Question 1005270
WHAT A MATH TEACHER THINKS:
The volume of a mix of two liquids is the sum of the volumes mixed together.
{{{Amount=Volume*Concentration}}}
No need to specify concentration/amount units, because they are self-explanatory.
So the math teacher would add {{{highlight(2/3)=about 0.667}}} Liters of solution QXJ to 1 Liter solution XRD and mix, expecting to get {{{about1.667L}}} of solution with a 0.6 concentration.


WHAT A SCIENTIST THINKS:
Chemists know that it is important to specify your units.
When a chemist says a solution is 50% sulfuric acid,
they usually mean it contains 50 kg sulfuric acid per 100 kg solution.
If they want to be clearer, they say it is 50%(w/w).
Biologists tend to describe how the solutions were prepared.
When you mix together two substances, the mass of the mixture is the sum of the masses of the components.
The same is not true about volumes.
Scientists know that, and so do construction workers.
Any construction worker knows that mixing 1 cubic yard of rocks and 1 cubic yard of fine sand does not yield 2 cubic yards of mixture.
A chemist knows that mixing {{{1}}} Liter of a solution with {{{x}}} Liters of another solution yields a volume usually close to {{{1+x}}} Liters, but not exactly {{{1+x}}}, and sometimes quite far from exactly that.
A synthetic chemist and a biologist shrug and say it is probably close enough for their purposes.
An analytical chemist says that will make my analysis results very wrong.


IF A BIOLOGIST IS INVOLVED:
The way the concentrations of those solutions are described,
maybe those solutions are usually prepared by a biologist,
who mixes water and concentrated sulfuric acid to make solutions as follows:
Solution XRD "half sulfuric acid" = 1L water + 1L concentrated sulfuric acid;
Solution QXJ "3/4 sulfur acid" = 1L water + 3L concentrated sulfuric acid.
Maybe that biologist wanted to make more of
Solution UVW "3/5 sulfuric acid" = 2L water + 3L concentrated sulfuric acid.
The biologist most likely had a bottle of "concentrated sulfuric acid" that contained 98g of sulfuric acid per 100g of liquid.
The label may have stated "Assay....98.0%, meaning that its concentration was 98.0%(w/w).
Data in a handbook says that at {{{20^o}}}{{{C}}} the density of that solution is {{{1.8361}}}{{{"kg / L"}}} .
 
Solution XRD, with {{{1.0000L=1.0000kg}}} water and {{{1.0000L=1.8361kg}}} concentrated acid, had a total mass of about
{{{1.0000kg+1.8361kg=2.8361kg}}} , and
a total amount of pure acid of about {{{0.98*1.8361kg=1.7994kg}}} .
(I say "about" because a biologist does not measure {{{1L}}} volumes with anything near a precision of {{{0.0001L}}} ).
The calculated acid concentration is {{{0.98*1.8361kg/"2.8361 kg"=0.634="63.4 % { w / w )"}}} .
The handbook says that the density of that solution is {{{1.5354}}}{{{"kg / L"}}} at {{{20^oC}}}{{{C}}} ,
so the concentration is {{{("0.634 kg  acid"/"1 kg  solution")(1.5354kgsolution/"1 L solution")=0.9741}}}{{{kg acid/"L solution"}}} .
 
Solution QXJ, with {{{1.0000L=1.0000kg}}} water and {{{3.0000L=3*1.8361kg=5.5083kg}}} concentrated acid, had a total mass of about
{{{1.0000kg+5.5083kg=6.5083kg}}} , and
about {{{0.98*5.5083kg=5.3981kg}}} of pure acid.
The calculated acid concentration is {{{5.3981kgacid/"6.5083 kgsolution"=0.829=82.9%}}} .
The handbook says that the density of that solution is {{{1.5354}}}{{{"kg / L"}}} at {{{20^o}}}{{{C}}} ,
so the concentration is {{{("0.829 kg  acid"/"1 kg  solution")(1.7584kgsolution/"1 L solution")=1.4585}}}{{{kg acid/"L solution"}}} .
Solution, with {{{2.0000L=2.0000kg}}} water and
{{{3.0000L=3*1.8361kg=5.5083kg}}} concentrated acid, had a total mass of about
{{{2.0000kg+5.5083kg=7.5083kg}}} , and
about {{{0.98*5.5083kg=5.3981kg}}} of pure acid.
The calculated acid concentration is {{{5.3981kgacid/"7.5083 kgsolution"=0.719=71.9%}}} .
The handbook says that the density of that solution is {{{1.6326}}}{{{"kg / L"}}} at {{{20^o}}} ,
so the concentration is {{{(0.7190kgacid/"1 kg  solution")(1.6326kgsolution/"1 Lsolution")=1.1738}}}{{{kg acid/"L solution"}}} .
 
Mixing {{{i.0000L=1.5354kg}}} of solution XRD,
containing {{{0.9741kg}}} pure acid and
{{{2/3}}}{{{L=(2/3)(1.7584kg)=1.1723kg}}} of Solution QXJ,
containing {{{(2/3)(1.4585kg)=0.9723kg}}} pure acid, the biologist gets
a total of {{{0.9741kg+0.9723kg=1.9464kg}}} pure acid in
a total of {{{1.5354kg+1.1723kg=2.7077kg}}} of solution.
The concentration is {{{1.9464/2.7077=0.7188}}} in kg pure acid/kg solution,
which still rounds to {{{71.9%}}} , close enough for the biologist.
The final volume of solution obtained is
{{{2.7077kgsolution(1Lsolution/1.6326kgsolution)=1.659L}}} , also close enough for the biologist.
 
IF A CHEMIST WAS DESCRIBING THOSE SOLUTIONS:
When a chemist says a solution is 50% sulfuric acid,
they usually mean it contains 50 kg sulfuric acid per 100 kg solution.
If they want to be clearer, they say it is 50%(w/w).
That is a pretty dense solution;
At {{{20^oC}}} , {{{1}}} Liter has a mass of {{{1.3951}}} kg.
When someone says a solution is 60% sulfuric acid,
they usually mean it contains 60 kg sulfuric acid per 100 kg solution.
If they want to be clearer, they say it is 60%(w/w).
That is a denser solution.
At {{{20^oC}}} , {{{1}}} Liter has a mass of {{{1.4983}}} kg.
When someone says a solution is 75% sulfuric acid,
they usually mean it contains 75 kg sulfuric acid per 100 kg solution.
If they want to be clearer, they say it is 75%(w/w).
That is an even denser solution.
At {{{20^oC}}} , {{{1}}} Liter has a mass of {{{1.6692}}} kg.
If at {{{20^oC}}} you measure {{{1}}} Liter of 50% sulfuric acid solution,
with a total mass of {{{1.3951kg}}} , containing {{{0.5(1.3951kg)=0.0.6976kg}}} sulfuric acid, and
{{{2/3}}} Liter of 75% sulfuric solution with a mass of {{{(2/3)1.6692kg=1.1128kg}}} , containing {{{0.75(1.1128kg)=0.8346kg}}} sulfuric acid, you get
a total mass of {{{1.3951kg+1.1128kg=2.5079kg}}} of solution containing
{{{0.6976kg+0.8346kg=1.5322kg}}} of sulfuric acid.
The concentration of the resulting solution is
{{{1.5322kg/"2.5079 kg"=0.611(rounded)="61.1%(rounded)"}}} .
Looking in a handbook, we find that a solution with that final concentration will have a density of {{{1.5102}}}{{{"kg / L"}}} .
So, the {{{2.5079kg}}} of final solution will have a volume of
{{{(2.5079kg)*(1L/"1.5102 kg")=1.661L(rounded)}}} .