# How to calculate the maximum number of molecules or ions from a given amount of substance?

Which of the following solutions has the greatest number of particles (atoms or ions) of solute per liter?

(a) $1~\mathrm{M}\ \ce{NaCl}$
(b) $1~\mathrm{M}\ \ce{CaCl2}$
(c) $1~\mathrm{M}$ ethanol
(d) $1~\mathrm{M}$ acetic acid

The correct answer is (b), but I dont know why. I would have thought it was ethanol ($\ce{C2H6O}$) because it has the greatest number of moles of atoms, and shouldn't that mean it has the greatest number of atoms? I noticed answer (b) has the highest molar mass ($110.984~\mathrm{g/mol}$), but does that mean it also has the highest number of atoms?

• The question is poorly worded. Apparently, they wanted the number of "ions or molecules", so that ethanol molecule counts as 1, but $\ce{NaCl}$ dissociates into ions and hence counts as 2, and so on. – Ivan Neretin Jan 25 '16 at 18:30

The way this question is asked, (c) would indeed be correct. As you correctly noted, ethanol has nine atoms per molecule, and a $1~\mathrm{M}$ solution would thus contain $9~\mathrm{mol}$ of atoms per litre. For comparison: acetic acid has eight, calcium chloride three and sodium chloride two.
However, they probably meant molecules in the question and not atoms — because it really makes no chemical sense to separate ethanol molecules into their atoms (they won’t separate in a solution anyway). So with that reasoning, counting ‘particles’ (whatever they may be) we arrive at $1~\mathrm{mol}$ of ethanol molecules for (c), $2~\mathrm{mol}$ of ions for (a), $3~\mathrm{mol}$ of ions for (b) and under two moles of ions/molecules (combining both of them) for (d) (all per litre of solution).