A waste gas contains \(0.5 \%\) toluene in air and occupies a volume of \(2500 \mathrm{~m}^{3}\) at \(298 \mathrm{~K}\) and \(101.3 \mathrm{kPa}\). To reduce the toluene content of this gas, it is exposed to \(100 \mathrm{~kg}\) of activated carbon, initially free of toluene. The system is allowed to reach equilibrium at constant temperature and pressure.

If the air does not adsorb on the carbon, calculate the equilibrium concentration of toluene in the gaseous phase, and the amount of toluene adsorbed by the carbon. The adsorption equilibrium for this system is given by the Freundlich isotherm (USEPA, 1987):

where \(W\) is the carbon equilibrium adsorptivity, in \(\mathrm{kg}\) of toluene/kg of carbon, and \(p^{*}\) is the equilibrium toluene partial pressure, in \(\mathrm{Pa}\), and must be between 0.7 and \(345 \mathrm{~Pa}\).

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Blowdown 2000 mg/L total solids Water recirculation 8970 kg/s Condensers Cooling tower Air out saturated Makeup 500 mg/L total solids Windage losses Air in 0.016 kg water/kg dry air 2000 mg/L total solids Figure 1.13 Flowsheet for Problem 1.8.