H2 + C2N2 = HCN

H_2 hydrogen + C_2N_2 cyanogen ⟶ HCN hydrogen cyanide

Balance the chemical equation algebraically: H_2 + C_2N_2 ⟶ HCN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 C_2N_2 ⟶ c_3 HCN Set the number of atoms in the reactants equal to the number of atoms in the products for H, C and N: H: | 2 c_1 = c_3 C: | 2 c_2 = c_3 N: | 2 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 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2 + C_2N_2 ⟶ 2 HCN

+ ⟶

hydrogen + cyanogen ⟶ hydrogen cyanide

Construct the equilibrium constant, K, expression for: H_2 + C_2N_2 ⟶ HCN 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: H_2 + C_2N_2 ⟶ 2 HCN 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 H_2 | 1 | -1 C_2N_2 | 1 | -1 HCN | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 1 | -1 | ([H2])^(-1) C_2N_2 | 1 | -1 | ([C2N2])^(-1) HCN | 2 | 2 | ([HCN])^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 = ([H2])^(-1) ([C2N2])^(-1) ([HCN])^2 = ([HCN])^2/([H2] [C2N2])

Construct the rate of reaction expression for: H_2 + C_2N_2 ⟶ HCN 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: H_2 + C_2N_2 ⟶ 2 HCN 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 H_2 | 1 | -1 C_2N_2 | 1 | -1 HCN | 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 H_2 | 1 | -1 | -(Δ[H2])/(Δt) C_2N_2 | 1 | -1 | -(Δ[C2N2])/(Δt) HCN | 2 | 2 | 1/2 (Δ[HCN])/(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[H2])/(Δt) = -(Δ[C2N2])/(Δt) = 1/2 (Δ[HCN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | cyanogen | hydrogen cyanide formula | H_2 | C_2N_2 | HCN Hill formula | H_2 | C_2N_2 | CHN name | hydrogen | cyanogen | hydrogen cyanide IUPAC name | molecular hydrogen | oxalonitrile | formonitrile

| hydrogen | cyanogen | hydrogen cyanide molar mass | 2.016 g/mol | 52.036 g/mol | 27.026 g/mol phase | gas (at STP) | gas (at STP) | liquid (at STP) melting point | -259.2 °C | | -13.4 °C boiling point | -252.8 °C | -21.17 °C | 25.6 °C density | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.002127 g/cm^3 (at 25 °C) | 0.697 g/cm^3 solubility in water | | very soluble | miscible surface tension | | 0.02282 N/m | 0.0172 N/m dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | 9.8×10^-6 Pa s (at 15 °C) | 1.83×10^-4 Pa s (at 25 °C) odor | odorless | |