Suppose $335$ gallons of a mixture containing $4wt\%$NaCl $($sodium chloride$)$ and $96wt\%$ water $($solution density $=1\mathrm{.}0253\frac{g}{c}{m}^3)$ is mixed with an unknown volume of solution that is $20wt\%$NaCl and $80wt\%$ water $($solution density $=1\mathrm{.}1453\frac{g}{c}{m}^3).$ Complete the questions to determine the volume of the second feed solution required to produce a mixture containing $15wt\%$NaCl.

Label the flow chart of the mixing process. Do not leave any spaces empty.

How many unknowns are in the problem statement?

number of unknowns:

Which independent equations can be written to solve for the yolume of the second feed solution?

The sum of the weight fractions of the $20wt\%$NaCl solution is equal to $1.$

The density of the $20wt\%$NaCl solution relates the solution mass to volume.

mass balance on NaCl

The sum of the weight fractions of the product solution is equal to $1.$

volume balance on NaCl

The sum of the weight fractions of the $4wt\%$NaCl solution is equal to $1.$

The density of the $4wt\%$NaCl solution relates the solution mass to volume.

volume balance on water

volume balance on the total amount of fluid

mass balance on water

What is the volume of the second feed solution?

volume of solution:

gallons