How to calculate the parts-per-million concentration from a percent concentration?

Question

I am asked to find the concentration of magnesium ions in ppm for a $0.025\ \%$ solution of $\ce{MgCl2}$. I can use this formula: $$\text{concentration in ppm} = \frac{\text{mass solute}_\mathrm{(g)}}{\text{mass solution}_\mathrm{(g)}}\times10^6$$

Assuming $100\ \mathrm g$ of solution, $2.5 \mathrm g$ solute/$\ce{MgCl2}$, and $97.5\ \mathrm g$ solvent, I get $\pu{95.205u}$ for $\ce{MgCl2}$, and then $0.026259\ \mathrm{mol}$ of $\ce{MgCl2}$, and thus $0.026259\ \mathrm{mol}$ of $\ce{Mg}$. That times $24.305\ \mathrm{g\ mol}^{-1}$ for $ \ce{Mg}$ gives me $0.63823\ \mathrm g$ of $\ce{Mg}$. $\frac{0.63823\ \mathrm g}{100\ \mathrm g}$ solution gives me $0.00638$, so that multiplied by $10^6$ would be $6382.28$. But the only options for the questions don't go over $500$. Like $64\ \mathrm{ppm}$ or $500\ \mathrm{ppm}$. Nothing even close to as high as I'm getting.

Answer 1

You're using $2.5\ \mathrm g$ of solute out of $100\ \mathrm g$ of solution, which is $2.5\ \%$, but the initial question is asking about a $0.025\ \%$ solution, which is why your answer is two orders of magnitude too large. You should be using $0.025\ \mathrm g$ of solute and $99.975\ \mathrm g$ of solvent.

As a general helpful hint for answering multiple choice questions, when you notice that one of the answers has the same coefficient but is off by a couple orders of magnitude (in this case the $64\ \mathrm{ppm}$ answer) go and double check all your initial concentrations and volumes, you probably forgot to account for a "$\%$" or a "$\mathrm k$" somewhere.