H2O + O3 + CrSO4 = H2SO4 + O2 + H2Cr2O7

H_2O water + O_3 ozone + CrSO4 ⟶ H_2SO_4 sulfuric acid + O_2 oxygen + H_2Cr_2O_7 dichromic acid

Balance the chemical equation algebraically: H_2O + O_3 + CrSO4 ⟶ H_2SO_4 + O_2 + H_2Cr_2O_7 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_3 + c_3 CrSO4 ⟶ c_4 H_2SO_4 + c_5 O_2 + c_6 H_2Cr_2O_7 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cr and S: H: | 2 c_1 = 2 c_4 + 2 c_6 O: | c_1 + 3 c_2 + 4 c_3 = 4 c_4 + 2 c_5 + 7 c_6 Cr: | c_3 = 2 c_6 S: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = (4 c_1)/9 + 2/3 c_3 = (2 c_1)/3 c_4 = (2 c_1)/3 c_5 = 1 c_6 = c_1/3 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 3 and solve for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + 2 O_3 + 2 CrSO4 ⟶ 2 H_2SO_4 + O_2 + H_2Cr_2O_7

+ + CrSO4 ⟶ + +

water + ozone + CrSO4 ⟶ sulfuric acid + oxygen + dichromic acid

Construct the equilibrium constant, K, expression for: H_2O + O_3 + CrSO4 ⟶ H_2SO_4 + O_2 + H_2Cr_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: 3 H_2O + 2 O_3 + 2 CrSO4 ⟶ 2 H_2SO_4 + O_2 + H_2Cr_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 H_2O | 3 | -3 O_3 | 2 | -2 CrSO4 | 2 | -2 H_2SO_4 | 2 | 2 O_2 | 1 | 1 H_2Cr_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 H_2O | 3 | -3 | ([H2O])^(-3) O_3 | 2 | -2 | ([O3])^(-2) CrSO4 | 2 | -2 | ([CrSO4])^(-2) H_2SO_4 | 2 | 2 | ([H2SO4])^2 O_2 | 1 | 1 | [O2] H_2Cr_2O_7 | 1 | 1 | [H2Cr2O7] 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])^(-3) ([O3])^(-2) ([CrSO4])^(-2) ([H2SO4])^2 [O2] [H2Cr2O7] = (([H2SO4])^2 [O2] [H2Cr2O7])/(([H2O])^3 ([O3])^2 ([CrSO4])^2)

Construct the rate of reaction expression for: H_2O + O_3 + CrSO4 ⟶ H_2SO_4 + O_2 + H_2Cr_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: 3 H_2O + 2 O_3 + 2 CrSO4 ⟶ 2 H_2SO_4 + O_2 + H_2Cr_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 H_2O | 3 | -3 O_3 | 2 | -2 CrSO4 | 2 | -2 H_2SO_4 | 2 | 2 O_2 | 1 | 1 H_2Cr_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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) O_3 | 2 | -2 | -1/2 (Δ[O3])/(Δt) CrSO4 | 2 | -2 | -1/2 (Δ[CrSO4])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) H_2Cr_2O_7 | 1 | 1 | (Δ[H2Cr2O7])/(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 = -1/3 (Δ[H2O])/(Δt) = -1/2 (Δ[O3])/(Δt) = -1/2 (Δ[CrSO4])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) = (Δ[O2])/(Δt) = (Δ[H2Cr2O7])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | ozone | CrSO4 | sulfuric acid | oxygen | dichromic acid formula | H_2O | O_3 | CrSO4 | H_2SO_4 | O_2 | H_2Cr_2O_7 Hill formula | H_2O | O_3 | CrO4S | H_2O_4S | O_2 | Cr_2H_2O_7 name | water | ozone | | sulfuric acid | oxygen | dichromic acid IUPAC name | water | ozone | | sulfuric acid | molecular oxygen | hydroxy-(hydroxy-dioxo-chromio)oxy-dioxo-chromium

| water | ozone | CrSO4 | sulfuric acid | oxygen | dichromic acid molar mass | 18.015 g/mol | 47.997 g/mol | 148.05 g/mol | 98.07 g/mol | 31.998 g/mol | 218 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | gas (at STP) | melting point | 0 °C | -192.2 °C | | 10.371 °C | -218 °C | boiling point | 99.9839 °C | -111.9 °C | | 279.6 °C | -183 °C | density | 1 g/cm^3 | 0.001962 g/cm^3 (at 25 °C) | | 1.8305 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 1.66 g/cm^3 solubility in water | | | | very soluble | | surface tension | 0.0728 N/m | | | 0.0735 N/m | 0.01347 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.021 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless | odorless |