   SEARCH HOME Math Central Quandaries & Queries  Subject: Alligation Name: Shanah Who are you: Student Orders: 360 mL of 75% acetic acid Stock: 99% acetic acid and distilled water Find the volume of acetic acid and distilled water to get the needed concentration. Any help with this is greatly appreciated, Thanks Hi Shanah.

If you want 360mL of solution which is 75% acetic acid, then how many mL of it is pure acetic acid? Answer: 75% x 360mL. Let's call this quantity A.

So that's how much acetic acid you need. Your stock is 99% acetic acid, so to get A mL of acetic acid, you need 99% x S = A where S is the volume of the stock acid. We can rewrite this as S = A / 99%.

Substituting in the expression for A into this, we get:

S = (75% x 360 mL) / 99%

which gives the number of mL of stock acid to pour. Then just top it up to the 360mL level with distilled water: W = 360mL - S.

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.