A chemist wishes to create 12L of 30% acid by mixing water with a solution that is 80% acid. How much of each should be mixed together?

Question

I dont understand this question i just know you draw boxes and add but idk how you're supposed to know what to add multiply or subtract

Answer 1

This problem is a little tricky because you must assume that volumes of water and volumes of concentrated acid are additive (in reality this is generally not true).  Also, it helps to assume that the percent values are given in mass/volume units.  Using these assumptions, the answer is as follows:

 

x L_water = 12 L_{30g/100mL acid soln} - L_{80g/100mL acid soln}  =  12 L - ((12 L_{30g/100mL acid soln})(30 g_acid / 0.1 L_{30g/100mL acid soln})/(80 g_{80g/100 mL acid soln} / 0.1 L_{80g/100mL acid soln}))

 

= 12 - ((12)(30)/80) = 12 - 4.5 = 7.5 L_water