KNO3 + K = N2 + K2O

KNO_3 potassium nitrate + K potassium ⟶ N_2 nitrogen + K_2O potassium oxide

Balance the chemical equation algebraically: KNO_3 + K ⟶ N_2 + K_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KNO_3 + c_2 K ⟶ c_3 N_2 + c_4 K_2O Set the number of atoms in the reactants equal to the number of atoms in the products for K, N and O: K: | c_1 + c_2 = 2 c_4 N: | c_1 = 2 c_3 O: | 3 c_1 = 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 = 10 c_3 = 1 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KNO_3 + 10 K ⟶ N_2 + 6 K_2O

+ ⟶ +

potassium nitrate + potassium ⟶ nitrogen + potassium oxide

Construct the equilibrium constant, K, expression for: KNO_3 + K ⟶ N_2 + K_2O 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 KNO_3 + 10 K ⟶ N_2 + 6 K_2O 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 KNO_3 | 2 | -2 K | 10 | -10 N_2 | 1 | 1 K_2O | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 2 | -2 | ([KNO3])^(-2) K | 10 | -10 | ([K])^(-10) N_2 | 1 | 1 | [N2] K_2O | 6 | 6 | ([K2O])^6 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 = ([KNO3])^(-2) ([K])^(-10) [N2] ([K2O])^6 = ([N2] ([K2O])^6)/(([KNO3])^2 ([K])^10)

Construct the rate of reaction expression for: KNO_3 + K ⟶ N_2 + K_2O 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 KNO_3 + 10 K ⟶ N_2 + 6 K_2O 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 KNO_3 | 2 | -2 K | 10 | -10 N_2 | 1 | 1 K_2O | 6 | 6 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 KNO_3 | 2 | -2 | -1/2 (Δ[KNO3])/(Δt) K | 10 | -10 | -1/10 (Δ[K])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) K_2O | 6 | 6 | 1/6 (Δ[K2O])/(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[KNO3])/(Δt) = -1/10 (Δ[K])/(Δt) = (Δ[N2])/(Δt) = 1/6 (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium nitrate | potassium | nitrogen | potassium oxide formula | KNO_3 | K | N_2 | K_2O name | potassium nitrate | potassium | nitrogen | potassium oxide IUPAC name | potassium nitrate | potassium | molecular nitrogen | dipotassium oxygen(2-)

| potassium nitrate | potassium | nitrogen | potassium oxide molar mass | 101.1 g/mol | 39.0983 g/mol | 28.014 g/mol | 94.196 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | melting point | 334 °C | 64 °C | -210 °C | boiling point | | 760 °C | -195.79 °C | density | | 0.86 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | solubility in water | soluble | reacts | insoluble | surface tension | | | 0.0066 N/m | dynamic viscosity | | | 1.78×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless |