Chapter 9, Problem 9.55P

Ammonia scrubbing is one of many processes for removing sulfur dioxide from flue gases. The gases are bubbled through an aqueous solution of ammonium sulfite, and the SO? reacts to form ammonium bisulfite:

   ${\left(N{H}_4\right)}_{2}S{O}_3\left(aq\right)+H_{2}O\left(l\right)\to 2N{H}_{4}HS{O}_3\left(aq\right)$

Subsequent process steps yield concentrated $S{O}_2$and regenerate ammonium sulfite, which is recycled to the scrubber. The sulfur dioxide is either oxidized and absorbed in water to form sulfuric acid or reduced to elemental sulfur.

Flue gas from a power-plant boiler containing 0.30% $S{O}_2$by volume enters a scrubber at a rate of 50,000 mol/h at 50°C. The gas is bubbled through an aqueous solution containing 10.0 mole% ammonium sulfite that enters the scrubber at 25°C. The gas and liquid effluents from the scrubber both emerge at 35°C. The scrubber removes 90% of the $S{O}_2$entering with the flue gas. The effluent liquid is analyzed and is found to contain 1.5 moles ${\left(N{H}_4\right)}_{2}S{O}_3$per mole of $N{H}_{4}HS{O}_3$. The heat of formation of ${\left(N{H}_4\right)}_{2}S{O}_3$(aq) at 25°C is —890.0 kJ/mol, and that of $N{H}_{4}HS{O}_3\left(aq\right)$is —760 kJ/mol. The heat capacities of all liquid solutions may be taken to be 4.0 J/(g·°C) and that of the flue gas may be taken to be that of nitrogen. Evaporation of water may be neglected. Calculate the required rate of heat transfer to or from the scrubber (kW).