P + KClO2 = KCl + P2O5

P red phosphorus + KClO2 ⟶ KCl potassium chloride + P2O5

Balance the chemical equation algebraically: P + KClO2 ⟶ KCl + P2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 P + c_2 KClO2 ⟶ c_3 KCl + c_4 P2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for P, K, Cl and O: P: | c_1 = 2 c_4 K: | c_2 = c_3 Cl: | c_2 = c_3 O: | 2 c_2 = 5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 5/2 c_3 = 5/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 5 c_3 = 5 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 P + 5 KClO2 ⟶ 5 KCl + 2 P2O5

+ KClO2 ⟶ + P2O5

red phosphorus + KClO2 ⟶ potassium chloride + P2O5

Construct the equilibrium constant, K, expression for: P + KClO2 ⟶ KCl + P2O5 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: 4 P + 5 KClO2 ⟶ 5 KCl + 2 P2O5 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 P | 4 | -4 KClO2 | 5 | -5 KCl | 5 | 5 P2O5 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression P | 4 | -4 | ([P])^(-4) KClO2 | 5 | -5 | ([KClO2])^(-5) KCl | 5 | 5 | ([KCl])^5 P2O5 | 2 | 2 | ([P2O5])^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 = ([P])^(-4) ([KClO2])^(-5) ([KCl])^5 ([P2O5])^2 = (([KCl])^5 ([P2O5])^2)/(([P])^4 ([KClO2])^5)

Construct the rate of reaction expression for: P + KClO2 ⟶ KCl + P2O5 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: 4 P + 5 KClO2 ⟶ 5 KCl + 2 P2O5 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 P | 4 | -4 KClO2 | 5 | -5 KCl | 5 | 5 P2O5 | 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 P | 4 | -4 | -1/4 (Δ[P])/(Δt) KClO2 | 5 | -5 | -1/5 (Δ[KClO2])/(Δt) KCl | 5 | 5 | 1/5 (Δ[KCl])/(Δt) P2O5 | 2 | 2 | 1/2 (Δ[P2O5])/(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 = -1/4 (Δ[P])/(Δt) = -1/5 (Δ[KClO2])/(Δt) = 1/5 (Δ[KCl])/(Δt) = 1/2 (Δ[P2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| red phosphorus | KClO2 | potassium chloride | P2O5 formula | P | KClO2 | KCl | P2O5 Hill formula | P | ClKO2 | ClK | O5P2 name | red phosphorus | | potassium chloride | IUPAC name | phosphorus | | potassium chloride |

| red phosphorus | KClO2 | potassium chloride | P2O5 molar mass | 30.973761998 g/mol | 106.5 g/mol | 74.55 g/mol | 141.94 g/mol phase | solid (at STP) | | solid (at STP) | melting point | 579.2 °C | | 770 °C | boiling point | | | 1420 °C | density | 2.16 g/cm^3 | | 1.98 g/cm^3 | solubility in water | insoluble | | soluble | dynamic viscosity | 7.6×10^-4 Pa s (at 20.2 °C) | | | odor | | | odorless |