The U.S. Environmental Protection Agency set a maximum contaminant level (MCL) for tetrachloroethylene (TCE, C2Cl4) in drinking water of 0.005 ppm (by mass). If the water in your home contains 7 percent of the allowable MCL, what is the molarity of TCE in your home?
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In general, a part per million is equal to one microgram per gram. Because a milliliter of water has a mass of near a gram, a part per million for aqueous solutions is equal to one microgram of solute per milliliter of solvent.
If your home contains 7% of the MCL, your home contains:
0.005 ppm * 0.07 = 0.00035 ppm TCE
This corresponds to 0.00035 ug / mL. You can convert the mass of TCE (0.00035 ug) to moles by dividing by the molar mass of TCE:
0.00035 * 10^-6 g / (165.84 g/mol) = 2.1 * 10^-12 mol
This gives us 2.1 * 10^-12 mol / 1 mL. Now, we just need to convert from mol/mL to mol/L to find molarity. To do this, multiply by 1000 mL, because there are 1000 mL in 1 L. This gives a final concentration of 2.1 * 10^-9 M, or 2.1 nM.
If your home contains 7% of the MCL, your home contains:
0.005 ppm * 0.07 = 0.00035 ppm TCE
This corresponds to 0.00035 ug / mL. You can convert the mass of TCE (0.00035 ug) to moles by dividing by the molar mass of TCE:
0.00035 * 10^-6 g / (165.84 g/mol) = 2.1 * 10^-12 mol
This gives us 2.1 * 10^-12 mol / 1 mL. Now, we just need to convert from mol/mL to mol/L to find molarity. To do this, multiply by 1000 mL, because there are 1000 mL in 1 L. This gives a final concentration of 2.1 * 10^-9 M, or 2.1 nM.