KNO3 + P = P2O5 + KNO2

KNO_3 potassium nitrate + P red phosphorus ⟶ P2O5 + KNO_2 potassium nitrite

Balance the chemical equation algebraically: KNO_3 + P ⟶ P2O5 + KNO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KNO_3 + c_2 P ⟶ c_3 P2O5 + c_4 KNO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, N, O and P: K: | c_1 = c_4 N: | c_1 = c_4 O: | 3 c_1 = 5 c_3 + 2 c_4 P: | c_2 = 2 c_3 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 = 5 c_2 = 2 c_3 = 1 c_4 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 KNO_3 + 2 P ⟶ P2O5 + 5 KNO_2

+ ⟶ P2O5 +

potassium nitrate + red phosphorus ⟶ P2O5 + potassium nitrite

Construct the equilibrium constant, K, expression for: KNO_3 + P ⟶ P2O5 + KNO_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: 5 KNO_3 + 2 P ⟶ P2O5 + 5 KNO_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 KNO_3 | 5 | -5 P | 2 | -2 P2O5 | 1 | 1 KNO_2 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KNO_3 | 5 | -5 | ([KNO3])^(-5) P | 2 | -2 | ([P])^(-2) P2O5 | 1 | 1 | [P2O5] KNO_2 | 5 | 5 | ([KNO2])^5 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])^(-5) ([P])^(-2) [P2O5] ([KNO2])^5 = ([P2O5] ([KNO2])^5)/(([KNO3])^5 ([P])^2)

Construct the rate of reaction expression for: KNO_3 + P ⟶ P2O5 + KNO_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: 5 KNO_3 + 2 P ⟶ P2O5 + 5 KNO_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 KNO_3 | 5 | -5 P | 2 | -2 P2O5 | 1 | 1 KNO_2 | 5 | 5 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 | 5 | -5 | -1/5 (Δ[KNO3])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) P2O5 | 1 | 1 | (Δ[P2O5])/(Δt) KNO_2 | 5 | 5 | 1/5 (Δ[KNO2])/(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 = -1/5 (Δ[KNO3])/(Δt) = -1/2 (Δ[P])/(Δt) = (Δ[P2O5])/(Δt) = 1/5 (Δ[KNO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium nitrate | red phosphorus | P2O5 | potassium nitrite formula | KNO_3 | P | P2O5 | KNO_2 Hill formula | KNO_3 | P | O5P2 | KNO_2 name | potassium nitrate | red phosphorus | | potassium nitrite IUPAC name | potassium nitrate | phosphorus | | potassium nitrite

| potassium nitrate | red phosphorus | P2O5 | potassium nitrite molar mass | 101.1 g/mol | 30.973761998 g/mol | 141.94 g/mol | 85.103 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) melting point | 334 °C | 579.2 °C | | 350 °C density | | 2.16 g/cm^3 | | 1.915 g/cm^3 solubility in water | soluble | insoluble | | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) | | odor | odorless | | |