An ozone (O₃) treatment system is proposed to oxidize organic materials from wastewater. The first step in this process is to dissolve O₃ in the wastewater. The wastewater has been stripped of all dissolved oxygen and ozone-demanding substances, and the pH is sufficiently low that the ozone decomposition will be insignificant. The wastewater is filled to volume of 80 m³ within a holding pond maintained at 283 K. A compressed ozone/air mixture containing 4.0 mole% ozone (O₃) is fed to the pond 3.20 m below the liquid surface using eight spargers, with each sparger delivering 17.8 m³/h of the gas mixture. The O₃ absorbs into the wastewater by a liquid film controlling interphase mass-transfer process. At 283 K, the Henry’s law constant for ozone dissolved in water is 67.7 m³ atm/kgmole, and the Henry’s law for O₂ dissolved in water is 588 m³ · atm/kgmole; the diffusion coefficient of ozone dissolved in water is 1.7 × 10^-5 cm²/s, and the diffusion coefficient of O₂ dissolved in water is 2.1 × 10^-5 cm²/s. For purposes of this calculation, it may be assumed that the rate of O₃ transferred to the liquid is small relative to molar flow rate of O₃ in the aeration gas. 

a. Estimate the volumetric mass-transfer coefficient, k_L(A/V), using the Eckenfelder plot and Penetration theory to scale k_L(A/V) for O₂ inter phase mass-transfer to O₃ inter phase mass-transfer. 

b. Estimate the time required for the dissolved ozone concentration to reach 25% of its saturation value. What is the dissolved oxygen (O₂) concentration at this time?