A gaseous stream containing sulfur trioxide $($SO$3)$ is passed to the base of an absorption column. The stream is stripped of sulfur trioxide by contact with $99\%$ w$/$w sulfuric acid fed to the top of the column. A liquid stream containing $99\mathrm{.}5\%$ w$/$w sulfuric acid is removed from the base of the column, which is diluted with water in a tank to produce $99\%$ w$/$w sulfuric acid. A portion of the acid is removed as product and the remainder is recycled back to the absorption column. The system works without accumulation. If $100000$ kg per day of $99\%$ w$/$w sulfuric acid is to be produced, determine: $($a$)$ the water flow in kg required for dissolution and $($b$)$ the weight of $99\%$ w$/$w sulfuric acid recycled to the column the day.