# Chapter 17: Calculating the Molarity of Bottled Liquids

You need three pieces of information to perform this calculation:

The molecular mass of the acid. This is usually written on the bottle and can be easily calculated if it is not. For concentrated acids: sulfuric acid is 98 g/mol, hydrochloric acid is 36.5 g/mol, ethanoic acid is 60 g/mol, and nitric acid is 63 g/mol

The percent purity of the compound. This might be expressed as a percent (e.g. 31% HCl), with the symbol

`\(m/m\)`

(e.g.`\(m/m\)`

= 68%) or with the word purity (”98% pure”). If you cannot find this information, see the note at the end.The density (ρ) or specific gravity (s.g.) of the acid. This should be in grams per cubic centimeter (cc or

`\(cm^3\)`

).

Then, you can calculate the molarity of your concentrated acid with this formula:

`$$\mathrm{molarity} = M = \frac{(\mathrm{\text{percent purity}})(\mathrm{density})(1000 \frac{cm^3}{L})}{\mathrm{\text{molecular mass}}}$$`

For example, the molarity of an acid bottle labeled “H2SO4, 98%, s.g. 1.84” we would calculate:

`$$ \mathrm{molarity} = M = \frac{(0.98)(1.84 \frac{g}{cm^3})(1000 \frac{cm^3}{L})}{98 \frac{g}{mol} } $$`

Note that we used 0.98 for 98%. Convert all percents to decimals.

Once you do this work, take out a permanent pen and label your stock bottle with its molarity. Then no one needs to do this calculation again.

Note: since you will correct the concentration of your solutions with relative standardization, you really just need to know the approximate molarity of your liquid stock reagent. For new bottles of concentrated acid, you may assume that sulfuric acid is about 18 M, hydrochloric acid is about 12 M, and that both nitric acid and ethanoic (acetic) acid are about 16 M. Battery acid should be 4.5 M H2SO4.