Parts per Million (ppm) - Online Tutor, Practice Problems & Exam Prep

When measuring extremely dilute solution concentrations, the terms parts per million (ppm) and parts per billion (ppb) are used. These units can represent mass or volume. Ppm indicates the number of parts, in grams or milliliters, per one million parts, with one ppm being equivalent to one milligram per liter. The formula for ppm in terms of mass is:

grams of solutegrams of solution×10⁶ For volume, it's milliliters of solute per milliliters of solution multiplied by 10⁶. Similarly, ppb denotes the number of parts per one billion, with one ppb equal to one microgram per liter. The calculation for ppb in mass is:

grams of solutegrams of solution×10⁹ and for volume, it's milliliters of solute per milliliters of solution times 10⁹. These measurements are crucial for expressing concentrations in aqueous solutions when dealing with very low solute quantities.

Parts per Million (ppm) Concept 1

Here we're going to see that extremely dilute solution concentrations are expressed in parts per million, abbreviated as PPM, or parts per billion. I'll bring it as PPB. Now we're going to say here units can either be in mass or volume when it comes to PPM or PPB.

Now let's take a look at parts per million. We're going to say this represents the number of parts either in grams or milliliters per 1,000,000 parts. And remember 1,000,000 is 106 in aqueous solution. A helpful thing to help you with parts per million is that one parts per million is equivalent to 1 milligram per one liter.

So here if we take a look at parts per million, we can look at it, look at it in either our form of mass or in a form of volume. If we're looking at parts per million in terms of mass, we're going to say it equals grams of solute divided by grams of solution times 106. And if we're looking at parts per million in terms of volume, then it becomes milliliters of solute divided by milliliters of solution times 106.

So this setup should be kind of reminiscent of mass percent where it be grams over grams times 100%. Now instead of doing 100%, we're now dealing with 106 because we're dealing with million parts, 1,000,000 parts, all right. So just keep in mind we deal with PPM and later on PPB when discussing very extremely diluted concentrations.

Parts per Million (ppm) Example 1

What is the concentration in parts per million of DDT on non biodegradable pesticide in 2 milligrams in one kilogram needle fish tissue. All right, so we want parts per million. So that's going to equal the grams of our solute divided by grams of solution times 10 to the six.

We have an issue though. These units are not in grams. Ones in milligrams, ones in kilograms. Convert them both to grams first, so we have 2 milligrams and remember 1 milligram. One milli is 10 to the -3, so that's 2.0 * 10 to the 10-3G. And then remember, 1 kilogram is equivalent to 1000 grams.

So we take that and we plug it in. So we have 2.0 * 10 to the 10-3G divided by 1000g * 10 to the six. When we do that, we get back 2.0 PPM, so that will be our part per million of DDT for this particular example question.

Parts per Million (ppm) Concept 2

PPB, otherwise known as parts per billion, represents the number of parts either in grams or milliliters per 1 billion parts. And remember, 1 billion is 109. Now when in aqueous solutions, just remember that we can make the connection that one PPB equals one microgram per one liter.

Now when dealing with parts per billion in terms of mass, we're going to say it's equal to grams of solute divided by grams of solution times 109. And when looking at parts per billion in terms of volume, it then becomes milliliters of solution divided by milliliters or milliliters of solute divided by milliliters of solution times 109.

So just keep in mind when dealing with parts per billion in aqueous solution, there's this connection and also the difference between parts per billion when dealing with mass and when dealing with volume.

Parts per Million (ppm) Example 2

A 2.4 liter sample of an aqueous solution contains 0.012 milliliters of ammonia. What is the concentration of ammonia in the solution expressed as parts per billion? All right, since we're dealing with volume here, that must mean we're dealing with parts per billion in terms of volume.

So we'd say here parts per billion would equal the milliliters of our solute divided by milliliters of our solution, which in this case is our sample times 10⁹. Here we plug in 0.012 milliliters of our ammonia, which is our solute divided by. Now we need to convert liters into milliliters and remember that for every milli, it's 10^-3 liters.

So here that comes out to 2400 milliliters, which is what we're going to place over here and then times 10⁹. When we do that, that's going to give me as an answer 5000 parts per billion. And out of the choices shown, option B will be the correct answer. So B, 5000 parts per billion would be the correct concentration of NH₃ expressed in parts per billion.

A 5.12 L sample of solution contains 0.230 g of potassium sulfate, K₂SO₄. Determine the concentration of K₂SO₄ in ppm if the density of the solution is 1.30 g/mL.

• A. 34.6 ppm
• B. 28.9 ppm
• C. 22.3 ppm
• D. 43.6 ppm

Calculate the concentration in parts per billion of the following aqueous solution:0.91 mg of caffeine in a total volume of 131 mL.

• A. 0.14 ppb
• B. 0.0069 ppb
• C. 140 ppb
• D. 6900 ppb

Glucose makes up about 0.102% by mass of human blood. Calculate this concentration in ppm.

• A. 102 ppm
• B. 0.102 ppm
• C. 0.00102 ppm
• D. 1020 ppm

The average human body contains about 5,000 grams of blood. What mass of arsenic is present in the body if the amount in blood is 0.86 ppb?

• A. 5.8 × 10¹² g
• B. 4.3 × 10¹² g
• C. 4.3 × 10^–6 g
• D. 5.8 × 10^–6 g

A water sample contains the pollutant chlorobenzene with a concentration of 16 ppm (by volume). What volume of this water contains 5.01×10² mL of chlorobenzene?

• A. 3.1 × 10⁷ mL
• B. 3.2 × 10⁴ mL
• C. 1.6 × 10⁶ mL
• D. 8.0 × 10¹⁰ mL

Here’s what students ask on this topic:

What is parts per million?

Parts per million, often abbreviated as ppm, is a unit of measurement used to express very dilute concentrations of substances. It is equivalent to 1 milligram of a substance in 1 liter of water (mg/L) or 1 milligram of a substance in 1 kilogram of a solid material. Essentially, if you imagine dividing a substance into one million equal parts, one part per million would be one of those parts. It's a way to quantify small concentrations in scientific and technical fields, such as chemistry, physics, and environmental science. For example, when measuring the amount of a pollutant in water or the concentration of a mineral in soil, ppm is a convenient and precise unit to use. It allows for easy comparison and understanding of how much of a substance is present in a larger mixture or solution.

How do you calculate parts per million?

To calculate parts per million (ppm), you're essentially determining how many parts of a specific substance are in a million parts of the total mixture or solution. Here's a simple way to do it:

1. Take the mass of the substance you're interested in (the solute) and divide it by the total mass of the solution or mixture.
2. Multiply the result by 1,000,000.

The formula looks like this:

PPM = (^{mass of solute}/_{total mass of solution}) x 1,000,000

For example, if you have 1 gram of salt dissolved in 1000 grams of water, the calculation would be:

PPM = (¹/₁₀₀₀) x 1,000,000 = 1000 ppm

Remember, this calculation assumes that the mass of the solution is the sum of the mass of the solute and the mass of the solvent. This is a common approximation for dilute solutions where the solute's mass doesn't significantly change the total mass.