NH3])^2 ([Mg])^6)

Construct the rate of reaction expression for: NH_3 + Mg ⟶ H_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: 2 NH_3 + 6 Mg ⟶ 3 H_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 NH_3 | 2 | -2 Mg | 6 | -6 H_2 | 3 | 3 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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) Mg | 6 | -6 | -1/6 (Δ[Mg])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(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 = -1/2 (Δ[NH3])/(Δt) = -1/6 (Δ[Mg])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[Mg3N])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | magnesium | hydrogen | Mg3N formula | NH_3 | Mg | H_2 | Mg3N Hill formula | H_3N | Mg | H_2 | Mg3N name | ammonia | magnesium | hydrogen | IUPAC name | ammonia | magnesium | molecular hydrogen |

| ammonia | magnesium | hydrogen | Mg3N molar mass | 17.031 g/mol | 24.305 g/mol | 2.016 g/mol | 86.922 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | melting point | -77.73 °C | 648 °C | -259.2 °C | boiling point | -33.33 °C | 1090 °C | -252.8 °C | density | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.738 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | reacts | | surface tension | 0.0234 N/m | | | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |