KClO3 + P = KCl + P2O5

KClO_3 (potassium chlorate) + P (red phosphorus) ⟶ KCl (potassium chloride) + P2O5

Balance the chemical equation algebraically: KClO_3 + P ⟶ KCl + P2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KClO_3 + c_2 P ⟶ c_3 KCl + c_4 P2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, K, O and P: Cl: | c_1 = c_3 K: | c_1 = c_3 O: | 3 c_1 = 5 c_4 P: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/3 c_2 = 2 c_3 = 5/3 c_4 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 5 c_2 = 6 c_3 = 5 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 KClO_3 + 6 P ⟶ 5 KCl + 3 P2O5

+ ⟶ + P2O5

potassium chlorate + red phosphorus ⟶ potassium chloride + P2O5

Construct the equilibrium constant, K, expression for: KClO_3 + P ⟶ 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: 5 KClO_3 + 6 P ⟶ 5 KCl + 3 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 KClO_3 | 5 | -5 P | 6 | -6 KCl | 5 | 5 P2O5 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KClO_3 | 5 | -5 | ([KClO3])^(-5) P | 6 | -6 | ([P])^(-6) KCl | 5 | 5 | ([KCl])^5 P2O5 | 3 | 3 | ([P2O5])^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 = ([KClO3])^(-5) ([P])^(-6) ([KCl])^5 ([P2O5])^3 = (([KCl])^5 ([P2O5])^3)/(([KClO3])^5 ([P])^6)

Construct the rate of reaction expression for: KClO_3 + P ⟶ 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: 5 KClO_3 + 6 P ⟶ 5 KCl + 3 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 KClO_3 | 5 | -5 P | 6 | -6 KCl | 5 | 5 P2O5 | 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 KClO_3 | 5 | -5 | -1/5 (Δ[KClO3])/(Δt) P | 6 | -6 | -1/6 (Δ[P])/(Δt) KCl | 5 | 5 | 1/5 (Δ[KCl])/(Δt) P2O5 | 3 | 3 | 1/3 (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 = -1/5 (Δ[KClO3])/(Δt) = -1/6 (Δ[P])/(Δt) = 1/5 (Δ[KCl])/(Δt) = 1/3 (Δ[P2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium chlorate | red phosphorus | potassium chloride | P2O5 formula | KClO_3 | P | KCl | P2O5 Hill formula | ClKO_3 | P | ClK | O5P2 name | potassium chlorate | red phosphorus | potassium chloride | IUPAC name | potassium chlorate | phosphorus | potassium chloride |

| potassium chlorate | red phosphorus | potassium chloride | P2O5 molar mass | 122.5 g/mol | 30.973761998 g/mol | 74.55 g/mol | 141.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 356 °C | 579.2 °C | 770 °C | boiling point | | | 1420 °C | density | 2.34 g/cm^3 | 2.16 g/cm^3 | 1.98 g/cm^3 | solubility in water | soluble | insoluble | soluble | dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) | | odor | | | odorless |