H2O + KClO3 + P2S5 = H2SO4 + KCl + H3PO4

H_2O water + KClO_3 potassium chlorate + P_2S_5 phosphorus pentasulfide ⟶ H_2SO_4 sulfuric acid + KCl potassium chloride + H_3PO_4 phosphoric acid

Balance the chemical equation algebraically: H_2O + KClO_3 + P_2S_5 ⟶ H_2SO_4 + KCl + H_3PO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KClO_3 + c_3 P_2S_5 ⟶ c_4 H_2SO_4 + c_5 KCl + c_6 H_3PO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, K, P and S: H: | 2 c_1 = 2 c_4 + 3 c_6 O: | c_1 + 3 c_2 = 4 c_4 + 4 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 P: | 2 c_3 = c_6 S: | 5 c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 20/3 c_3 = 1 c_4 = 5 c_5 = 20/3 c_6 = 2 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 24 c_2 = 20 c_3 = 3 c_4 = 15 c_5 = 20 c_6 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 24 H_2O + 20 KClO_3 + 3 P_2S_5 ⟶ 15 H_2SO_4 + 20 KCl + 6 H_3PO_4

+ + ⟶ + +

water + potassium chlorate + phosphorus pentasulfide ⟶ sulfuric acid + potassium chloride + phosphoric acid

Construct the equilibrium constant, K, expression for: H_2O + KClO_3 + P_2S_5 ⟶ H_2SO_4 + KCl + H_3PO_4 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: 24 H_2O + 20 KClO_3 + 3 P_2S_5 ⟶ 15 H_2SO_4 + 20 KCl + 6 H_3PO_4 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 H_2O | 24 | -24 KClO_3 | 20 | -20 P_2S_5 | 3 | -3 H_2SO_4 | 15 | 15 KCl | 20 | 20 H_3PO_4 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 24 | -24 | ([H2O])^(-24) KClO_3 | 20 | -20 | ([KClO3])^(-20) P_2S_5 | 3 | -3 | ([P2S5])^(-3) H_2SO_4 | 15 | 15 | ([H2SO4])^15 KCl | 20 | 20 | ([KCl])^20 H_3PO_4 | 6 | 6 | ([H3PO4])^6 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 = ([H2O])^(-24) ([KClO3])^(-20) ([P2S5])^(-3) ([H2SO4])^15 ([KCl])^20 ([H3PO4])^6 = (([H2SO4])^15 ([KCl])^20 ([H3PO4])^6)/(([H2O])^24 ([KClO3])^20 ([P2S5])^3)

Construct the rate of reaction expression for: H_2O + KClO_3 + P_2S_5 ⟶ H_2SO_4 + KCl + H_3PO_4 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: 24 H_2O + 20 KClO_3 + 3 P_2S_5 ⟶ 15 H_2SO_4 + 20 KCl + 6 H_3PO_4 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 H_2O | 24 | -24 KClO_3 | 20 | -20 P_2S_5 | 3 | -3 H_2SO_4 | 15 | 15 KCl | 20 | 20 H_3PO_4 | 6 | 6 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 H_2O | 24 | -24 | -1/24 (Δ[H2O])/(Δt) KClO_3 | 20 | -20 | -1/20 (Δ[KClO3])/(Δt) P_2S_5 | 3 | -3 | -1/3 (Δ[P2S5])/(Δt) H_2SO_4 | 15 | 15 | 1/15 (Δ[H2SO4])/(Δt) KCl | 20 | 20 | 1/20 (Δ[KCl])/(Δt) H_3PO_4 | 6 | 6 | 1/6 (Δ[H3PO4])/(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 = -1/24 (Δ[H2O])/(Δt) = -1/20 (Δ[KClO3])/(Δt) = -1/3 (Δ[P2S5])/(Δt) = 1/15 (Δ[H2SO4])/(Δt) = 1/20 (Δ[KCl])/(Δt) = 1/6 (Δ[H3PO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium chlorate | phosphorus pentasulfide | sulfuric acid | potassium chloride | phosphoric acid formula | H_2O | KClO_3 | P_2S_5 | H_2SO_4 | KCl | H_3PO_4 Hill formula | H_2O | ClKO_3 | P_2S_5 | H_2O_4S | ClK | H_3O_4P name | water | potassium chlorate | phosphorus pentasulfide | sulfuric acid | potassium chloride | phosphoric acid

| water | potassium chlorate | phosphorus pentasulfide | sulfuric acid | potassium chloride | phosphoric acid molar mass | 18.015 g/mol | 122.5 g/mol | 222.3 g/mol | 98.07 g/mol | 74.55 g/mol | 97.994 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) melting point | 0 °C | 356 °C | 282 °C | 10.371 °C | 770 °C | 42.4 °C boiling point | 99.9839 °C | | | 279.6 °C | 1420 °C | 158 °C density | 1 g/cm^3 | 2.34 g/cm^3 | 2.09 g/cm^3 | 1.8305 g/cm^3 | 1.98 g/cm^3 | 1.685 g/cm^3 solubility in water | | soluble | | very soluble | soluble | very soluble surface tension | 0.0728 N/m | | | 0.0735 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.021 Pa s (at 25 °C) | | odor | odorless | | | odorless | odorless | odorless