NH3 + CH4 = H2 + HCN

NH_3 ammonia + CH_4 methane ⟶ H_2 hydrogen + HCN hydrogen cyanide

Balance the chemical equation algebraically: NH_3 + CH_4 ⟶ H_2 + HCN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 CH_4 ⟶ c_3 H_2 + c_4 HCN Set the number of atoms in the reactants equal to the number of atoms in the products for H, N and C: H: | 3 c_1 + 4 c_2 = 2 c_3 + c_4 N: | c_1 = c_4 C: | c_2 = c_4 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 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NH_3 + CH_4 ⟶ 3 H_2 + HCN

+ ⟶ +

ammonia + methane ⟶ hydrogen + hydrogen cyanide

Construct the equilibrium constant, K, expression for: NH_3 + CH_4 ⟶ H_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: NH_3 + CH_4 ⟶ 3 H_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 NH_3 | 1 | -1 CH_4 | 1 | -1 H_2 | 3 | 3 HCN | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 1 | -1 | ([NH3])^(-1) CH_4 | 1 | -1 | ([CH4])^(-1) H_2 | 3 | 3 | ([H2])^3 HCN | 1 | 1 | [HCN] 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 = ([NH3])^(-1) ([CH4])^(-1) ([H2])^3 [HCN] = (([H2])^3 [HCN])/([NH3] [CH4])

Construct the rate of reaction expression for: NH_3 + CH_4 ⟶ H_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: NH_3 + CH_4 ⟶ 3 H_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 NH_3 | 1 | -1 CH_4 | 1 | -1 H_2 | 3 | 3 HCN | 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_3 | 1 | -1 | -(Δ[NH3])/(Δt) CH_4 | 1 | -1 | -(Δ[CH4])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) HCN | 1 | 1 | (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[NH3])/(Δt) = -(Δ[CH4])/(Δt) = 1/3 (Δ[H2])/(Δt) = (Δ[HCN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | methane | hydrogen | hydrogen cyanide formula | NH_3 | CH_4 | H_2 | HCN Hill formula | H_3N | CH_4 | H_2 | CHN name | ammonia | methane | hydrogen | hydrogen cyanide IUPAC name | ammonia | methane | molecular hydrogen | formonitrile

| ammonia | methane | hydrogen | hydrogen cyanide molar mass | 17.031 g/mol | 16.04 g/mol | 2.016 g/mol | 27.026 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) melting point | -77.73 °C | -182.47 °C | -259.2 °C | -13.4 °C boiling point | -33.33 °C | -161.48 °C | -252.8 °C | 25.6 °C density | 6.96×10^-4 g/cm^3 (at 25 °C) | 6.67151×10^-4 g/cm^3 (at 20 °C) | 8.99×10^-5 g/cm^3 (at 0 °C) | 0.697 g/cm^3 solubility in water | | soluble | | miscible surface tension | 0.0234 N/m | 0.0137 N/m | | 0.0172 N/m dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | 1.114×10^-5 Pa s (at 25 °C) | 8.9×10^-6 Pa s (at 25 °C) | 1.83×10^-4 Pa s (at 25 °C) odor | | odorless | odorless |