Let amount of QXJ solution to add, be q

It's best to change the fractions to decimals. 

In so doing,  becomes: .5;  becomes: .75,  becomes .6, and we get: 

.5(1) + .75(q) = .6(1 + q)

.5 + .75q = .6 + .6q

.75q - .6q = .6 - .5 

.15q = - .1

q, or amount of QXJ solution to add = .1/.15, or  L 

Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
 WHAT A MATH TEACHER THINKS:

The volume of a mix of two liquids is the sum of the volumes mixed together.



No need to specify concentration/amount units, because they are self-explanatory.

So the math teacher would add  Liters of solution QXJ to 1 Liter solution XRD and mix, expecting to get  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  Liter of a solution with  Liters of another solution yields a volume usually close to  Liters, but not exactly , 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  the density of that solution is  .

 

Solution XRD, with  water and  concentrated acid, had a total mass of about

 , and

a total amount of pure acid of about  .

(I say "about" because a biologist does not measure  volumes with anything near a precision of  ).

The calculated acid concentration is  .

The handbook says that the density of that solution is  at  ,

so the concentration is  .

 

Solution QXJ, with  water and  concentrated acid, had a total mass of about

 , and

about  of pure acid.

The calculated acid concentration is  .

The handbook says that the density of that solution is  at  ,

so the concentration is  .

Solution, with  water and

 concentrated acid, had a total mass of about

 , and

about  of pure acid.

The calculated acid concentration is  .

The handbook says that the density of that solution is  at  ,

so the concentration is  .

 

Mixing  of solution XRD,

containing  pure acid and

 of Solution QXJ,

containing  pure acid, the biologist gets

a total of  pure acid in

a total of  of solution.

The concentration is  in kg pure acid/kg solution,

which still rounds to  , close enough for the biologist.

The final volume of solution obtained is

 , 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  ,  Liter has a mass of  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  ,  Liter has a mass of  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  ,  Liter has a mass of  kg.

If at  you measure  Liter of 50% sulfuric acid solution,

with a total mass of  , containing  sulfuric acid, and

 Liter of 75% sulfuric solution with a mass of  , containing  sulfuric acid, you get

a total mass of  of solution containing

 of sulfuric acid.

The concentration of the resulting solution is

 .

Looking in a handbook, we find that a solution with that final concentration will have a density of  .

So, the  of final solution will have a volume of

 . 

RELATED QUESTIONS

How many liters of pure acid should be added to 4 liters of a 10% acid solution to make a  (answered by richwmiller)

How many liters of acid should be mixed with 4 L of a 10% acid solution to produce a... (answered by richwmiller)

How many liters of water should be added to 20 L of a 30% acid solution to make a... (answered by Alan3354)

A chemist has one solution that 34% acid and a second solution that is 58 % acid. How... (answered by stanbon)

Suppose that x liters of pure acid (100% acid) are added to 280 liters of a 25% acid... (answered by jorel1380)

  One solution is 10% acid and another is 25% acid. How many liters of each should be... (answered by scott8148)

A chemist has one solution that is 25 percent acid and a second that is 50 percent acid.... (answered by josmiceli,rwm)

a chemist has one solution that is 25% acid and a second that is 50% acid. how many... (answered by Earlsdon)

A chemist needs to combine two solutions of a certain acid.  How many liters of a 30%... (answered by ptaylor)