N2 + Si = Si3N4

N_2 nitrogen + Si silicon ⟶ Si_3N_4 silicon nitride

Balance the chemical equation algebraically: N_2 + Si ⟶ Si_3N_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2 + c_2 Si ⟶ c_3 Si_3N_4 Set the number of atoms in the reactants equal to the number of atoms in the products for N and Si: N: | 2 c_1 = 4 c_3 Si: | 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 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 N_2 + 3 Si ⟶ Si_3N_4

+ ⟶

nitrogen + silicon ⟶ silicon nitride

| nitrogen | silicon | silicon nitride molecular enthalpy | 0 kJ/mol | 0 kJ/mol | -743.5 kJ/mol total enthalpy | 0 kJ/mol | 0 kJ/mol | -743.5 kJ/mol | H_initial = 0 kJ/mol | | H_final = -743.5 kJ/mol ΔH_rxn^0 | -743.5 kJ/mol - 0 kJ/mol = -743.5 kJ/mol (exothermic) | |

Construct the equilibrium constant, K, expression for: N_2 + Si ⟶ Si_3N_4 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 N_2 + 3 Si ⟶ Si_3N_4 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 N_2 | 2 | -2 Si | 3 | -3 Si_3N_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression N_2 | 2 | -2 | ([N2])^(-2) Si | 3 | -3 | ([Si])^(-3) Si_3N_4 | 1 | 1 | [Si3N4] 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 = ([N2])^(-2) ([Si])^(-3) [Si3N4] = ([Si3N4])/(([N2])^2 ([Si])^3)

Construct the rate of reaction expression for: N_2 + Si ⟶ Si_3N_4 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 N_2 + 3 Si ⟶ Si_3N_4 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 N_2 | 2 | -2 Si | 3 | -3 Si_3N_4 | 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 N_2 | 2 | -2 | -1/2 (Δ[N2])/(Δt) Si | 3 | -3 | -1/3 (Δ[Si])/(Δt) Si_3N_4 | 1 | 1 | (Δ[Si3N4])/(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[N2])/(Δt) = -1/3 (Δ[Si])/(Δt) = (Δ[Si3N4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen | silicon | silicon nitride formula | N_2 | Si | Si_3N_4 Hill formula | N_2 | Si | N_4Si_3 name | nitrogen | silicon | silicon nitride IUPAC name | molecular nitrogen | silicon |

| nitrogen | silicon | silicon nitride molar mass | 28.014 g/mol | 28.085 g/mol | 140.28 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) melting point | -210 °C | 1410 °C | 1900 °C boiling point | -195.79 °C | 2355 °C | density | 0.001251 g/cm^3 (at 0 °C) | 2.33 g/cm^3 | 3.44 g/cm^3 solubility in water | insoluble | insoluble | surface tension | 0.0066 N/m | | dynamic viscosity | 1.78×10^-5 Pa s (at 25 °C) | | odor | odorless | |