NH4Cl + Mg3N2 = NH3 + MgCl2

NH_4Cl ammonium chloride + Mg_3N_2 magnesium nitride ⟶ NH_3 ammonia + MgCl_2 magnesium chloride

Balance the chemical equation algebraically: NH_4Cl + Mg_3N_2 ⟶ NH_3 + MgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4Cl + c_2 Mg_3N_2 ⟶ c_3 NH_3 + c_4 MgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N and Mg: Cl: | c_1 = 2 c_4 H: | 4 c_1 = 3 c_3 N: | c_1 + 2 c_2 = c_3 Mg: | 3 c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 8 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NH_4Cl + Mg_3N_2 ⟶ 8 NH_3 + 3 MgCl_2

+ ⟶ +

ammonium chloride + magnesium nitride ⟶ ammonia + magnesium chloride

Construct the equilibrium constant, K, expression for: NH_4Cl + Mg_3N_2 ⟶ NH_3 + MgCl_2 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 NH_4Cl + Mg_3N_2 ⟶ 8 NH_3 + 3 MgCl_2 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_4Cl | 6 | -6 Mg_3N_2 | 1 | -1 NH_3 | 8 | 8 MgCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4Cl | 6 | -6 | ([NH4Cl])^(-6) Mg_3N_2 | 1 | -1 | ([Mg3N2])^(-1) NH_3 | 8 | 8 | ([NH3])^8 MgCl_2 | 3 | 3 | ([MgCl2])^3 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 = ([NH4Cl])^(-6) ([Mg3N2])^(-1) ([NH3])^8 ([MgCl2])^3 = (([NH3])^8 ([MgCl2])^3)/(([NH4Cl])^6 [Mg3N2])

Construct the rate of reaction expression for: NH_4Cl + Mg_3N_2 ⟶ NH_3 + MgCl_2 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 NH_4Cl + Mg_3N_2 ⟶ 8 NH_3 + 3 MgCl_2 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_4Cl | 6 | -6 Mg_3N_2 | 1 | -1 NH_3 | 8 | 8 MgCl_2 | 3 | 3 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_4Cl | 6 | -6 | -1/6 (Δ[NH4Cl])/(Δt) Mg_3N_2 | 1 | -1 | -(Δ[Mg3N2])/(Δt) NH_3 | 8 | 8 | 1/8 (Δ[NH3])/(Δt) MgCl_2 | 3 | 3 | 1/3 (Δ[MgCl2])/(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[NH4Cl])/(Δt) = -(Δ[Mg3N2])/(Δt) = 1/8 (Δ[NH3])/(Δt) = 1/3 (Δ[MgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium chloride | magnesium nitride | ammonia | magnesium chloride formula | NH_4Cl | Mg_3N_2 | NH_3 | MgCl_2 Hill formula | ClH_4N | Mg_3N_2 | H_3N | Cl_2Mg name | ammonium chloride | magnesium nitride | ammonia | magnesium chloride IUPAC name | ammonium chloride | | ammonia | magnesium dichloride

| ammonium chloride | magnesium nitride | ammonia | magnesium chloride molar mass | 53.49 g/mol | 100.93 g/mol | 17.031 g/mol | 95.2 g/mol phase | solid (at STP) | | gas (at STP) | solid (at STP) melting point | 340 °C | | -77.73 °C | 714 °C boiling point | | | -33.33 °C | density | 1.5256 g/cm^3 | 2.71 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 2.32 g/cm^3 solubility in water | soluble | | | soluble surface tension | | | 0.0234 N/m | dynamic viscosity | | | 1.009×10^-5 Pa s (at 25 °C) |