Question 934237
I have no idea what math teachers' answers would be, but I would bet that they would be wrong. For starters, what do they mean by 32% HCl, and what do they mean by 5% HCl?
When I buy hydrochloric acid solution for the lab, it comes in a bottle whose label states something like "assay ... 35.9%" and that means that there are 35.9 grams of HCl in 100 grams of solution.
When someone tells me to make a 5% solution of HCL,
they precisely specify whether they want a 5% (w/w) solution (5% by weight),
containing a 5 gram mass of HCl in a 100 gram mass of solution,
or they want a 5% (w/v) solution,
which would contain 5 grams of HCl in 100 milliliters of solution.
If it is not specified, the percent is percent by weight.
A math teacher may think 32% HCl is 32 grams HCl in 100 mililliters of solution. Hopefully, no one would think it means 32 liters HCl in 100 liters of solution, because HCl is a gas, and the volume of any amount of gas changes with temperature and pressure.
No one would
1) measure 32 liters of HCL gas measured at a certain temperature and pressure,
2) dissolve it in water and dilute it to 100 liters, and
3) then call that 32% HCl.


THE CHEMICAL ENGINEER ANSWER:
It could be that you have a concentrated hydrochloric acid solution containing 32% HCl by weight.  We would call that solution concentrated hydrochloric acid, while hydrogen chloride is what we call HCl gas, when we buy it in a small gas cylinder for chemical synthesis purposes.
Such a solution would have 32 grams of HCl gas and 68 grams of water in a 100 gram amount of solution.
At {{{20^o}}}{{{C}}} a 32% HCl by weight solution will have a density of 1.593 grams per milliliter,
so 100 grams of solution would have a volu,me of
{{{100g(1mL/"1.593 g")=62.8mL}}} .
A 5% solution by weight would contain 5 gram HCl in a total of 100 grams of solution (5 grams HCl and 95 grams of water), and at {{{20^o}}}{{{C}}} would have a density of 1.02563 grams per milliliter. As a consequence the 100 grams of solution would have a volume of 97.5 milliliters.
{{{(100g)(1mL/"1.02563 g")=97.5mL}}}
A gallon is 3.785 liters, or 3785 milliliters, so a volume of 350 gallons is
{{{(350gallons)(3.785L/"1 gallon")=1324.75L}}} or {{{(350gallons)(3785mL/"1 gallon")=1324750mL}}} .
A volume of 350 gallons of a 5% by weight HCl solution would weigh
{{{(350gallons)(3785mL/"1 gallon")(1.02563g/"1 mL")=1358700g=1358.7kg}}}
and to make that much solution you would need
{{{(350gallons)(3785mL/"1 gallon")(1.02563g/"1 mL")(5g/100g)=67938g=67.9375kg}}} of HCl,
which will be contained in
{{{(350gallons)(3785mL/"1 gallon")(1.02563g/"1 mL")(5g/100g)(100g/32g)=212297g=212.3kg}}} of your concentrated solution.
You will not weigh it (too dangerous, horrible corrosive fumes), so you will need to measure it by volume.
The volume you need to measure is
{{{(350gallons)(3785mL/"1 gallon")(1.02563g/"1 mL")(5g/100g)(100g/32g)(1mL/1.593g)=133269mL=133.269L}}}
That amount (212.3kg, 133.269L) of concentrated acid will have the 67.9kg HCl you need plus a good amount of water.
The amount of water in that much concentrated acid is
{{{212.3kg-67.9kg=144.4kg}}}.
You will need to mix that concentrated acid with some extra water to obtain the 1358.7kg total weight of solution.
How much water will you mix with 212.3kg concentrated acid?
{{{1358.7kg-212.3kg=1146.4kg}}} .
At {{{20^o}}}{{{C}}} , pure water has a density of 0.9982343g/mL=0.9982343kg/L, so that mass of water will have a volume of
{{{1146.4kg(1L/"0.9982343 kg")=1148.4L}}}
So you would measure 1148.4 liters of water,
slowly add 133.3 liters of concentrated acid, while stirring,
and after the mixture cools back to {{{20^o}}}{{{C}}} ,
you will have the 1324.75L (350 gallons) of 5% by weight acid that you wanted
The volumes you added add up to {{{1148.4L+133.3L=1281.7L}}} , but volume is not additive when you are mixing chemicals.