SOLUTION: How much of 60% HCl and 25% HCl would be needed to mix and produce 75 liters of 50% HCl?

Question 1061791: How much of 60% HCl and 25% HCl would be needed to mix and produce 75 liters of 50% HCl?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
For the purposes of answering this question we must assume that:
1) A bottle of some liquid labeled "HCl" was used to make the following solutions
"60% HCl" = a mixture of that liquid and water containing 60 liters of that liquid in 100 liters of solution, and
"25% HCl" = a mixture of that liquid and water containing 25 liters of that liquid in 100 liters of solution.
2) When we mix "60% HCl" and "25% HCl" the final volume is the sum of the volumes mixed.
3) what we need to obtain is 75 liters of a solution that will be labeled "50% HCl, and contains water and 50 liters of the liquid labeled "HCl" per 100 liters of solution.

With that, we define
= volume (in liters) of "60% HCl" to be used, and
= volume (in liters) of "25% HCl" to be used.
We reason that
= the volume (in liters) of "HCl" in liters of "60% HCl",
= the volume (in liters) of "HCl" in liters of "25% HCl", and
= the volume (in liters) of "HCl" in liters of "50% HCl"
For the total volume accounting, our equation is
.
To account for the amount of "HCl" in initial and final solutions, our equation is
<--> .
Then we solve the system of linear equations form by those two equations:
-->-->-->-->-->-->-->-->--> .
Obviously, those number are exact solutions, but not what we would measure in liters. We would round.
Since and , we might mix
liters of "60% HCl" and liters of "25% HCl",
or maybe we would mix
liters of "60% HCl" and liters of "25% HCl".

NOTES:
1) Hydrogen chloride (HCl) is a gas that synthetic chemists use out of a gas cylinder for certain chemical reactions.
For those purposes, water would not be a good solvent.
You can dissolve that gas in other solvents too,
and a chemist may need to make or buy a solution of HCl in methanol, for example.
What most chemists know as hydrochloric acid is a solution of HCl gas in water, containing about 36 grams of HCl gas per 100 grams of solution,
with a density of about 1.18 grams/milliliter at room temperature.
You cannot have it much more concentrated than that.
2) when you mix liquids, the final volume is not exactly the sum of the volumes,
it will differ by an amount that may be important if you needs precise results (as my chemical engineering professor once pointed out).

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