H2O2 + I2O5 = H2O + O2 + HI

H_2O_2 hydrogen peroxide + I_2O_5 iodopentoxide ⟶ H_2O water + O_2 oxygen + HI hydrogen iodide

Balance the chemical equation algebraically: H_2O_2 + I_2O_5 ⟶ H_2O + O_2 + HI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 I_2O_5 ⟶ c_3 H_2O + c_4 O_2 + c_5 HI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and I: H: | 2 c_1 = 2 c_3 + c_5 O: | 2 c_1 + 5 c_2 = c_3 + 2 c_4 I: | 2 c_2 = c_5 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_2 = 1 c_3 = c_1 - 1 c_4 = c_1/2 + 3 c_5 = 2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 4 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O_2 + I_2O_5 ⟶ H_2O + 4 O_2 + 2 HI

+ ⟶ + +

hydrogen peroxide + iodopentoxide ⟶ water + oxygen + hydrogen iodide

Construct the equilibrium constant, K, expression for: H_2O_2 + I_2O_5 ⟶ H_2O + O_2 + HI 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 H_2O_2 + I_2O_5 ⟶ H_2O + 4 O_2 + 2 HI 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_2 | 2 | -2 I_2O_5 | 1 | -1 H_2O | 1 | 1 O_2 | 4 | 4 HI | 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_2 | 2 | -2 | ([H2O2])^(-2) I_2O_5 | 1 | -1 | ([I2O5])^(-1) H_2O | 1 | 1 | [H2O] O_2 | 4 | 4 | ([O2])^4 HI | 2 | 2 | ([HI])^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 = ([H2O2])^(-2) ([I2O5])^(-1) [H2O] ([O2])^4 ([HI])^2 = ([H2O] ([O2])^4 ([HI])^2)/(([H2O2])^2 [I2O5])

Construct the rate of reaction expression for: H_2O_2 + I_2O_5 ⟶ H_2O + O_2 + HI 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 H_2O_2 + I_2O_5 ⟶ H_2O + 4 O_2 + 2 HI 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_2 | 2 | -2 I_2O_5 | 1 | -1 H_2O | 1 | 1 O_2 | 4 | 4 HI | 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_2 | 2 | -2 | -1/2 (Δ[H2O2])/(Δt) I_2O_5 | 1 | -1 | -(Δ[I2O5])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) O_2 | 4 | 4 | 1/4 (Δ[O2])/(Δt) HI | 2 | 2 | 1/2 (Δ[HI])/(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[H2O2])/(Δt) = -(Δ[I2O5])/(Δt) = (Δ[H2O])/(Δt) = 1/4 (Δ[O2])/(Δt) = 1/2 (Δ[HI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | iodopentoxide | water | oxygen | hydrogen iodide formula | H_2O_2 | I_2O_5 | H_2O | O_2 | HI name | hydrogen peroxide | iodopentoxide | water | oxygen | hydrogen iodide IUPAC name | hydrogen peroxide | iodic acid iodyl ester | water | molecular oxygen | hydrogen iodide

| hydrogen peroxide | iodopentoxide | water | oxygen | hydrogen iodide molar mass | 34.014 g/mol | 333.804 g/mol | 18.015 g/mol | 31.998 g/mol | 127.912 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | gas (at STP) melting point | -0.43 °C | | 0 °C | -218 °C | -50.76 °C boiling point | 150.2 °C | | 99.9839 °C | -183 °C | -35.55 °C density | 1.44 g/cm^3 | 5 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.005228 g/cm^3 (at 25 °C) solubility in water | miscible | | | | very soluble surface tension | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | 0.001321 Pa s (at -39 °C) odor | | | odorless | odorless |