Extensive or Intensive? A Simple, Guided Inquiry

A Simple Guided Inquiry 

to Highlight the Difference Between Extensive and Intensive Properties

Student often don't understand the difference between extensive and intensive properties.  This guided inquiry activity helps them explore the difference.  Students will be deciding if the density of tap water is intensive or extensive.

The only way I know how to do this is to determine the density of a small quantity of water and compare it to the density of a large quantity of water.  That's what I expect students to do in this lab. 

You will need equipment to measure the mass and volume of water.  I use dollar store measuring cups to measure out the volume of water for squirrley groups, glassware for the mellow classes.  (1 cup = 0.24 liters)

I mass the tap water on a triple beam balance by pouring the water in a paper cup, and massing the cup + water.

WARNING:  many students try to fudge on the mass of water by "knowing that 1 ml = 1 g water".  This is only true for pure water, not tap water.  Besides, this is more or less what the students are trying to prove.

Here my half hour activity, step by step.



5 minutes

Warm Up:

Define "intensive" and "extensive" and give examples. 

• An intensive property does not change when the amount of material changes.

1. The freezing point of water is an intensive property of water, since a little water freezes at 0C and a lot of water freezes at 0C.
2. The conductivity of copper is an intensive property of copper, since a small amount of copper conducts and a large amount of copper also conducts.
3. The number of pennies per dollar is an intensive property of a dollar, since one dollar is worth 100 pennies per dollar and $1,000,000 is worth 100 pennies per dollar.

• An extensive property does change when the amount of material changes. 

1. The volume of water is an extensive property of water, since a little water has a smaller volume than a lot of water.
2. The mass of copper is an extensive property of copper, since a small amount of copper has less mass than a large amount of copper.
3. The total number of pennies is an extensive property of money, since one dollar has fewer pennies than $1,000,000.

Check to see if the student know what you are talking about:

• Is the air temperature right now extensive or intensive?

(intensive, since a little air will have the same temperature as a lot of air)

• Is your weight extensive or intensive?

(extensive, since your weight increases as you grow bigger)

 25 minutes

The activity

Group up the students.  I like pairs, but sometimes use groups of 3.

You, (the teacher), say:  Is the density of tap water extensive or intensive?  You have 25 minutes to design and perform an experiment to determine which.

The panic

Here is the guided part.  Have the students tell you explicitly what it would mean if the density of tap water were extensive and what it would mean if the density of tap water were intensive.  Sooner or later, someone in the group will figure out that you have to change volumes.  If no one can, have them talk with another group.  Since it takes about 15 minutes to do two density measurements, you can let some groups struggle for a few minutes until you get to them.  If you are working with 30 students, however, you might have them all take time to talk through how to do the experiment for a few minutes and then do some guiding. If none of your student panic, hooray!  You are an amazing teacher.  Almost all of my students stare at me like deer in the headlights.

Here's what I do to guide the needier groups.

I say:

"Suppose I want to know if the weight of water is extensive or intensive.  I would take a little bit of water and find out how much it weighed.  I would take a lot of water and find out how much it weighed.  If the weight changed, it would be extensive.  If it didn't change, it would be intensive."

If the light still doesn't turn on, I would continue:  "Suppose I want to know if the volume of water is extensive or intensive.  I would take a little bit of water and find its volume.  I would take a lot of water and find its volume.  If the volume changed, it would be extensive.  If the volume didn't change, it would be extensive."

I have even resorted to:  "Suppose I want to know if the property X is extensive or intensive.  I would take a little bit of water an determine its X.  I would take a lot of water and find its X.  If property X changed, it would be extensive.  If property X didn't change, it would be intensive." 

What the students should do once they "get it"

Students should take a small volume of water, maybe 1/2 cup and take its mass.  Then, they should take a larger volume of water, maybe 1 cup and take its mass.  They should compute the density of the small volume, (by dividing small mass/small volume).  They should also compute the density of the large volume.

Typical Problems

The two densities won't be the same, most likely.  This could be because they don't use significant digits correctly.

• 1.0004 is actually equal to 1.01 to two significant digits, and most likely you are only able to get two significant digits.

This can also result from bad measuring.  If a group is goofing around or working way too quickly, I will challenge them if their results are bad.
 
The Write Up

I typically have the students take data during the activity and write it up to turn in after the activity is over.  The data you are looking for, of course, is the mass and volume of a small quantity of water, and the mass and volume of a larger quantity of water.  I use a simplified lab write up form, which I will post in the future.  I have groups turn in their original data sheet with their lab write up. 

Occasionally, I just have groups talk with me about what they have done and learned.