O2 + NH3 + CH4 = H2O + HCN

O_2 (oxygen) + NH_3 (ammonia) + CH_4 (methane) ⟶ H_2O (water) + HCN (hydrogen cyanide)

Balance the chemical equation algebraically: O_2 + NH_3 + CH_4 ⟶ H_2O + HCN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 NH_3 + c_3 CH_4 ⟶ c_4 H_2O + c_5 HCN Set the number of atoms in the reactants equal to the number of atoms in the products for O, H, N and C: O: | 2 c_1 = c_4 H: | 3 c_2 + 4 c_3 = 2 c_4 + c_5 N: | c_2 = c_5 C: | c_3 = c_5 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 = 3/2 c_2 = 1 c_3 = 1 c_4 = 3 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 6 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 O_2 + 2 NH_3 + 2 CH_4 ⟶ 6 H_2O + 2 HCN

+ + ⟶ +

oxygen + ammonia + methane ⟶ water + hydrogen cyanide

Construct the equilibrium constant, K, expression for: O_2 + NH_3 + CH_4 ⟶ H_2O + 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: 3 O_2 + 2 NH_3 + 2 CH_4 ⟶ 6 H_2O + 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 O_2 | 3 | -3 NH_3 | 2 | -2 CH_4 | 2 | -2 H_2O | 6 | 6 HCN | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 3 | -3 | ([O2])^(-3) NH_3 | 2 | -2 | ([NH3])^(-2) CH_4 | 2 | -2 | ([CH4])^(-2) H_2O | 6 | 6 | ([H2O])^6 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 = ([O2])^(-3) ([NH3])^(-2) ([CH4])^(-2) ([H2O])^6 ([HCN])^2 = (([H2O])^6 ([HCN])^2)/(([O2])^3 ([NH3])^2 ([CH4])^2)

Construct the rate of reaction expression for: O_2 + NH_3 + CH_4 ⟶ H_2O + 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: 3 O_2 + 2 NH_3 + 2 CH_4 ⟶ 6 H_2O + 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 O_2 | 3 | -3 NH_3 | 2 | -2 CH_4 | 2 | -2 H_2O | 6 | 6 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 O_2 | 3 | -3 | -1/3 (Δ[O2])/(Δt) NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) CH_4 | 2 | -2 | -1/2 (Δ[CH4])/(Δt) H_2O | 6 | 6 | 1/6 (Δ[H2O])/(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 = -1/3 (Δ[O2])/(Δt) = -1/2 (Δ[NH3])/(Δt) = -1/2 (Δ[CH4])/(Δt) = 1/6 (Δ[H2O])/(Δt) = 1/2 (Δ[HCN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | ammonia | methane | water | hydrogen cyanide formula | O_2 | NH_3 | CH_4 | H_2O | HCN Hill formula | O_2 | H_3N | CH_4 | H_2O | CHN name | oxygen | ammonia | methane | water | hydrogen cyanide IUPAC name | molecular oxygen | ammonia | methane | water | formonitrile

| oxygen | ammonia | methane | water | hydrogen cyanide molar mass | 31.998 g/mol | 17.031 g/mol | 16.04 g/mol | 18.015 g/mol | 27.026 g/mol phase | gas (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) | liquid (at STP) melting point | -218 °C | -77.73 °C | -182.47 °C | 0 °C | -13.4 °C boiling point | -183 °C | -33.33 °C | -161.48 °C | 99.9839 °C | 25.6 °C density | 0.001429 g/cm^3 (at 0 °C) | 6.96×10^-4 g/cm^3 (at 25 °C) | 6.67151×10^-4 g/cm^3 (at 20 °C) | 1 g/cm^3 | 0.697 g/cm^3 solubility in water | | | soluble | | miscible surface tension | 0.01347 N/m | 0.0234 N/m | 0.0137 N/m | 0.0728 N/m | 0.0172 N/m dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | 1.114×10^-5 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 1.83×10^-4 Pa s (at 25 °C) odor | odorless | | odorless | odorless |