3. (30 points) We are trying to remove acetone from nitrogen gas using an adsorption column with diameter 5 cm and length 20 cm. The column is packed with 150 g of activated carbon. The inlet gas stream enters the column with the mass flow rate of 5 g/min. The molar fraction of acetone in the feed mixture is 0.005. The experimental breakthrough curve could be fitted to the following Klinkenberg equation. 1 C=- 1 +0.5 1+erf | V101 - 60+ 8V10t 8V60 2 ) =o.s[1+ The unit of time t is in hours in this equation. Determine the break-point time, the fraction of total capacity used up to the break point, and the length of unused bed. Determine the saturation loading capacity of the carbon. Calculate the total length of the column that is needed to get 3 kg of pure nitrogen gas. (Note: Use Microsoft Excel to plot the breakthrough curve and evaluate the integrals. 2 The error function, erf (x) Tale*du is a standard function defined in Excel)