HClO4 = H2O + Cl2O7

HClO_4 perchloric acid ⟶ H_2O water + Cl_2O_7 dichlorine heptoxide

Balance the chemical equation algebraically: HClO_4 ⟶ H_2O + Cl_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HClO_4 ⟶ c_2 H_2O + c_3 Cl_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and O: Cl: | c_1 = 2 c_3 H: | c_1 = 2 c_2 O: | 4 c_1 = c_2 + 7 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 = 2 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HClO_4 ⟶ H_2O + Cl_2O_7

⟶ +

perchloric acid ⟶ water + dichlorine heptoxide

Construct the equilibrium constant, K, expression for: HClO_4 ⟶ H_2O + 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: 2 HClO_4 ⟶ H_2O + 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 | 2 | -2 H_2O | 1 | 1 Cl_2O_7 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HClO_4 | 2 | -2 | ([HClO4])^(-2) H_2O | 1 | 1 | [H2O] Cl_2O_7 | 1 | 1 | [Cl2O7] 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])^(-2) [H2O] [Cl2O7] = ([H2O] [Cl2O7])/([HClO4])^2

Construct the rate of reaction expression for: HClO_4 ⟶ H_2O + 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: 2 HClO_4 ⟶ H_2O + 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 | 2 | -2 H_2O | 1 | 1 Cl_2O_7 | 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 HClO_4 | 2 | -2 | -1/2 (Δ[HClO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Cl_2O_7 | 1 | 1 | (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 = -1/2 (Δ[HClO4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Cl2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| perchloric acid | water | dichlorine heptoxide formula | HClO_4 | H_2O | Cl_2O_7 Hill formula | ClHO_4 | H_2O | Cl_2O_7 name | perchloric acid | water | dichlorine heptoxide IUPAC name | perchloric acid | water | perchloryl perchlorate

| perchloric acid | water | dichlorine heptoxide molar mass | 100.5 g/mol | 18.015 g/mol | 182.9 g/mol phase | liquid (at STP) | liquid (at STP) | melting point | -112 °C | 0 °C | -91.5 °C boiling point | 90 °C | 99.9839 °C | 82 °C density | 1.77 g/cm^3 | 1 g/cm^3 | 1.9 g/cm^3 solubility in water | very soluble | | reacts surface tension | | 0.0728 N/m | dynamic viscosity | 8×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | odorless |