Assignment:
It is desired to adsorb 99.8% of the toluene originally present in the waste gas. Estimate how much activated carbon should be used if the system is allowed to reach equilibrium at constant temperature and pressure.
A waste gas contains 0.5 mol% toluene in air and occupies a volume of 2500 m3 at 298 K and 101.3 kPa. In an effort to reduce the toluene content of this gas, it is exposed to 100 kg of activated carbon, initially free of toluene. The system is allowed to reach equilibrium at constant temperature and pressure. Assuming that 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):
W = 0.208(p*)0.11
where W is the carbon equilibrium adsorptivity, in kg of toluenekg of carbon, and p* is the equilibrium toluene partial pressure, in Pa, and must be between 0.7 and 345 Pa.
Provide complete and step by step solution for the question and show calculations and use formulas.