The maximum acceptable concentration of lead in drinking water is 0.0100 ppm. If a water sample has a concentration of 55.0 nM, does it exceed the maximum acceptable concentration?
Understand the Problem
The question asks whether a water sample with a lead concentration of 55.0 nM exceeds the maximum acceptable concentration of lead in drinking water, which is given as 0.0100 ppm. To answer this, one must convert both concentrations to the same units and then compare them.
First convert ppm to molarity, and then convert nM to molarity and compare.
Answer
Yes, the water sample exceeds the maximum acceptable concentration of lead because $5.50 \times 10^{-8} \, \text{M} > 4.83 \times 10^{-8} \, \text{M}$.
Answer for screen readers
Yes, the water sample exceeds the maximum acceptable concentration of lead.
Steps to Solve
- Convert ppm to mg/L
Parts per million (ppm) is equivalent to milligrams per liter (mg/L) for dilute aqueous solutions. Thus, 0.0100 ppm is equal to 0.0100 mg/L.
- Convert mg/L to g/L
To convert from mg/L to g/L, divide by 1000: $0.0100 , \text{mg/L} = \frac{0.0100}{1000} , \text{g/L} = 0.0000100 , \text{g/L}$
- Convert g/L to mol/L (Molarity)
To convert from g/L to mol/L, divide by the molar mass of lead (Pb), which is 207.2 g/mol: $\frac{0.0000100 , \text{g/L}}{207.2 , \text{g/mol}} = 4.83 \times 10^{-8} , \text{mol/L} = 4.83 \times 10^{-8} , \text{M}$
- Convert nM to M
To convert from nanomolar (nM) to molar (M), divide by $10^9$: $55.0 , \text{nM} = \frac{55.0}{10^9} , \text{M} = 5.50 \times 10^{-8} , \text{M}$
- Compare the two molarity values
Compare the molarity of the water sample ($5.50 \times 10^{-8} , \text{M}$) with the maximum acceptable concentration ($4.83 \times 10^{-8} , \text{M}$).
$5.50 \times 10^{-8} , \text{M} > 4.83 \times 10^{-8} , \text{M}$
Since the concentration of the water sample is greater than the maximum acceptable concentration, it exceeds the limit.
Yes, the water sample exceeds the maximum acceptable concentration of lead.
More Information
The conversion from ppm to molarity involves several steps, including understanding the relationship between ppm and mg/L, and using the molar mass to convert between mass and moles. Nanomolar is a very small concentration unit, and converting to molar allows for easy comparison.
Tips
Common mistakes include:
- Incorrectly converting ppm to mg/L (or assuming they are different).
- Using the wrong molar mass for lead.
- Making errors in the powers of 10 during conversions between units like nM and M.
- Forgetting to convert to the same units before comparing the two concentrations.
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