NH3 + K = H2 + KNH2

NH_3 ammonia + K potassium ⟶ H_2 hydrogen + KNH_2 potassium amide

Balance the chemical equation algebraically: NH_3 + K ⟶ H_2 + KNH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 K ⟶ c_3 H_2 + c_4 KNH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N and K: H: | 3 c_1 = 2 c_3 + 2 c_4 N: | c_1 = c_4 K: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + 2 K ⟶ H_2 + 2 KNH_2

+ ⟶ + KNH_2

ammonia + potassium ⟶ hydrogen + potassium amide

Construct the equilibrium constant, K, expression for: NH_3 + K ⟶ H_2 + KNH_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_3 + 2 K ⟶ H_2 + 2 KNH_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_3 | 2 | -2 K | 2 | -2 H_2 | 1 | 1 KNH_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 2 | -2 | ([NH3])^(-2) K | 2 | -2 | ([K])^(-2) H_2 | 1 | 1 | [H2] KNH_2 | 2 | 2 | ([KNH2])^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 = ([NH3])^(-2) ([K])^(-2) [H2] ([KNH2])^2 = ([H2] ([KNH2])^2)/(([NH3])^2 ([K])^2)

Construct the rate of reaction expression for: NH_3 + K ⟶ H_2 + KNH_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_3 + 2 K ⟶ H_2 + 2 KNH_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_3 | 2 | -2 K | 2 | -2 H_2 | 1 | 1 KNH_2 | 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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) K | 2 | -2 | -1/2 (Δ[K])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) KNH_2 | 2 | 2 | 1/2 (Δ[KNH2])/(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[NH3])/(Δt) = -1/2 (Δ[K])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[KNH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | potassium | hydrogen | potassium amide formula | NH_3 | K | H_2 | KNH_2 Hill formula | H_3N | K | H_2 | H_2KN name | ammonia | potassium | hydrogen | potassium amide IUPAC name | ammonia | potassium | molecular hydrogen |

| ammonia | potassium | hydrogen | potassium amide molar mass | 17.031 g/mol | 39.0983 g/mol | 2.016 g/mol | 55.121 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | melting point | -77.73 °C | 64 °C | -259.2 °C | 335 °C boiling point | -33.33 °C | 760 °C | -252.8 °C | density | 6.96×10^-4 g/cm^3 (at 25 °C) | 0.86 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | reacts | | surface tension | 0.0234 N/m | | | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | | | odorless |