# How is sulfuric acid with a concentration of 12 M also 72% w/w?

According to LabChem, $$12~\mathrm{M}$$ of $$\ce{H2SO4}$$ is $$72~\mathrm{w/w\%}$$.

When I try to convert $$12~\mathrm{M}$$ of $$\ce{H2SO4}$$ to $$\mathrm{w/w\%}$$ I get $$117\%$$ which is obviously wrong.

$$\begin{multline} 12~\mathrm{M}\cdot\left(\frac{1~\mathrm{L}}{1000~\mathrm{ml}}\right) \left(1~\mathrm{\frac{ml}{g}}\ \ce{H2O}\right) \left(98.09~\mathrm{\frac{g}{mol}}\ \ce{H2SO4}\right)\\ = \frac{1177~\mathrm{g}}{1000~\mathrm{g}} = 1.177=1.177\cdot100\%=117.7\% \end{multline}$$

I must be doing something wrong. How do you convert it correctly?

As you just found out though, sometimes you really need to account for the change in density that occurs as you add solute. This webpage claims that the density of $12~\mathrm{M}$ sulfuric acid is about $1.634~\mathrm{g/mL}$.
Using this updated calculation, we still have the original $1177~\mathrm{g}$ of sulfuric acid. However, the solution mass is now $1000~\mathrm{mL}\cdot 1.634~\mathrm{g/mL} = 1634~\mathrm{g}$. Finally, we obtain that
$$\frac{ 1177~\mathrm{g} \, \ce{H2SO4}}{1634~\mathrm{g} \, \mathrm{solution}} = 72.03\% \; \mathrm{w/w}$$