Please Help - Dr. Collins Quantitative Sample Test 8

[joffi8]

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Please help - I red the solution, but i have no idea.(it says some physics material)
I think this is a simple math question, but i just don't get it.
Thanks for help.


1. How many ml's of pure HCl must be added to a 10ml of 40% to make a 60% solution?

a) 5mL
b) 10mL
c) 15mL
d) 20mL

The answer is a) 5mL.

 

[jaymin8]

The answer is A.

To make a 40% solution you need:
4 mL pure acid and 6 mL water (which they gave you)

Now to change that 40% to 60% you need more acid...the question is how much

If you add 5 mL of pure acid you get:
9 mL pure acid and 6 mL water (the previous answer plus 5 mL pure acid)
That gives you 9 mL of pure acid. You divide that by total volume.
9/(9+6)=9/15=3/5=60%

 

[CPham]

I worked this as if it were a dilution type problem by mass. Note the word "added". This will help you at the end of the calculations.

10mL.......x
------ = ------
40%.......60%

Cross multiply and you get:

(10mL)(60%)=(40%)(x)
600=40x
15=x

Now remember there was the word "added", so you look back at the initial mL and subtract from the final to figure out how much you would need to add. So in that case:

15mL - 10mL = 5mL (answer A)

This worked, but I am unsure if it is just coincidence! If someone could verify, that would greatly help!