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How many liters of a 20 percent alcohol solution must be mixed with 60 liters of 50 percent solution to get a 30 percent solution?
Wiki User
∙ 12y ago
0.2x+60*0.5=0.3y
also x + 60 = y
so 0.2x + 30 = 0.3(x+60)=0.3x+18
=>0.1x = 12
=>x = 120 liters
Added note
to deal with the so called 'dilution contraction' of total volume
If it were % by MASS ( %m/m), it's quite easy to do (based on the 'Mass Conservation Law). You calculate with mass (kg) and mass-% (%m/m) i.s.o. volume (L) and vol% (%v/v).
However if the meaning was: % by Volume ( %v/v) then calculation appears to become quite complicated, but not impossible if you know at least the density values of all solutions (original 20%v/v or 50%v/v and final 30%v/v).
DO NOT use: (orig. volume) + (added volume) = final volume, as done above, if exact figures are necessary.
It's only a rule of thump, an approximation. This is because fluids can contract on mixing at dilution. There is no rule such as: conservation of volume.
Your case: 120 L + 60 L (is not equal but) < 180 L final solution.
Wiki User
∙ 12y ago
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