Math CentralQuandaries & 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,

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.

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