# Week 32 – Counting by Weighing

For this section of our weekly lesson, we will be working between the macroscale world (the one we inhabit) and the microscale world (the world of atoms and molecules).

To begin, imagine you have a 10-pound (4.54 kg) bag of potatoes.  You are tasked with counting the number of potatoes in the bag.  For potatoes, that’s pretty straight-forward.  You literally count each potato and the number you count is the number of potatoes in a 10-pound bag of potatoes.  Counting large objects is pretty easy.

Next, you are tasked with counting the number of grains of rice in a 20-pound (9.07 kg) bag of rice.  Suddenly, this job is a lot less easy.  Could you count all those grains of rice by hand?  Sure.  Do you want to?  No.  So what can do you do to estimate the number of grains of rice in the bag?  One solution is to use the technique of counting by weighing.

• You begin by trying to measure the mass of a single grain of rice. It turns out, the mass is to small to read out on your balance.  Also, what if the grain of rice you selected is not representative of a typical grain of rice?  Maybe you selected a grain of rice that is bigger or smaller than normal.
• You decide to be more scientific.  You count out a random sample of 100 grains of rice and then measure the mass using your balance.  You find that 100 grains of rice have a mass of 2.9 grams.  To calculate the average mass of one grain of rice, you divide 2.9 grams by 100 grains of rice, for an average of 0.029 grams per grain of rice.
• Finally, you have 9.07 kg of rice and you know that each grain of rice has an average mass of 0.029 g.
• 9.07 kg x 1000 g/kg = 9070 g of rice in the bag
• 9070 g x 1 grain of rice / 0.029 g = 312,759 grains of rice!
• Actually, since 0.029 grams only has 2 significant digits, we would actually estimate a total of 310,000 grains of rice.

Finally, it’s time to enter the microscale world of counting by weighing in chemistry.  Imagine you are tasked with counting how many atoms of gold are in a gold ring.  The ring has a mass of 10 grams.  Are you going to count each atom by hand?  Nope.  Instead, you turn to your trusty periodic table and find that gold, atomic symbol Au, has an average atomic mass of 197.0 amu.  You also remember Avogadro’s Number which tells you that 1 mole of gold has 6.02 x 1023 atoms.  That’s all you need!

• First, 197.0 amu = 197.0 g/mole
• Next, to figure out how many moles of gold are in 10 grams of gold: 10 g x 1 mole / 197.0 g = 0.051 moles of gold
• Finally, to figure out how many atoms of gold are in the ring: 0.051 moles x 6.02 x 1023 atoms / mole = 0.31 x 1023 atoms of gold (or 3.1 x 1022 atoms using correct scientific notation)

The video below will help reinforce your learning. Also, Lesson 75 in the textbook is titled “Counting by Weighing” and is an excellent resource for more review.  While not required, you are encouraged to read the lesson and practice the exercises at the end of the lesson.  These will not be entered into Synergy but I am happy to answer any questions you have and review your work if you need help.  When ready, complete the Week 32 – Counting by Weighing Google Form assignment.  Note: For this and all Google Form assignments, you can re-assess and your highest score will be entered into Synergy.  Obviously, do your best the first time through!