Fe + KNO3 = N2 + Fe2O3 + K2O

Fe iron + KNO_3 potassium nitrate ⟶ N_2 nitrogen + Fe_2O_3 iron(III) oxide + K_2O potassium oxide

Balance the chemical equation algebraically: Fe + KNO_3 ⟶ N_2 + Fe_2O_3 + K_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Fe + c_2 KNO_3 ⟶ c_3 N_2 + c_4 Fe_2O_3 + c_5 K_2O Set the number of atoms in the reactants equal to the number of atoms in the products for Fe, K, N and O: Fe: | c_1 = 2 c_4 K: | c_2 = 2 c_5 N: | c_2 = 2 c_3 O: | 3 c_2 = 3 c_4 + 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10/3 c_2 = 2 c_3 = 1 c_4 = 5/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 10 c_2 = 6 c_3 = 3 c_4 = 5 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 Fe + 6 KNO_3 ⟶ 3 N_2 + 5 Fe_2O_3 + 3 K_2O

+ ⟶ + +

iron + potassium nitrate ⟶ nitrogen + iron(III) oxide + potassium oxide

Construct the equilibrium constant, K, expression for: Fe + KNO_3 ⟶ N_2 + Fe_2O_3 + 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: 10 Fe + 6 KNO_3 ⟶ 3 N_2 + 5 Fe_2O_3 + 3 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 Fe | 10 | -10 KNO_3 | 6 | -6 N_2 | 3 | 3 Fe_2O_3 | 5 | 5 K_2O | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Fe | 10 | -10 | ([Fe])^(-10) KNO_3 | 6 | -6 | ([KNO3])^(-6) N_2 | 3 | 3 | ([N2])^3 Fe_2O_3 | 5 | 5 | ([Fe2O3])^5 K_2O | 3 | 3 | ([K2O])^3 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 = ([Fe])^(-10) ([KNO3])^(-6) ([N2])^3 ([Fe2O3])^5 ([K2O])^3 = (([N2])^3 ([Fe2O3])^5 ([K2O])^3)/(([Fe])^10 ([KNO3])^6)

Construct the rate of reaction expression for: Fe + KNO_3 ⟶ N_2 + Fe_2O_3 + 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: 10 Fe + 6 KNO_3 ⟶ 3 N_2 + 5 Fe_2O_3 + 3 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 Fe | 10 | -10 KNO_3 | 6 | -6 N_2 | 3 | 3 Fe_2O_3 | 5 | 5 K_2O | 3 | 3 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 Fe | 10 | -10 | -1/10 (Δ[Fe])/(Δt) KNO_3 | 6 | -6 | -1/6 (Δ[KNO3])/(Δt) N_2 | 3 | 3 | 1/3 (Δ[N2])/(Δt) Fe_2O_3 | 5 | 5 | 1/5 (Δ[Fe2O3])/(Δt) K_2O | 3 | 3 | 1/3 (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 = -1/10 (Δ[Fe])/(Δt) = -1/6 (Δ[KNO3])/(Δt) = 1/3 (Δ[N2])/(Δt) = 1/5 (Δ[Fe2O3])/(Δt) = 1/3 (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| iron | potassium nitrate | nitrogen | iron(III) oxide | potassium oxide formula | Fe | KNO_3 | N_2 | Fe_2O_3 | K_2O name | iron | potassium nitrate | nitrogen | iron(III) oxide | potassium oxide IUPAC name | iron | potassium nitrate | molecular nitrogen | | dipotassium oxygen(2-)

| iron | potassium nitrate | nitrogen | iron(III) oxide | potassium oxide molar mass | 55.845 g/mol | 101.1 g/mol | 28.014 g/mol | 159.69 g/mol | 94.196 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | melting point | 1535 °C | 334 °C | -210 °C | 1565 °C | boiling point | 2750 °C | | -195.79 °C | | density | 7.874 g/cm^3 | | 0.001251 g/cm^3 (at 0 °C) | 5.26 g/cm^3 | solubility in water | insoluble | soluble | insoluble | insoluble | surface tension | | | 0.0066 N/m | | dynamic viscosity | | | 1.78×10^-5 Pa s (at 25 °C) | | odor | | odorless | odorless | odorless |