The units of parts per million (ppm) and parts per billion...

The units of parts per million (ppm) and parts per billion (ppb) are commonly used by environmental chemists. In general, 1 ppm means 1 part of solute for every $10^{6}$ parts of solution. (Both solute and solution are measured using the same units.) Mathematically, by mass: $$ \mathrm{ppm}=\frac{\mu \mathrm{g} \text { solute }}{\mathrm{g} \text { solution }}=\frac{\mathrm{mg} \text { solute }}{\mathrm{kg} \text { solution }} $$ In the case of very dilute aqueous solutions, a concentration of 1.0 ppm is equal to $1.0 \mu \mathrm{g}$ of solute per $1.0 \mathrm{mL}$ of solution, which equals $1.0 \mathrm{g}$ of solution. Parts per billion is defined in a similar fashion. Calculate the molarity of each of the following aqueous solutions. a. $5.0 \mathrm{ppb} \mathrm{Hg}$ in $\mathrm{H}_{2} \mathrm{O}$ b. $1.0 \mathrm{ppb} \mathrm{CHCl}_{3}$ in $\mathrm{H}_{2} \mathrm{O}$ c. 10.0 ppm As in $\mathrm{H}_{2} \mathrm{O}$ d. 0.10 ppm DDT $\left(\mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}\right)$ in $\mathrm{H}_{2} \mathrm{O}$

The units of parts per million (ppm) and parts per billion (ppb) are commonly used by environmental chemists. In general, 1 ppm means 1 part of solute for every $10^{6}$ parts of solution. (Both solute and solution are measured using the same units.) Mathematically, by mass:
$$
\mathrm{ppm}=\frac{\mu \mathrm{g} \text { solute }}{\mathrm{g} \text { solution }}=\frac{\mathrm{mg} \text { solute }}{\mathrm{kg} \text { solution }}
$$
In the case of very dilute aqueous solutions, a concentration of 1.0 ppm is equal to $1.0 \mu \mathrm{g}$ of solute per $1.0 \mathrm{mL}$ of solution, which equals $1.0 \mathrm{g}$ of solution. Parts per billion is defined in a similar fashion. Calculate the molarity of each of the following aqueous solutions.
a. $5.0 \mathrm{ppb} \mathrm{Hg}$ in $\mathrm{H}_{2} \mathrm{O}$
b. $1.0 \mathrm{ppb} \mathrm{CHCl}_{3}$ in $\mathrm{H}_{2} \mathrm{O}$
c. 10.0 ppm As in $\mathrm{H}_{2} \mathrm{O}$
d. 0.10 ppm DDT $\left(\mathrm{C}_{14} \mathrm{H}_{9} \mathrm{Cl}_{5}\right)$ in $\mathrm{H}_{2} \mathrm{O}$

Key Concepts

Dilute Aqueous Solutions Approximation

In very dilute aqueous solutions, it is assumed that the density of the solution is very close to that of water (about 1 g/mL). This approximation simplifies calculations by allowing the equivalence of 1 mL of solution to 1 gram of solution, which directly relates mass-based concentration units like ppm to volume-based units like molarity.

Mass to Mole Conversion

This concept involves converting the mass of a solute into the number of moles using the solute’s molecular weight (molar mass). The formula for this conversion is moles = mass (in grams) divided by molecular weight, and it is a key step when transforming a concentration given in mass units (like ppm or ppb) into molarity.

Parts per Million (ppm)

This concept describes a unit of concentration where one part of a solute is present per one million parts of the solution. In environmental chemistry, ppm is typically used to indicate trace levels of a substance. When measuring by mass in aqueous solutions, 1 ppm is equivalent to 1 microgram of solute per gram of solution, assuming that the density of water is approximately 1 g/mL.

Parts per Billion (ppb)

Parts per billion is another unit of concentration used to quantify even smaller amounts of a substance. It is defined analogously to ppm, with 1 ppb meaning 1 part of solute per one billion parts of solution. When considering aqueous solutions, it is expressed as 1 microgram of solute per kilogram of solution.

Molarity

Molarity is a measure of concentration that is defined as the number of moles of solute per liter of solution. It is a central concept in solution chemistry because it provides a direct measure of the number of reacting particles, making it useful in stoichiometric calculations and reaction kinetics.

Transcript

00:01 In this problem, we are going to be looking at doing calculations regarding parts per million and parts per billion.

00:06 And we use parts per million and parts per billion, especially in environmental chemistry to express concentrations that are extremely low.

00:15 So parts per million is just what it sounds like.

00:17 It is one part of solute.

00:22 In most cases, it's going to be matching units and we're going to make it grams.

00:26 Per 1 million, which is 1 times 10 to the 6th.

00:29 Parts solution.

00:35 And a part per billion is one part of solute per one times 10 to the ninth parts solution.

00:50 That's one billion.

00:52 And these aren't great to work with.

00:54 So we were given in the problem that one nanogram of solute, excuse me, one microgram, microgram of solute per one gram of solution is equivalent to a part per million and since this is such a low concentration one gram is equal to one milliliter so a microgram of solute per milligram of solution is the you what part per million is designed to be now let's switch colors here and go to a lighter blue one part per billion would be a nanogram of solute per milligram, milliliter of solution.

01:53 So these are the two factors that we're going to use to solve our four problems.

02:00 Let's begin.

02:03 Okay, our first problem, we are given 5 .0 parts per billion of mercury in water, and we're asked to convert this to molarity.

02:18 Remember, parts per billion is 5 .0 nanograms of mercury per mil -liter of solution.

02:31 And we need to convert this to molarity, which is moles per liter.

02:37 So we need to convert milliliters to liter.

02:40 Let's do that first.

02:42 There are 1 ,000 milliliters in 1 liter.

02:47 And then let's convert nanograms to grams.

02:52 There's 1 times 10 to the 9th nanograms and one gram.

02:57 And then let's use molar mass of mercury, which is 200 .59 grams per mole.

03:09 And we're done with this math, we will have 10 .5 times 10 to the minus eighth molar.

03:15 And that's the concentration of the mercury.

03:21 That's our first one.

03:22 Our second problem is also in parts per billion.

03:26 And we are given 1 .0 parts per billion of tricloral methane, ch, c .l3, also in water.

03:41 So we're going to set up this problem the same way...

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