How much acud should be added to 400 ml of 15% acid solution to increase its strength to 32%?

Question

it is a maths question.

Answer 1

The amount of acid in 15% acid of 400 ml is 60 ml.

 

Let x ml of acid be add to this solution.

The total volume is (400 + x), of which 32% is acid

The amount of acid in this solution is x + 60

 

.32(400 + x) = x + 60

128 + .32x = x + 60

0.68x = 68

x = 100 ml of acid.

 

Answer 2

Question: How much acid should be added to 400 ml of 15% acid solution to increase its strength to 32%?

 

I call X the content of non acid liquid in 400 ml. Because the initial concentration of acid in 400 ml is 15%, it is concluded that the initial concentration of non acid liquid is 85%.Then X = 0.85*400 ml = 340 ml.

 

Now, we add more acid until increase the concentration of acid to 32%. It means that the new concentration of non acid liquid is 68%. 

 

The original total content (non acid fluid + acid) is 400 ml. Now we add a new Y content of acid. Then, the total content is 400 ml + Y.

 

Because the content of non acid fluid X has not changed after adding Y content of acid, we have the following relation:

 

  0.68*(400 ml+Y) = 340 ml

 

  272 ml +0.68*Y = 340 ml

 

               0.68*Y = 340 ml - 272 ml

           

                       Y = 68 ml / 0.68  = 100 ml    

 

                       Y = 100 ml

 

You have to add 100 ml of acid to get a strength of 32% acid solution

Answer 3

What do we know:

400 ml is the total amount of solution right now

15% Acid means 60ml of the solution

400*.15 = 60 ml acid

400*.85 = 340 ml of non acidic fluid

 

then we can solve this by a ratio:

340/x = 0.68/0.32 

 

solve for x = 160 ml of total acid

 

to find out how much needs to be added to the solution subtract the previous amount of acid 60ml

therefore 160ml - 60ml = 100 ml is the amount needed acid to be added. 

 

if you need a single equation to be formulated we can work on this.

hope this helps :-)