N2 + C = (CN)2

N_2 nitrogen + C activated charcoal ⟶ C_2N_2 cyanogen

Balance the chemical equation algebraically: N_2 + C ⟶ C_2N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 N_2 + c_2 C ⟶ c_3 C_2N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for N and C: N: | 2 c_1 = 2 c_3 C: | 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 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | N_2 + 2 C ⟶ C_2N_2

+ ⟶

nitrogen + activated charcoal ⟶ cyanogen

Construct the equilibrium constant, K, expression for: N_2 + C ⟶ C_2N_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 + 2 C ⟶ C_2N_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 C | 2 | -2 C_2N_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) C | 2 | -2 | ([C])^(-2) C_2N_2 | 1 | 1 | [C2N2] 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) ([C])^(-2) [C2N2] = ([C2N2])/([N2] ([C])^2)

Construct the rate of reaction expression for: N_2 + C ⟶ C_2N_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 + 2 C ⟶ C_2N_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 C | 2 | -2 C_2N_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) C | 2 | -2 | -1/2 (Δ[C])/(Δt) C_2N_2 | 1 | 1 | (Δ[C2N2])/(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[C])/(Δt) = (Δ[C2N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitrogen | activated charcoal | cyanogen formula | N_2 | C | C_2N_2 name | nitrogen | activated charcoal | cyanogen IUPAC name | molecular nitrogen | carbon | oxalonitrile

| nitrogen | activated charcoal | cyanogen molar mass | 28.014 g/mol | 12.011 g/mol | 52.036 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) melting point | -210 °C | 3550 °C | boiling point | -195.79 °C | 4027 °C | -21.17 °C density | 0.001251 g/cm^3 (at 0 °C) | 2.26 g/cm^3 | 0.002127 g/cm^3 (at 25 °C) solubility in water | insoluble | insoluble | very soluble surface tension | 0.0066 N/m | | 0.02282 N/m dynamic viscosity | 1.78×10^-5 Pa s (at 25 °C) | | 9.8×10^-6 Pa s (at 15 °C) odor | odorless | |