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### Goals:

- To establish understanding about atomic weight and molar mass.
- To introduce students to the concept of counting large numbers of objects using only the mass of the objects.
- Relate the students counting the objects in the lab to chemists counting atoms and molecules by using only the mass of the sample.

### Prerequisites:

Students should:

- Be able to use a triple beam balance to mass a sample.
- Be able to determine the atomic mass of an element using the periodic table. Be able to calculate the molar mass of a compound.

At the end of the lesson students should be able to:

- Articulate the concept of atomic weight and molar mass
- Explain how chemists use the mass of a sample to determine the number of formula units in the sample.

### Background:

Each group of students will relate the time and effort required to count out by hand a large number of small objects to the time and effort required to count the same sample using only the mass of the sample. The group will then be asked to determine the number of objects in a different sample as a check in exercise. The students can then apply what they have learned in the lab to solve the challenge question that was posed at the beginning of the lab.

How does this relate to atoms, atomic weight, molar mass and moles?

Each atom has an average atomic weight. This is the decimal number on the periodic table. The average mass of a paper clip is like the atomic weight of an atom.

To get the average mass of a compound, chemists add up the atomic weights of the individual atoms. For example, water has a formula of H_{2}O. One mole of water has the mass of the mass of two hydrogen atoms and one oxygen atom.

Water = 18 g/mole = 1 Hhydrogen (1 g/mole) + 1 Hydrogen (1 g/mole) + 1 Oxygen (16 g/mole)

I can tell how many moles of water I have by determining the mass of the water and then dividing by the mass of one mole. Therefore 180 grams of water would be 10 moles of water.

180 grams / 18 grams/mole

There are many tutorials available on the internet. One you can check out is:

An interesting site that is also worth checking out is:

Before implementing this lesson, you should figure out the average mass of one large paper clip. You will provide this number to students in Step 9 of the procedure.

### Materials:

**Sample Student/Class Lab Sheet**- About 100 small paperclips per group
- About 100 large paperclips per group
- Any small and larger object can be used. (For example, copper BBs and plastic airsoft pellets)
- Balance
- Stop watch

### Procedure:

This lesson can be completed in one extended block.

The lesson starts with a challenge question which the students will answer at the end of the lab as a check out exercise.

__Challenge question__

Your favorite game store is running a contest where you must guess the number of Acme brand candy corn pieces that are in a sealed fish bowl. You only have 20 minutes before the contest ends, and the owner says you can do anything except open the bowl. The store next door is a general store that carries normal household items and the same fish bowl and candy corn. Create a procedure that lets you determine the number of candy corn in the bowl without counting them manually. (There just isn’t enough time!)

__Procedure__

- Please see Sample Student/Class Lab Sheet.
- Count out exactly 100 small paper clips. Using a stop watch record the amount of time this takes. Record this time on your data chart in the appropriate column.
*Students will notice this is a time consuming task.* - Use the Triple Beam Balance to find the mass of the 100 small paper clips you just counted out, and record this mass on your data chart in the appropriate column. Remember to record the mass of the empty plastic tray.
- Find the mass of exactly 20 small paper clips.
*We are using 20 paper clips because it is a small enough number that it isn't quite as time consuming to count out as 100 paper clips, but it is still a large enough number to reduce error.*Use this number to determine the average mass of one small paper clip.

Average mass of small paper clip = mass of 20 small paper clips – mass of plastic tray / 20

- Multiply the average mass of 1 paper clip you calculated in step 4 by 100 to calculate the mass of 100 small paper clips. This will be referred to as the
*calculated mass*. Record this number on your data chart in the appropriate column. - Calculate the % error:

(*Calculated mass* of small paper clips – Actual mass of small paper clips / C*alculated mass* of small paper clips) X 100.

Record this number on your data chart in the appropriate column. *Students will notice that the actual mass is very close to the calculated mass and that it was much quicker to calculate the mass than to count out 100 paper clips and weigh them.*

- Measure a mass of small paper clips equal to the calculated mass. Set the balance to the mass of the plastic tray + the calculated mass of 100 small paper clips. Slowly add small paper clips till the arm of the balance starts to move, then add or remove small paper clips one by one till the balance reads zero. Use a stop watch record the amount of time this takes. Record this time on your data chart in the appropriate column.
*Again, students will notice this is much faster than counting out 100 paper clips one by one.* - Count out the number of small paper clips you actually obtained in step 7 and compare this to 100. Calculate the % error:

(100 – Actual number of small paper clips / 100) X 100.

Record these numbers on your lab sheet in the appropriate column. *Students will notice that this quicker method is still fairly accurate.*

- You will now be given an unknown number of
**large**paper clips. Use the method of ‘counting by mass’ to determine the number of large paper clips you have been given. The average mass of a large paper clip will be provided for you by your teacher.*Students can weigh the large paper clips and then divide their result by the average mass you have provided to determine the number of large paper clips.*Now actually count out the number of paper clips. Was your calculation close to the actual number of paper clips? - Clean up your lab table. Put all the small paper clips in the glass bottle, and put the bottle and the stopwatch and the plastic tray into the large bowl.
- Return to you seat for class discussion.

Given the time and materials, a good tie in to a robotics program might be for the students to design and execute a robot to count out metal BBs or a simular product.

Now ask the students to answer the challenge question and turn the answer in as an "exit ticket."

__Challenge question__

Your favorite game store is running a contest where you must guess the number of Acme brand candy corn pieces that are in a sealed fish bowl. You only have 20 minutes before the contest ends and the owner says you can do anything except open the bowl. The store next door is a general store that carries normal household items and the same fish bowl and candy corn. Create a procedure that lets you determine the number of candy corn in the bowl without counting then manually. (There just isn’t enough time!)

__Sample Lab Report Questions__

- Compare the time it took to count out the small paper clips compared to the time it took to get a number of small paper clips by mass.
- Based on your percent error calculations, how accurate is counting small paper clips by mass?
- Why is counting atoms by mass like counting small paper clips by mass?

John Tracey, teacher of physics and chemistry, currently at Mount Olive High School