# Question #0b2e8

Mar 12, 2015

The first thing you must do is determine exactly how much acetic acid you get from 25.0 g of vinegar.

Now, you could eyeball it and say that, because vinegar is 5% acetic acid, 25 grams of vinegar would have 4 times less acetic acid than 100 g of vinegar, which means you get roughly 1.25 g of acetic acid to work with (because 100 g of vinegar would have 5 g of acetic acid).

However, vinegar is 5% acetic acid by volume, which means you get 5 g of acetic acid per 100 mL of vinegar. Since vinegar has a density of 1.01 g/mL, that mass of vinegar would have a volume of

$\text{25.0 g vinegar" * "1 mL"/"1.01 g" = "24.75 mL vinegar}$

Using the 5% percent concentration by volume you know you have, that much volume of vinegar would contain

$\text{24.75 mL vinegar" * "5 g acetic acid"/"100 mL vinegar" = "1.2375 g acetic acid}$

To determine how many molecules of acetic acid are present in that many grams, you need to figure out how many moles you have; this is done by using acetic acid's molar mass of 60.05 g/mol

$\text{1.2375 g" * "1 mole"/"60.05 g" = "0.0206 moles acetic acid}$

Because 1 mole of any substance contains exactly $6.022 \cdot {10}^{23}$ molecules of that substance - this is know as Avogadro's number- the number of molecules of acetic acid will be

$\text{0.0206 moles" * (6.022 * 10^(23)"molecules")/"1 mole" = 1.24 * 10^(22)"molecules}$

SIDE NOTE If you were supposed to use vinegar's 5% acetic acid concentration as being by mass, use the 1.25 g mass as a starting point to figure out the number of moles first, and then the number of molecules.