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

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.

• 100 ppm = 1/100 th % Feb 8 '20 at 20:34

## 1 Answer

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.