Question $2$

The diagram provided illustrates a process for the production of solid potassium chloride $(KCl)$ flakes, which are commonly used as a de$-$icing agent on roads during winter. The initial feed to the process consists of $10,000l\frac{b}{h}r$ of a $40\%$ aqueous $KCl$ solution. This feed is combined with the recycled filtrate from the crystallizer and directed to the evaporator, where water is evaporated to produce a $50\%KCl$ solution. The resulting solution is then fed to the crystallizer. Within the crystallizer, a filter cake is formed, containing $95\%KCl$ crystals and $5\%$ solution, which itself comprises $45\%KCl.$ The filtrate obtained from the crystallizer contains $45\%KCl.$

a$)$ Your task is to determine the rate of water removal by the evaporator and the recycling rate for this process.

b$)$ Suppose that the production rate of $KCl$ flakes remains the same, but the filtrate is no longer recycled. In this scenario, what would be the total feed rate of the $40\%KCl$ solution? It should be assumed that the resulting solution from the evaporator still contains $50\%KCl.$