NH = H2 + N2

NH ⟶ H_2 hydrogen + N_2 nitrogen

Balance the chemical equation algebraically: NH ⟶ H_2 + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH ⟶ c_2 H_2 + c_3 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N and H: N: | c_1 = 2 c_3 H: | c_1 = 2 c_2 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 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH ⟶ H_2 + N_2

NH ⟶ +

NH ⟶ hydrogen + nitrogen

Construct the equilibrium constant, K, expression for: NH ⟶ H_2 + N_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: 2 NH ⟶ H_2 + N_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 | 2 | -2 H_2 | 1 | 1 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH | 2 | -2 | ([NH])^(-2) H_2 | 1 | 1 | [H2] N_2 | 1 | 1 | [N2] 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 = ([NH])^(-2) [H2] [N2] = ([H2] [N2])/([NH])^2

Construct the rate of reaction expression for: NH ⟶ H_2 + N_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: 2 NH ⟶ H_2 + N_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 | 2 | -2 H_2 | 1 | 1 N_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 NH | 2 | -2 | -1/2 (Δ[NH])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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[NH])/(Δt) = (Δ[H2])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| NH | hydrogen | nitrogen formula | NH | H_2 | N_2 Hill formula | HN | H_2 | N_2 name | | hydrogen | nitrogen IUPAC name | | molecular hydrogen | molecular nitrogen

| NH | hydrogen | nitrogen molar mass | 15.015 g/mol | 2.016 g/mol | 28.014 g/mol phase | | gas (at STP) | gas (at STP) melting point | | -259.2 °C | -210 °C boiling point | | -252.8 °C | -195.79 °C density | | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.001251 g/cm^3 (at 0 °C) solubility in water | | | insoluble surface tension | | | 0.0066 N/m dynamic viscosity | | 8.9×10^-6 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) odor | | odorless | odorless