H2O + K3N = KOH + NH3

H_2O water + K3N ⟶ KOH potassium hydroxide + NH_3 ammonia

Balance the chemical equation algebraically: H_2O + K3N ⟶ KOH + NH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K3N ⟶ c_3 KOH + c_4 NH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K and N: H: | 2 c_1 = c_3 + 3 c_4 O: | c_1 = c_3 K: | 3 c_2 = c_3 N: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + K3N ⟶ 3 KOH + NH_3

+ K3N ⟶ +

water + K3N ⟶ potassium hydroxide + ammonia

Construct the equilibrium constant, K, expression for: H_2O + K3N ⟶ KOH + NH_3 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 H_2O + K3N ⟶ 3 KOH + NH_3 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_2O | 3 | -3 K3N | 1 | -1 KOH | 3 | 3 NH_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) K3N | 1 | -1 | ([K3N])^(-1) KOH | 3 | 3 | ([KOH])^3 NH_3 | 1 | 1 | [NH3] 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 = ([H2O])^(-3) ([K3N])^(-1) ([KOH])^3 [NH3] = (([KOH])^3 [NH3])/(([H2O])^3 [K3N])

Construct the rate of reaction expression for: H_2O + K3N ⟶ KOH + NH_3 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 H_2O + K3N ⟶ 3 KOH + NH_3 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_2O | 3 | -3 K3N | 1 | -1 KOH | 3 | 3 NH_3 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) K3N | 1 | -1 | -(Δ[K3N])/(Δt) KOH | 3 | 3 | 1/3 (Δ[KOH])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(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[H2O])/(Δt) = -(Δ[K3N])/(Δt) = 1/3 (Δ[KOH])/(Δt) = (Δ[NH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | K3N | potassium hydroxide | ammonia formula | H_2O | K3N | KOH | NH_3 Hill formula | H_2O | K3N | HKO | H_3N name | water | | potassium hydroxide | ammonia

| water | K3N | potassium hydroxide | ammonia molar mass | 18.015 g/mol | 131.302 g/mol | 56.105 g/mol | 17.031 g/mol phase | liquid (at STP) | | solid (at STP) | gas (at STP) melting point | 0 °C | | 406 °C | -77.73 °C boiling point | 99.9839 °C | | 1327 °C | -33.33 °C density | 1 g/cm^3 | | 2.044 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) solubility in water | | | soluble | surface tension | 0.0728 N/m | | | 0.0234 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 0.001 Pa s (at 550 °C) | 1.009×10^-5 Pa s (at 25 °C) odor | odorless | | |