Mixing Up Parts Per Million (and Billion)

Students follow steps to dilute a colored dye in water until the dye is one part per million. Then students consider atmospheric gases that are present in trace quantities, like ozone, and discuss how pollutants can be hazardous at very small concentrations.

Learning Objectives

• Students will understand that a mixing ratio is the concentration of a certain substance expressed in parts per million or parts per billion by volume.
• Students will be able to explain that some substances, such as ozone, have profound effects even when they occur in very small concentrations or mixing ratios.
• Students will be able to work with exponential notation and unit conversions to express results numerically.

Materials

For each team of students:

• 10 ml graduated cylinder
• Test tube rack
• 10 test tubes
• Masking tape
• Markers
• Pipette or eyedropper
• Pitcher or jug of water
• A colored liquid (a very strong color such as carmine red or indigo blue is most desirable. Food coloring will work, but is not quite as good.)

Preparation

Prepare to project the instructions and questions in the classroom.

Directions

1. Introduction: Explain that certain gases, such as ozone, occur in the atmosphere in very tiny amounts. In the stratosphere, for instance, you may find only one to ten ozone molecules for every one million molecules of other gases. This amount is called one to ten parts per million (ppm). Measurements such as parts per million can be expressed in terms of volume or mass. With gases in the atmosphere, we usually think in terms of volume and may express this as parts per million by volume (ppmv). You can also use the units parts per billion by volume (ppbv), and parts per trillion by volume (pptv). Measurements such as ppmv, ppbv, and pptv are called mixing ratios. Tell students that they will make liquid mixtures that have one part per million and one part per billion of colored dye.
2. Hand out supplies and review the following steps of the procedure with students before they begin.
   1. Using masking tape and markers, label the test tubes 1 through 10.
   2. Put 9 ml water in test tubes 2 through 10.
   3. Put 10 ml colored liquid in test tube 1.
   4. Draw 1 ml of water into the pipette or eyedropper and mark the level using a marker pen. After marking the water level, you may empty the pipette or eyedropper.
   5. Using the pipette or eyedropper with the measure for 1 ml, draw 1 ml of the colored liquid from test tube 1 into the pipette or eyedropper and transfer it to test tube 2. Shake the test tube to mix the colored liquid and the water.
   6. Draw 1 ml of the liquid in test tube 2 into the pipette or eyedropper and transfer it to test tube 3. Shake the test tube to mix the colored liquid and the water.
      Continue this process with all test tubes.
   7. Next, fill out the mixing ratio in the chart provided. Test tube 1 contains pure color, so its mixing ratio is one part in one = 1/1 = 1. Write this down for the mixing ratio in the parts by volume column in Table 1.
   8. Test tube 2 has one part coloring for ten parts liquid. What is this mixing ratio? (1/10 or 10-1) Write it on your chart and translate it into exponential notation. A mixing ratio of 1/10 is written ____, 1/100 is ____, etc. Continue this process for all ten containers.
   9. Now convert into parts per million by volume by multiplying the parts by volume (the second column) by ___. This will tell you how many parts per million by volume you have in each test tube.
   10. Convert to ppbv.
3. Students should answer the following questions.
   • Which containers have the highest concentration? Which have the lowest concentration?
   • Which container has the highest mixing ratio? Which has the lowest mixing ratio?
   • What happens to the color of the liquid as the mixing ratio decreases? Why does this happen?
   • Does the liquid ever become colorless? If so, at what mixing ratios is the liquid colorless? Why do you think it is colorless?
   • Which test tube contains one ppmv of coloring? Which test tube contains one ppbv of coloring?
   • Ozone in the stratosphere has a mixing ratio in the range of one to ten ppmv. Which containers represent one and ten ppmv?
   • A typical mixing ratio for ozone in the troposphere is 10 to 100 ppbv. Which test tubes represent this range of mixing ratios?
4. Discussion: Review the answers to the questions with students (below).
   • Which containers have the highest concentration? (# 1) The lowest concentration? (# 10)
   • Which container has the highest mixing ratio? (# 1) Which has the lowest mixing ratio? (# 10)
   • What happens to the color of the liquid as the mixing ratio decreases? (becomes lighter) Why does this happen? (The number of dye molecules becomes diluted ten times by water in each progression of the serial dilution.)
   • Does the liquid ever become colorless? (yes). If so, at what mixing ratios is the liquid colorless? (Answers will vary depending upon the strength of the initial solution.) Why do you think it is colorless? (So few dye molecules are present that they are not visible.)
     Which test tube contains one ppmv of coloring? (7) Which test tube contains one ppbv of coloring? (10)
   • Ozone in the stratosphere has a mixing ratio in the range of one to ten ppmv. Which containers represent one and ten ppmv? (7 and 6)
   • A typical mixing ratio for ozone in the troposphere is 10 to 100 ppbv. Which test tubes represent this range of mixing ratios? (8 and 9)
5. Tell students that, in this activity, the water and dye are a model for pollutants in the air. Discuss how this model is accurate and how it is different than what it is approximating.
6. Extend the discussion to help students make connections to air pollution. For example, ask students if they would drink the liquid with one part per billion of the dye. Some students should question whether the dye is dangerous to consume. Some may recognize that the dye might be dangerous to consume in large amounts but not in small amounts. If students don't offer this, explain the idea that the amount of a substance matters. Let students know that the U.S. EPA safe threshold for ozone in the troposphere is 70 ppb, although no amount of ozone is truly healthy to breathe. Every few years the EPA reviews the dangerous amount, taking into account the latest scientific research about the health impacts of ozone. Over the past several decades, they have reduced the threshold because research has taught us that ozone is dangerous at lower levels.

Assessment

Have students calculate how much a part per million or billion represents in terms of common objects (e.g., how much chlorine in a swimming pool makes one part per billion, how much lemon in a pitcher of iced tea is a part per million, etc.). Perhaps have students express the answers in common units such as one teaspoon in a swimming pool, or have them become familiar with metric units of volume, such as liters and milliliters.

Let students think of their own common objects and have them guess reasonable dimensions for these objects and calculate their volume. Have them write down their work so that their guesses and assumptions are recorded. Scientists and engineers frequently have to guess at approximate answers to problems they are considering and then justify their assumptions. This is an important skill to learn.

Background

Certain gases such as ozone occur in the atmosphere in very tiny amounts. In the stratosphere, for instance, you may find only one to ten ozone molecules for every one million molecules of other gases. This amount is called one to ten parts per million (ppm). Measurements such as parts per million can be expressed in terms of volume or mass. With gases in the atmosphere, we usually think in terms of volume and may express this as parts per million by volume (ppmv). You can also use the units parts per billion by volume (ppbv), and parts per trillion by volume (pptv). Measurements such as ppmv, ppbv, and pptv are called mixing ratios.

For more information about ozone, see:

• About Ozone
• Ozone molecules
• Ozone in the Troposphere

In the United States, the Environmental Protection Agency (EPA) regulates the amount of ozone via the National Ambient Air Quality Standards (NAAQS).

Modifications for Alternative Learners

English Language Learners may have fewer problems with mathematics than with language, so few modifications may be needed to the dilution part of the activity and table. Pairing with a language-skilled student might be helpful for following the written instructions. Be aware that some students will find the mixing ratio calculations challenging, and will need extra time to puzzle it through. Have a follow-up assignment ready for the fastest students.

Credits

• This activity was created at UCAR as part of the Project LEARN curriculum.