Practice problem $$ Please write out the set$-$up of this problems, following ALL the steps given in Chapter $1$

$($including a title for the problem!$),$ and number each step or set of steps in the solution using the Chapter

$1$ numbers and headings.

$1.$ A steady state, constant T and P mixing process is being used to combine two input streams and

produce one output $($product$)$ stream. Feed $1$ contains components A and B$,$ Feed $2$ contains components

B and C$,$ and there is no chemical reaction.

a$.$ Provide a title, System, Contents, Process, Assumptions, and fully labeled drawing, with all variables

defined. Make sure to include ALL composition variables on your feed arrows, even if you know they are

$=0.$

b$.$ Using the variables you have defined, write out the overall mass balance for this process. Also write

out all the stream balances $($how many are there?$).$ Given these equations, how many independent

component balances are there? Write them out.

c$.$ How many variables are needed to fully describe this process $($please count T and P separately from the

ones appearing in the material balance equations$)?$ Now subtract the total number of equations in part b

from the total number of variables in part c $($not counting T and P$)$ to get the number of independent

specifications needed to enable you to solve this system of equations.

d$.$ How would your answers to parts a$-$c change if the mixing process produced two separate phases?

Please be specific.

e$.$ There are $2$Givens$$ in the problem statement above. What are they? Write them out in terms of the

variables you have defined.

f$.$ Below are four different problem statements that could apply to this process. For each one, please

write out the $$givens$$ and the $$finds$,$ including the two $$Givens$$ from the initial problem statement

above, and solve, algebraically first, for the $$find$$ or $$finds$$ following the strategies given in Chapter $1.$

Make sure to number and annotate all of your steps, and don$$t leave any steps out!

$($i$)100$ kg$/$h of feed $1$ is to be processed. Feed $1$ is $50\%$ A by weight and $50\%$ B by weight, and

feed $2$ is $20\%$ B by weight. How much feed $2$ must be fed per hour to produce a mixture that is

$45\%$ B by weight? What will the composition of the product be$,$ and what will its flow rate be$?$

Which $$given$$ in this problem statement is redundant, and therefore not independent?

$($ii$)$ What will the steady state product composition be if the feed ratio, F$1$:F$2,$ is $1\mathrm{.}5$:$1$ and each

feed is $25\%$ B$?$ Can you find the product flow rate from this set of $$givens$?$ Explain.

$($iii$)$ What composition of feed $2$ will give a product composition that is $25\%$ A$,35\%$ B$,$ and the

rest C if feed $1$ is $40\%$ A and both feeds enter with the same mass flow rate? What will the

product flow rate be$?$

$($iv$)$ What should the feed ratio, F$1$:F$2,$ be if the desired product composition is $25\%$ A$,35\%$ B and

the rest C$,$ feed $1$ is $60\%$ A$,$ and feed $2$ is $25\%$ B