N2 + CaH2 = H2 + Ca3N2

N_2 nitrogen + CaH_2 calcium hydride ⟶ H_2 hydrogen + Ca_3N_2 calcium nitride

Balance the chemical equation algebraically: N_2 + CaH_2 ⟶ H_2 + Ca_3N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2 + c_2 CaH_2 ⟶ c_3 H_2 + c_4 Ca_3N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N, Ca and H: N: | 2 c_1 = 2 c_4 Ca: | c_2 = 3 c_4 H: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | N_2 + 3 CaH_2 ⟶ 3 H_2 + Ca_3N_2

+ ⟶ +

nitrogen + calcium hydride ⟶ hydrogen + calcium nitride

Construct the equilibrium constant, K, expression for: N_2 + CaH_2 ⟶ H_2 + Ca_3N_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: N_2 + 3 CaH_2 ⟶ 3 H_2 + Ca_3N_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 N_2 | 1 | -1 CaH_2 | 3 | -3 H_2 | 3 | 3 Ca_3N_2 | 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 | 1 | -1 | ([N2])^(-1) CaH_2 | 3 | -3 | ([CaH2])^(-3) H_2 | 3 | 3 | ([H2])^3 Ca_3N_2 | 1 | 1 | [Ca3N2] 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])^(-1) ([CaH2])^(-3) ([H2])^3 [Ca3N2] = (([H2])^3 [Ca3N2])/([N2] ([CaH2])^3)

Construct the rate of reaction expression for: N_2 + CaH_2 ⟶ H_2 + Ca_3N_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: N_2 + 3 CaH_2 ⟶ 3 H_2 + Ca_3N_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 N_2 | 1 | -1 CaH_2 | 3 | -3 H_2 | 3 | 3 Ca_3N_2 | 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 | 1 | -1 | -(Δ[N2])/(Δt) CaH_2 | 3 | -3 | -1/3 (Δ[CaH2])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) Ca_3N_2 | 1 | 1 | (Δ[Ca3N2])/(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 = -(Δ[N2])/(Δt) = -1/3 (Δ[CaH2])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[Ca3N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen | calcium hydride | hydrogen | calcium nitride formula | N_2 | CaH_2 | H_2 | Ca_3N_2 name | nitrogen | calcium hydride | hydrogen | calcium nitride IUPAC name | molecular nitrogen | calcium hydride | molecular hydrogen | calcium azanidylidenecalcium

| nitrogen | calcium hydride | hydrogen | calcium nitride molar mass | 28.014 g/mol | 42.094 g/mol | 2.016 g/mol | 148.25 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | melting point | -210 °C | 190 °C | -259.2 °C | boiling point | -195.79 °C | | -252.8 °C | density | 0.001251 g/cm^3 (at 0 °C) | | 8.99×10^-5 g/cm^3 (at 0 °C) | 2.63 g/cm^3 solubility in water | insoluble | | | surface tension | 0.0066 N/m | | | dynamic viscosity | 1.78×10^-5 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |