KClO3 + P = KCl + P2O3

KClO_3 potassium chlorate + P red phosphorus ⟶ KCl potassium chloride + P_2O_3 phosphorus trioxide

Balance the chemical equation algebraically: KClO_3 + P ⟶ KCl + P_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KClO_3 + c_2 P ⟶ c_3 KCl + c_4 P_2O_3 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 = 3 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | KClO_3 + 2 P ⟶ KCl + P_2O_3

+ ⟶ +

potassium chlorate + red phosphorus ⟶ potassium chloride + phosphorus trioxide

Construct the equilibrium constant, K, expression for: KClO_3 + P ⟶ KCl + P_2O_3 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: KClO_3 + 2 P ⟶ KCl + P_2O_3 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 | 1 | -1 P | 2 | -2 KCl | 1 | 1 P_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KClO_3 | 1 | -1 | ([KClO3])^(-1) P | 2 | -2 | ([P])^(-2) KCl | 1 | 1 | [KCl] P_2O_3 | 1 | 1 | [P2O3] 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])^(-1) ([P])^(-2) [KCl] [P2O3] = ([KCl] [P2O3])/([KClO3] ([P])^2)

Construct the rate of reaction expression for: KClO_3 + P ⟶ KCl + P_2O_3 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: KClO_3 + 2 P ⟶ KCl + P_2O_3 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 | 1 | -1 P | 2 | -2 KCl | 1 | 1 P_2O_3 | 1 | 1 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 | 1 | -1 | -(Δ[KClO3])/(Δt) P | 2 | -2 | -1/2 (Δ[P])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) P_2O_3 | 1 | 1 | (Δ[P2O3])/(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 = -(Δ[KClO3])/(Δt) = -1/2 (Δ[P])/(Δt) = (Δ[KCl])/(Δt) = (Δ[P2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium chlorate | red phosphorus | potassium chloride | phosphorus trioxide formula | KClO_3 | P | KCl | P_2O_3 Hill formula | ClKO_3 | P | ClK | O_3P_2 name | potassium chlorate | red phosphorus | potassium chloride | phosphorus trioxide IUPAC name | potassium chlorate | phosphorus | potassium chloride |

| potassium chlorate | red phosphorus | potassium chloride | phosphorus trioxide molar mass | 122.5 g/mol | 30.973761998 g/mol | 74.55 g/mol | 109.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 356 °C | 579.2 °C | 770 °C | 23.8 °C boiling point | | | 1420 °C | 173.1 °C density | 2.34 g/cm^3 | 2.16 g/cm^3 | 1.98 g/cm^3 | 2.135 g/cm^3 solubility in water | soluble | insoluble | soluble | decomposes dynamic viscosity | | 7.6×10^-4 Pa s (at 20.2 °C) | | odor | | | odorless |