Absorb ammonia from air into water at (20.0^{circ} mathrm{C}) and (1.5 mathrm{~atm}) pressure. Inlet water is recycled

Question:

Absorb ammonia from air into water at \(20.0^{\circ} \mathrm{C}\) and \(1.5 \mathrm{~atm}\) pressure. Inlet water is recycled from a stripper and contains \(0.2 \mathrm{wt} \%\) ammonia. Gas flow rate is \(100.0 \mathrm{kmol} / \mathrm{h}\). Inlet gas is \(3.1 \mathrm{~mol} \%\) ammonia. Exit gas should be 0.31 \(\mathrm{mol} \%\) ammonia. Assume L/V is constant. Equilibrium data are in Table 12-3.

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a. What is the minimum flow rate of water in \(\mathrm{kg} / \mathrm{h}\) ?

b. What is the exit concentration of the liquid, and how many equilibrium stages are needed if \(\mathrm{L}=1.5 \times \mathrm{L}_{\text {min }}\) ?

Keep your units straight. In Table 12-3, 10.0 weight \(\mathrm{NH}_{3}\) per 100.0 weight water \(=10.0\) weight \(/ 110.0\) weight solution \(=0.090909\) mass fraction.

Approach 1: Convert all units to either mass or to moles. [MW \(\mathrm{NH}_{3}=\) 17.0, \(\mathrm{MW} \mathrm{H}_{2} \mathrm{O}=18.0\), \(\mathrm{MW}\) air \(\left.=28.9\right]\)

Approach 2: Keep liquid in weight fraction and gas in mole fraction, and plot equilibrium in this form. In the \(\mathrm{NH}_{3}\) mass balance, if \(\mathrm{y}\) is mole fraction \(\mathrm{NH}_{3}\) in gas and \(\mathrm{x}\) is weight fraction ammonia in liquid, \(\mathrm{Vy}=\) \((\mathrm{kmol}\) gas \(/ \mathrm{h})\left(\mathrm{kmol} \mathrm{NH} \mathrm{N}_{3} / \mathrm{kmol}\right.\) gas \()=\mathrm{kmol} \mathrm{NH}_{3} / \mathrm{h}\), and \(\mathrm{Lx}=(\mathrm{kg}\) liquid \(/ \mathrm{h})\) \(\left(\mathrm{kg} \mathrm{NH}_{3} / \mathrm{kg}\right.\) liquid \()=\mathrm{kg} \mathrm{NH} / \mathrm{h}\).

Then adjust the \(\mathrm{NH}_{3}\) mass balance with the molecular weight of \(\mathrm{NH}_{3}\) so that all terms are in \(\mathrm{kg} \mathrm{NH}_{3} /\) h. Derive the operating equation from this form of mass balance.

c. Estimate the overall efficiency from the O'Connell correlation, and estimate the number of actual stages required.