H2O + Cl2O7 = HClO4

H_2O (water) + Cl_2O_7 (dichlorine heptoxide) ⟶ HClO_4 (perchloric acid)

Balance the chemical equation algebraically: H_2O + Cl_2O_7 ⟶ HClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cl_2O_7 ⟶ c_3 HClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Cl: H: | 2 c_1 = c_3 O: | c_1 + 7 c_2 = 4 c_3 Cl: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + Cl_2O_7 ⟶ 2 HClO_4

+ ⟶

water + dichlorine heptoxide ⟶ perchloric acid

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

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

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

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