Consider the mixing flow sheet in Figure $1$ used to dissolve a substance $A$ in water. The flow rates of streams $1$ and $5$ are $5$ and $200$ tph respectively. Stream $1$ is $100\%$ A and stream $5$ is $5\%$ A$.($Note$,$ the splitter controls the amount of solution that is recycled. The compositions of streams $6$ and $4$ are the same.$)$

a$)$ Calculate the flow rate and composition of the product $($stream $4).($Do an overall balance that "hides" the recycle.$)$

b$)$ Assume that the flow rate of stream $6$ is $50tph.$ Calculate the flow rates and composition of streams $2$ and $3,$ and the flow rate of $A$ in stream $2.$

c$)$ Comment on and explain the flow rate and composition of stream $4.$

d$)$ Repeat $($b$)$ and $($c$)$ assuming the flow rate of stream $6$ is $100tph,200tph,500tph.$

e$)$ From your observations what do you learn about the nature of systems that have recycle streams?

Consider the following two$-$unit process in Figure $2$ used to separate two components A and $B.$