HClO4 + P4O10 = H3PO4 + Cl2O7

HClO_4 (perchloric acid) + P_4O_10 (phosphorus pentoxide) ⟶ H_3PO_4 (phosphoric acid) + Cl_2O_7 (dichlorine heptoxide)

Balance the chemical equation algebraically: HClO_4 + P_4O_10 ⟶ H_3PO_4 + Cl_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HClO_4 + c_2 P_4O_10 ⟶ c_3 H_3PO_4 + c_4 Cl_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O and P: Cl: | c_1 = 2 c_4 H: | c_1 = 3 c_3 O: | 4 c_1 + 10 c_2 = 4 c_3 + 7 c_4 P: | 4 c_2 = c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 12 c_2 = 1 c_3 = 4 c_4 = 6 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HClO_4 + P_4O_10 ⟶ 4 H_3PO_4 + 6 Cl_2O_7

+ ⟶ +

perchloric acid + phosphorus pentoxide ⟶ phosphoric acid + dichlorine heptoxide

Construct the equilibrium constant, K, expression for: HClO_4 + P_4O_10 ⟶ H_3PO_4 + Cl_2O_7 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: 12 HClO_4 + P_4O_10 ⟶ 4 H_3PO_4 + 6 Cl_2O_7 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 HClO_4 | 12 | -12 P_4O_10 | 1 | -1 H_3PO_4 | 4 | 4 Cl_2O_7 | 6 | 6 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HClO_4 | 12 | -12 | ([HClO4])^(-12) P_4O_10 | 1 | -1 | ([P4O10])^(-1) H_3PO_4 | 4 | 4 | ([H3PO4])^4 Cl_2O_7 | 6 | 6 | ([Cl2O7])^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 = ([HClO4])^(-12) ([P4O10])^(-1) ([H3PO4])^4 ([Cl2O7])^6 = (([H3PO4])^4 ([Cl2O7])^6)/(([HClO4])^12 [P4O10])

Construct the rate of reaction expression for: HClO_4 + P_4O_10 ⟶ H_3PO_4 + Cl_2O_7 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: 12 HClO_4 + P_4O_10 ⟶ 4 H_3PO_4 + 6 Cl_2O_7 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 HClO_4 | 12 | -12 P_4O_10 | 1 | -1 H_3PO_4 | 4 | 4 Cl_2O_7 | 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 HClO_4 | 12 | -12 | -1/12 (Δ[HClO4])/(Δt) P_4O_10 | 1 | -1 | -(Δ[P4O10])/(Δt) H_3PO_4 | 4 | 4 | 1/4 (Δ[H3PO4])/(Δt) Cl_2O_7 | 6 | 6 | 1/6 (Δ[Cl2O7])/(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 = -1/12 (Δ[HClO4])/(Δt) = -(Δ[P4O10])/(Δt) = 1/4 (Δ[H3PO4])/(Δt) = 1/6 (Δ[Cl2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| perchloric acid | phosphorus pentoxide | phosphoric acid | dichlorine heptoxide formula | HClO_4 | P_4O_10 | H_3PO_4 | Cl_2O_7 Hill formula | ClHO_4 | O_10P_4 | H_3O_4P | Cl_2O_7 name | perchloric acid | phosphorus pentoxide | phosphoric acid | dichlorine heptoxide IUPAC name | perchloric acid | | phosphoric acid | perchloryl perchlorate

| perchloric acid | phosphorus pentoxide | phosphoric acid | dichlorine heptoxide molar mass | 100.5 g/mol | 283.89 g/mol | 97.994 g/mol | 182.9 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | -112 °C | 340 °C | 42.4 °C | -91.5 °C boiling point | 90 °C | | 158 °C | 82 °C density | 1.77 g/cm^3 | 2.3 g/cm^3 | 1.685 g/cm^3 | 1.9 g/cm^3 solubility in water | very soluble | | very soluble | reacts dynamic viscosity | 8×10^-4 Pa s (at 25 °C) | | | odor | odorless | | odorless |