O2 + K + Cl2O7 = KClO4

O_2 oxygen + K potassium + Cl_2O_7 dichlorine heptoxide ⟶ KClO_4 potassium perchlorate

Balance the chemical equation algebraically: O_2 + K + Cl_2O_7 ⟶ KClO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 K + c_3 Cl_2O_7 ⟶ c_4 KClO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, K and Cl: O: | 2 c_1 + 7 c_3 = 4 c_4 K: | c_2 = c_4 Cl: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 2 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | O_2 + 4 K + 2 Cl_2O_7 ⟶ 4 KClO_4

+ + ⟶

oxygen + potassium + dichlorine heptoxide ⟶ potassium perchlorate

Construct the equilibrium constant, K, expression for: O_2 + K + Cl_2O_7 ⟶ KClO_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: O_2 + 4 K + 2 Cl_2O_7 ⟶ 4 KClO_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 O_2 | 1 | -1 K | 4 | -4 Cl_2O_7 | 2 | -2 KClO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 1 | -1 | ([O2])^(-1) K | 4 | -4 | ([K])^(-4) Cl_2O_7 | 2 | -2 | ([Cl2O7])^(-2) KClO_4 | 4 | 4 | ([KClO4])^4 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 = ([O2])^(-1) ([K])^(-4) ([Cl2O7])^(-2) ([KClO4])^4 = ([KClO4])^4/([O2] ([K])^4 ([Cl2O7])^2)

Construct the rate of reaction expression for: O_2 + K + Cl_2O_7 ⟶ KClO_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: O_2 + 4 K + 2 Cl_2O_7 ⟶ 4 KClO_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 O_2 | 1 | -1 K | 4 | -4 Cl_2O_7 | 2 | -2 KClO_4 | 4 | 4 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 O_2 | 1 | -1 | -(Δ[O2])/(Δt) K | 4 | -4 | -1/4 (Δ[K])/(Δt) Cl_2O_7 | 2 | -2 | -1/2 (Δ[Cl2O7])/(Δt) KClO_4 | 4 | 4 | 1/4 (Δ[KClO4])/(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[O2])/(Δt) = -1/4 (Δ[K])/(Δt) = -1/2 (Δ[Cl2O7])/(Δt) = 1/4 (Δ[KClO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | potassium | dichlorine heptoxide | potassium perchlorate formula | O_2 | K | Cl_2O_7 | KClO_4 Hill formula | O_2 | K | Cl_2O_7 | ClKO_4 name | oxygen | potassium | dichlorine heptoxide | potassium perchlorate IUPAC name | molecular oxygen | potassium | perchloryl perchlorate | potassium perchlorate

| oxygen | potassium | dichlorine heptoxide | potassium perchlorate molar mass | 31.998 g/mol | 39.0983 g/mol | 182.9 g/mol | 138.54 g/mol phase | gas (at STP) | solid (at STP) | | solid (at STP) melting point | -218 °C | 64 °C | -91.5 °C | 400 °C boiling point | -183 °C | 760 °C | 82 °C | density | 0.001429 g/cm^3 (at 0 °C) | 0.86 g/cm^3 | 1.9 g/cm^3 | 2.5239 g/cm^3 solubility in water | | reacts | reacts | surface tension | 0.01347 N/m | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | | odor | odorless | | |