S + KClO3 + P = SO2 + KCl + P2O5

S mixed sulfur + KClO_3 potassium chlorate + P red phosphorus ⟶ SO_2 sulfur dioxide + KCl potassium chloride + P2O5

Balance the chemical equation algebraically: S + KClO_3 + P ⟶ SO_2 + KCl + P2O5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 S + c_2 KClO_3 + c_3 P ⟶ c_4 SO_2 + c_5 KCl + c_6 P2O5 Set the number of atoms in the reactants equal to the number of atoms in the products for S, Cl, K, O and P: S: | c_1 = c_4 Cl: | c_2 = c_5 K: | c_2 = c_5 O: | 3 c_2 = 2 c_4 + 5 c_6 P: | c_3 = 2 c_6 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_3 = (6 c_2)/5 - 4/5 c_4 = 1 c_5 = c_2 c_6 = (3 c_2)/5 - 2/5 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_2 = 4 and solve for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 c_4 = 1 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | S + 4 KClO_3 + 4 P ⟶ SO_2 + 4 KCl + 2 P2O5

+ + ⟶ + + P2O5

mixed sulfur + potassium chlorate + red phosphorus ⟶ sulfur dioxide + potassium chloride + P2O5

Construct the equilibrium constant, K, expression for: S + KClO_3 + P ⟶ SO_2 + 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: S + 4 KClO_3 + 4 P ⟶ SO_2 + 4 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 S | 1 | -1 KClO_3 | 4 | -4 P | 4 | -4 SO_2 | 1 | 1 KCl | 4 | 4 P2O5 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression S | 1 | -1 | ([S])^(-1) KClO_3 | 4 | -4 | ([KClO3])^(-4) P | 4 | -4 | ([P])^(-4) SO_2 | 1 | 1 | [SO2] KCl | 4 | 4 | ([KCl])^4 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 = ([S])^(-1) ([KClO3])^(-4) ([P])^(-4) [SO2] ([KCl])^4 ([P2O5])^2 = ([SO2] ([KCl])^4 ([P2O5])^2)/([S] ([KClO3])^4 ([P])^4)

Construct the rate of reaction expression for: S + KClO_3 + P ⟶ SO_2 + 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: S + 4 KClO_3 + 4 P ⟶ SO_2 + 4 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 S | 1 | -1 KClO_3 | 4 | -4 P | 4 | -4 SO_2 | 1 | 1 KCl | 4 | 4 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 S | 1 | -1 | -(Δ[S])/(Δt) KClO_3 | 4 | -4 | -1/4 (Δ[KClO3])/(Δt) P | 4 | -4 | -1/4 (Δ[P])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(Δt) KCl | 4 | 4 | 1/4 (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 = -(Δ[S])/(Δt) = -1/4 (Δ[KClO3])/(Δt) = -1/4 (Δ[P])/(Δt) = (Δ[SO2])/(Δt) = 1/4 (Δ[KCl])/(Δt) = 1/2 (Δ[P2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| mixed sulfur | potassium chlorate | red phosphorus | sulfur dioxide | potassium chloride | P2O5 formula | S | KClO_3 | P | SO_2 | KCl | P2O5 Hill formula | S | ClKO_3 | P | O_2S | ClK | O5P2 name | mixed sulfur | potassium chlorate | red phosphorus | sulfur dioxide | potassium chloride | IUPAC name | sulfur | potassium chlorate | phosphorus | sulfur dioxide | potassium chloride |

| mixed sulfur | potassium chlorate | red phosphorus | sulfur dioxide | potassium chloride | P2O5 molar mass | 32.06 g/mol | 122.5 g/mol | 30.973761998 g/mol | 64.06 g/mol | 74.55 g/mol | 141.94 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | melting point | 112.8 °C | 356 °C | 579.2 °C | -73 °C | 770 °C | boiling point | 444.7 °C | | | -10 °C | 1420 °C | density | 2.07 g/cm^3 | 2.34 g/cm^3 | 2.16 g/cm^3 | 0.002619 g/cm^3 (at 25 °C) | 1.98 g/cm^3 | solubility in water | | soluble | insoluble | | soluble | surface tension | | | | 0.02859 N/m | | dynamic viscosity | | | 7.6×10^-4 Pa s (at 20.2 °C) | 1.282×10^-5 Pa s (at 25 °C) | | odor | | | | | odorless |