N2 + Cr = CrN

N_2 nitrogen + Cr chromium ⟶ CrN

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

+ ⟶ CrN

nitrogen + chromium ⟶ CrN

Construct the equilibrium constant, K, expression for: N_2 + Cr ⟶ CrN 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 + 2 Cr ⟶ 2 CrN 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 Cr | 2 | -2 CrN | 2 | 2 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) Cr | 2 | -2 | ([Cr])^(-2) CrN | 2 | 2 | ([CrN])^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 = ([N2])^(-1) ([Cr])^(-2) ([CrN])^2 = ([CrN])^2/([N2] ([Cr])^2)

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

| nitrogen | chromium | CrN formula | N_2 | Cr | CrN name | nitrogen | chromium | IUPAC name | molecular nitrogen | chromium |

| nitrogen | chromium | CrN molar mass | 28.014 g/mol | 51.9961 g/mol | 66.003 g/mol phase | gas (at STP) | solid (at STP) | melting point | -210 °C | 1857 °C | boiling point | -195.79 °C | 2672 °C | density | 0.001251 g/cm^3 (at 0 °C) | 7.14 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 | odorless |